Metody opisu dyfuzji wielu składników, unifikacja metody dyfuzji wzajemnej i termodynamiki procesów nieodwracalnych Marek Danielewski Interdisciplinary Centre for Materials Modeling AGH Univ. of Sci. & Technology, Cracow, Poland Będlewo, Czerwiec 2013
Metody opisu dyfuzji wielu składników, unifikacja metody dyfuzji wzajemnej i termodynamiki procesów nieodwracalnych Marek Danielewski. Interdisciplinary Centre for Materials Modeling AGH Univ. o f Sci. & Technolog y , Cracow, Poland Będlewo, Czerwiec 2013. φ. φ. Quantum mechanics:. - PowerPoint PPT Presentation
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Transcript
Metody opisu dyfuzji wielu składnikoacutew
unifikacja metody dyfuzji wzajemnej i
termodynamiki procesoacutew nieodwracalnych
Marek Danielewski
Interdisciplinary Centre for Materials Modeling
AGH Univ of Sci amp Technology Cracow Poland
Będlewo Czerwiec 2013
Diffusion equation (Fourier)
2
2
Fundamental or only numerology
t x
Diffusion equationsHeat
T t
Θ 2 T
x 2
Θ = α m2s-1
Diffusion of mass (1855)
t
Θ 2 x 2
Θ = D m2s-1
Diffusion equations
Hydrodynamics (noncompressible fluid)
υ t
Θ 2υ
x 2
Θ = ν m2s-1
Diffusion equations
Quantum mechanics
2
2t x φφ
2
i
m
2 2
2
i
m
i
2 1i
i
Quantum mechanics
2 2
22i
t m x
free particlehellip
Question
Why
2
i
m
Answerhellip P-K-C hypothesis
Economyhellip
hellip diffusion equation
The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1997
for a new method to determinehellip the value of derivatives
Robert C MertonHarvard University
Myron S ScholesLong Term Capital Management Greenwich CT USA
Economy amp diffusionhellipButhellip money is not conserved
Merton amp Sholes Nobel price bdquohelped inrdquohellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
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Slide 125
Soccer Balls Diffract
httpwwwquantumunivieacatresearchc60
Professor Anton Zeilinger
Experiment amp theory for C60 and C70
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
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Slide 17
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Slide 21
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Slide 23
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Slide 25
Slide 26
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Slide 53
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Slide 101
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Slide 104
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Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Professor Anton Zeilinger
Experiment amp theory for C60 and C70
C60F48 world record (108 atoms) in matter interferometry
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
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Slide 16
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Slide 21
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Slide 24
Slide 25
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Slide 27
Slide 28
Slide 29
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Slide 32
Slide 33
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Slide 35
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Slide 40
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Slide 44
Slide 45
Slide 46
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Slide 48
Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
Slide 70
Slide 71
Slide 72
Slide 73
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Slide 75
Slide 76
Slide 77
Slide 78
Slide 79
Slide 80
Slide 82
Slide 83
Slide 84
Slide 86
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Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
J Clerk Maxwell Phil Trans R Soc Lond 155 (1865) 459-512
Already onhellip
bdquoPlanck-Kleinert Crystalrdquo
bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
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Slide 88
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Slide 99
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bdquoThe assumption therefore that gravitation arises fromthe action of the surrounding medium in the way pointedout leads to the conclusion that every part of this medium possesses when undisturbed an enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction As I am unable to understand in what way a medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitationrdquo
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
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Slide 51
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Slide 53
Slide 54
Slide 55
Slide 58
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Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Physics Today [1] rarr ldquoThe persistence of etherrdquo
Statistical mechanics [2] rarr dimensions become large
quantum properties emerge
Quantum space [3] rarr analogous to crystal
Kleinert [4] rarr Einstein gravity from a defect model
[1] F Wilczek Phys Today 52 11 (1999) [2] J L Lebowitz Rev of Modern Phys 71 S347-S357 (1999) [3] M Bojowald Nature 436 920-921 (2005)[4] H Kleinert Ann Phys 44 117 (1987)
Vacuumhellip No [5]rarr ldquoThere is no information without
representationrdquo
[5] W Żurek Nature 453 (2008) 23
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
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Slide 31
Slide 32
Slide 33
Slide 34
Slide 35
Slide 36
Slide 37
Slide 38
Slide 39
Slide 40
Slide 42
Slide 43
Slide 44
Slide 45
Slide 46
Slide 47
Slide 48
Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
Slide 70
Slide 71
Slide 72
Slide 73
Slide 74
Slide 75
Slide 76
Slide 77
Slide 78
Slide 79
Slide 80
Slide 82
Slide 83
Slide 84
Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Volume continuity div 0c
Conservation of mass div 0c
ct
DMomentum conservation Div grad
D m
mextV
t
DI law Grad div
D qJt
ddiv
d i i iic
t
div 0 for 1ii i
cc i r
t
DDiv grad
Di
extiii
Vt
D 1 grad div
D 3i
ii i i i qi i
p Jt
I
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
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Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
The Planck-Kleinert Crystal rarr World Crystal (three-dimensional quasi-continuum)
- Frenkel disorder
- defects form solid solution - defects diffuse
- bdquoclassicalrdquo conservation laws
- volume continuity amp material reference frame
- double valued deformation field
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
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Slide 8
Slide 9
Slide 10
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Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
divt
DDiv
D m
m
t
DDiv
D
e
t
Volume continuity
Mass conservation
Navier-Lame+ diffusion
Energy conservation
Div 2 graddiv divgrad u uσ σ
P-KC single crystal bdquosuper idealrdquo enormous intrinsic energy bounded () etchellip
div 0c
m d
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
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Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Included the entropy production as a result of defect formation and diffusionhellip
L D Landau E M Lifshits ldquoFluid Mechanicsrdquo 2nd ed (Butterworth-Heinemann Oxford 1987)
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
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Slide 58
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Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
+ stationary travelingamp
their combinations
Processes
1 Transverse wave
2 Longitudinal wave
3 lattice deformation (Kleinert 2003)
4 Pi diffusion (mass)
5 Heat transferhellip
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
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Slide 45
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Slide 49
Slide 50
Slide 51
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Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
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Slide 64
Slide 65
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Slide 67
Slide 68
Slide 69
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Slide 71
Slide 72
Slide 73
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Slide 75
Slide 76
Slide 77
Slide 78
Slide 79
Slide 80
Slide 82
Slide 83
Slide 84
Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
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Slide 94
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Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Physical Quantity Unit Symbol for unit Value in SI units SI unit Reference
Lattice parameter Planck length lP 161624(12)10-35 m NIST
Poisson ratio in ideal fcc crystal 025 -Cauchy ampPoisson
Mass of particle Planck mass mP 217645(16)10-8 kg NIST
Frequency of the internal process
Inverse of the Planck time
fP = 1tP 185486(98)1043 s-1 NIST
Lameacute constant Energy density 185323719410114 kgm-1s-2 This work
Number of particles in unit cell 4 This work
National Institute of Standards and Technology Reference on Constants Units and Uncertainty httpphysicsnistgov (2006)
The physical constants (ideal regular fcc lattice)
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
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Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
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Slide 27
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Slide 45
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Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
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Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
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Slide 71
Slide 72
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Slide 79
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Slide 83
Slide 84
Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Rem
Imm
Re Imm m mi
The energy of volume deformation field
The energy of the torsion field
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
Slide 33
Slide 34
Slide 35
Slide 36
Slide 37
Slide 38
Slide 39
Slide 40
Slide 42
Slide 43
Slide 44
Slide 45
Slide 46
Slide 47
Slide 48
Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
Slide 70
Slide 71
Slide 72
Slide 73
Slide 74
Slide 75
Slide 76
Slide 77
Slide 78
Slide 79
Slide 80
Slide 82
Slide 83
Slide 84
Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
divt
DDiv
D
e
t
Mass conservation
Energyconservation
Volume continuity div 0d
Gravity
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
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Slide 99
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Slide 104
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Slide 109
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Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
[defects] asymp const at T= const
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
Slide 33
Slide 34
Slide 35
Slide 36
Slide 37
Slide 38
Slide 39
Slide 40
Slide 42
Slide 43
Slide 44
Slide 45
Slide 46
Slide 47
Slide 48
Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
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Slide 71
Slide 72
Slide 73
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Slide 75
Slide 76
Slide 77
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Slide 80
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Slide 84
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Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
in Planck-Kleinert crystal
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
Slide 33
Slide 34
Slide 35
Slide 36
Slide 37
Slide 38
Slide 39
Slide 40
Slide 42
Slide 43
Slide 44
Slide 45
Slide 46
Slide 47
Slide 48
Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
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Slide 71
Slide 72
Slide 73
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Slide 76
Slide 77
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Slide 82
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Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
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Slide 95
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Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
div m dP P e
already Newtonhellip
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
Slide 33
Slide 34
Slide 35
Slide 36
Slide 37
Slide 38
Slide 39
Slide 40
Slide 42
Slide 43
Slide 44
Slide 45
Slide 46
Slide 47
Slide 48
Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
Slide 70
Slide 71
Slide 72
Slide 73
Slide 74
Slide 75
Slide 76
Slide 77
Slide 78
Slide 79
Slide 80
Slide 82
Slide 83
Slide 84
Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Redivgrad 4mMG
2where P PG l c m
Simeacuteon-Denis Poisson
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
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Slide 33
Slide 34
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Slide 36
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Slide 38
Slide 39
Slide 40
Slide 42
Slide 43
Slide 44
Slide 45
Slide 46
Slide 47
Slide 48
Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
Slide 70
Slide 71
Slide 72
Slide 73
Slide 74
Slide 75
Slide 76
Slide 77
Slide 78
Slide 79
Slide 80
Slide 82
Slide 83
Slide 84
Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
116674189 10G NIST data G = 66742(10) bull 10-11
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
Slide 33
Slide 34
Slide 35
Slide 36
Slide 37
Slide 38
Slide 39
Slide 40
Slide 42
Slide 43
Slide 44
Slide 45
Slide 46
Slide 47
Slide 48
Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
Slide 70
Slide 71
Slide 72
Slide 73
Slide 74
Slide 75
Slide 76
Slide 77
Slide 78
Slide 79
Slide 80
Slide 82
Slide 83
Slide 84
Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
4 The ldquodark energyrdquo rarr energy of the DIPPrsquos
1 The Diffusing Interstitial Planck Particles (DIPPrsquos) = WIMPrsquos
2 DIPPrsquos create the gravitational interaction between matter
3 The ldquodark matterrdquo rarr DIPPrsquos
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
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Slide 33
Slide 34
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Slide 45
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Slide 47
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Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
Slide 70
Slide 71
Slide 72
Slide 73
Slide 74
Slide 75
Slide 76
Slide 77
Slide 78
Slide 79
Slide 80
Slide 82
Slide 83
Slide 84
Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Remark 1 Planck length = Schwarzschild radius
2 P WIMP gravitonm m m m Higg s boson
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
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Slide 22
Slide 23
Slide 24
Slide 25
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Slide 27
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Slide 38
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Slide 47
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Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
Slide 59
Slide 60
Slide 62
Slide 63
Slide 64
Slide 65
Slide 66
Slide 67
Slide 68
Slide 69
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Slide 71
Slide 72
Slide 73
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Slide 76
Slide 77
Slide 78
Slide 79
Slide 80
Slide 82
Slide 83
Slide 84
Slide 86
Slide 87
Slide 88
Slide 89
Slide 91
Slide 92
Slide 93
Slide 94
Slide 95
Slide 96
Slide 97
Slide 98
Slide 99
Slide 100
Slide 101
Slide 102
Slide 103
Slide 104
Slide 106
Slide 108
Slide 109
Slide 110
Slide 111
Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Electromagnetism
Zero diffusion
So far
042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
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Slide 20
Slide 21
Slide 22
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Slide 24
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Slide 29
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Slide 33
Slide 34
Slide 35
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Slide 39
Slide 40
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Slide 44
Slide 45
Slide 46
Slide 47
Slide 48
Slide 49
Slide 50
Slide 51
Slide 52
Slide 53
Slide 54
Slide 55
Slide 58
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042223
Dgraddiv divgrad
DL L
P PP Pm f m ft
σ σNavier-Lame
amp no diffusion
Only transverse wave
1) 0d
2) ρ = ρ0 const
3) div 0
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
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Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
3 3
2
2 = 8 grad 8 grad divdiv
P P
P P
L Ll lm mt
xx + x
2
2
2 2 = rot rotLc ct
x
x + x
Transverse waves in P-KC
Equivalent form
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
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Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
2
3 1
2
2 = rotr
8
ot1
km299 792 s
P PLc l
t
m
c
xx
Equation of the transverse wave
299 792 5 (NIST)
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
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Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
= rotrotm Lt
x
B
t
0
B
t
rotE
mB
22
rot rotLP
P
ff
x
20
1 L
Pf
2rotPfE x
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
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Slide 112
Slide 113
Slide 114
Slide 115
Slide 116
Slide 117
Slide 118
Slide 119
Slide 120
Slide 121
Slide 124
Slide 125
Full set Maxwell eqs in vacuum
analogous simple transformations
divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
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divt
DDiv
D
e
t
Mass conservation
EnergyConservation
andhellip
Quantum mechanics
Re Imm m mi
Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip
bull all methods developed in math and physics will be usefull
Forthcoming
elec
tro-mechano-chemistry
d
i i
eli
chi
miB
Planck-Kleinert Crystal straightforward
vs
Remark
Complexity of diffusion processes in multicomponenthellip systems
E N D
Fundamentals I
Euler - the volume amp molar volume
1 1 r rkn kn T p k n n T p
hellip homogeneous of the 1st degree in the variables n1hellip nr
The volume and molar volume
Ni = cic is molar ratio
1 1 r rkn kn T p k n n T p
1 1 r rN N T p k n n T p
hellip homogeneous of the 1st degree in the variables N1hellip Nr
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Imm
Im Imgrad grad d m mM M M MJ B eB
The energy flux
1 The process that governs de Broglie waves is the fast internal process 2 We analyze the case when the driving force of the transport (the collective Planck mass movement ie the movement of a complex of
particles showing an energy E and mass M = E c-2) is controlled by the imaginary part of mechanical potential
Im
div
gradd mM M
ee
t
J eB
Imdiv grad mM
eB e
t
Im
0Re Im 0
div grad
exp 22
mM
m m
M P P
eB e
t
e i
B m M B
Re Im Re ImIm2 2
exp 2 div exp 2 gradm m m m
mP Pi im B
t c M c
Re Im Re ImIm2 2
2Re Im
exp 2 div exp 2 grad
exp
m m m mmP P
m m
i im B
t c M c
i c
2
2Imdiv grad mP Pm B
t M
2
div grad 2P Pm B c
Mi E
t
22 P Ph m B c
div4
grad i Et
h
M
The physical constants at the Planck scale and
four time scalesPhysical Quantity Value in SI units SI unit Reference
Volume of PC cell 4222 002 82810-105 m3 This work ampNIST
Planck density 2062 008 6621097 kg m-3 This work amp NIST
Young modulus 4633 092 98610114 kg m-1s-2 This work
Planck mass mobility 5391 213 98210-44 s This work
Defects self-diffusion coefficient 2422 685 81610-27 m2s-1 This work
Planck constant6626 069 31110-34
6626 069 3(11)10-34 kg m2 s-1 This workNIST
Gravitational constant66742(10)10-11
667417610-11 m3 kg-1 s-2 NISTThis work
Speed of longitudinal wave 519 255 240 m s-1 This work
Speed of transverse wave299 792 153299 792 458
m s-1 This workNIST
Physical reality at the Planck scale
bull Faster than light velocity of longitudinal wavehellip Kleinert fine-tuning to make all ldquosound speedsrdquo equal orhellip
consider
bull The different velocities are related to specific force field rarr a real quantities that mark different time-scales
bull The Diffusing Interstitial Planck Particles (DIPPrsquos) rarr gravity
bull The collective behavior of the Planck particles rarr the particle Schroumldinger equation follows
3L c
bull Transverse wave equiv electromagnetic wave
bull DIPPrsquos rarr Dark Matter rarr Dark Energy
bull Waves involving temperature equiv ldquothe second soundrdquo described by Landau and Lifschitz etchellip