Observations support spherically closed dynamic space ... SPIE San Diego, 5866-… · SPIE Conference 5866, THE NATURE OF LIGHT: WHAT IS A PHOTON? San Diego, August 1-2, 2005 Tuomo

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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005

Observations support spherically closed dynamic space without dark energySPIE Conference 5866, THE NATURE OF LIGHT: WHAT IS A PHOTON?

San Diego, August 1-2, 2005

Tuomo SuntolaSuntola Consulting Ltd., Tampere University of Technology, Finland

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Photon – the minimum dose of electromagnetic energy

The energy given by Planck’s equation

20hE hf cλ λ

= =

T. Suntola: Photon – the minimum dose of electromagnetic radiation SPIE, San Diego, August 1-2, 2005

describes the energy of one wavelength of radiation emitted by a single transition of an electron in a point source

in dynamic space where the line element in the fourth dimension is

4 id dt= ⋅s c

A. Einstein,Cosmological considerations1917

pages 187 to 188

4


24A rπ=

2 rπ2r

24A rπ=24A rπ=

r

Closing of two-dimensional surface

5



Closing of three dimensional volumecreates a surface of a 4-sphere

xR4

y z

24A rπ=

2 rπ2r

24A rπ=24A rπ=

2 33 2A V rπ= =

r

6



Closing of three dimensional volume creates a surface of a 4-sphere

xR4

y z

24A rπ=

2 rπ2r

24A rπ=24A rπ=

2 33 2A V rπ= =

r

αAB

AB

O

rAB

R4

4AB ABr R α= ⋅

Distance in spherically closed volume

7


αAB

AB

O

rAB(t0)

R4

4AB ABr R α= ⋅

AB

O

rAB(t1)

R4

αAB

A

B

O

rAB(t2)

R4

αAB

t

Distance in spherically closed expanding volume

8


αAB

AB

O

rAB(t0)

R4

4AB ABr R α= ⋅

AB

O

rAB(t1)

R4

αAB

A

B

O

rAB(t2)

R4

αAB

t

4 44 4 0

4 4

AB ABrecession AB AB AB AB

dr dR r cv c c r H rdt dt R R

α α= = ⋅ = ⋅ = ⋅ = ⋅ = = the Hubble law

Distance in spherically closed volume expanding at velocity c :

9


αAB

AB

O

rAB(t0)

R4

4AB ABr R α= ⋅

AB

O

rAB(t1)

R4

αAB

A

B

O

rAB(t2)

R4

αAB

t

4 44 4 0

4 4

AB ABrecession AB AB AB AB

dr dR r cv c c r H rdt dt R R

α α= = ⋅ = ⋅ = ⋅ = ⋅ = = the Hubble law

Distance in spherically closed volume expanding at velocity c :

4 id dt= ⋅s c

10

2

4 0

2 sing

GmME dR

π φ φπ φ

Σ= − ∫

D=φR4

R4

dM

Im(x0,y0,z0)

mφ

Gravitation in spherically closed space


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2

4 4 40

2 sin "0.776gGmM GmM GmME d

R R R

π φ φπ φ

Σ Σ= − = − ⋅ = −∫

D=φR4

R4

dM

Im(x0,y0,z0)

mφImR4

M”=0.776 MΣ

4

"g

GmMER

= −

m

Gravitation in spherically closed space


24 4 4 4 4mE v v m mv= = =p v

12

ImR4

M”=0.776 MΣ

4

"g

GmMER

= −

m

The balance of motion and gravitation

24

4

" 0m gGmME E mv

R+ = − =


24 4 4 4 4mE v v m mv= = =p v

13

ImR4

M”=0.776 MΣ

4

"g

GmMER

= −

m

24

4

" 0m gGmME E mv

R+ = − =

84

m3 10s

v c⎡ ⎤≈ ± ⋅ = ±⎢ ⎥⎣ ⎦

[ ] [ ]9 264

211

2

27 27( )2 2

14 10 l.y. 1.32 10 m

Nm6.67 10kg

kg kg5 10 5 10 0.55m m c Friedmann

R

G

ρ ρ

−

− −

= ⋅ = ⋅

⎡ ⎤= ⋅ ⎢ ⎥

⎣ ⎦⎡ ⎤ ⎡ ⎤= ⋅ = ⋅ = ⋅⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

4 4ids c dt= 2m restE mc E= =



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Energy of gravitation

Energy of motion

Time

−

Contraction Expansion

∞ ∞

∞

−∞

The cycle of physical existence

The rest energy of matter is gained against release of gravitational energy in a contraction phase …

… and paid back to gravitation in the expansion phase after singularity


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Gravitational energy

Rest energy

Time

ExpansionContraction

Singularity


mE

gE

24 4 4 4 4mE c c m mc= = =p c

4

"g

GmMER

= −

24

4

" 0m gGmME E mc

R+ = − =


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Conservation of the energies of motion and gravitation


m

Im0

Re0

04

"" igGmME

R= −

0 0 0 0"mE c c mc= =p0 0m=p c

M”

" ?gEΔ =

17

Conservation of the energies of motion and gravitation


m

M

M”

φRδ

0δc

Im0

Re0δ

Imδ

Reδ

δc

Rphysical

R0δ

ffv

M”ρ = Μ”−Μ ≈ M”

( ) ( )4 200,0 ffmE c mc p= +

( ) 24

"" 1 igGmM GME

R c R δδ⎛ ⎞= − −⎜ ⎟⎝ ⎠

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The effects of gravitation and motion on the energetic excitation of mass

R4

m

Im

vc

β =

M”

( )2

0 1gE c mcβ β= −

R4

0c

m

M

0 cosc c φ=

ffv

φ

M”M”

( ) 00,mE c mcδ =

( ) ( )2 20 0 0, 1 1 1IE c mc c mcδ β β δ β= − = − −


hypothetical homogeneous space

apparent homogeneous space for frame M2

M1

M2M3

R1

The system of cascaded energy frames

( ) ( )2 20,

1

1 1i i

n

i iresti

E mcβ δ δ β=

⎡ ⎤= − −⎣ ⎦∏

apparent homogeneous space for frame M3

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0restE c mc=

0c

The system of cascaded energy frames

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Extragalactic space

Acceleratorframe

Milky Way frame

Ion frame

Solar frame

Earth frame

Hypothetical homogeneous space( ) ( ) 0 00 0,0I restE E c mc= =

( ) ( ) ( ) 20 1 1XG XGI XG restE E δ β= − −

( ) ( ) ( ) 21 1MW MWI MW I XGE E δ β= − −

( ) ( ) ( ) 21 1S SI S I MWE E δ β= − −

( ) ( ) ( ) 21 1E EI E I SE E δ β= − −

( ) ( )21 AI A I EE E β= −

( ) ( ) ( )2 2(0,0)

1

1 1 1n

Ion rest i iI Ion I Ai

E E Eβ δ β=

= − = − −∏


21


4 2 2 22

2 30 28

en e

e m Z ZE m cn nh

αε

= =

22

1, 20 1 2

1 12n n ef Z m c

h n nα ⎡ ⎤

= −⎢ ⎥⎣ ⎦

22 2

1, 21 2

1 12n n ef Z m c

h n nα ⎡ ⎤

= −⎢ ⎥⎣ ⎦

Balmer’s formula for characteristic frequencies:

( ) ( ) ( ) 2, 0 ,0 1 1I If fβ δ β δ δ β= − −

( ) ( ) ( ) 2, 0,0

1

1 1n

i iI Ii

f fβ δ δ β=

⎡ ⎤= − −⎣ ⎦∏

Characteristic frequencies of hydrogen like atoms

Physical and optical recession velocities

R4c0(t0)

Im2m1

α

Im1

22

c0

m2

( ) 0 04 1rec opt

D zv c cR z

= =+

( ) ( )0 0 ln 1rec physv c c zα= = +


Propagation of light in dynamic space

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R4 = 1 (observer)

z=0.5

z=1

z=2

z=5

0.67

0.5

0.33

0.17


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0,01 0,1 1 10 100Redshift

q0=0

q0=0,5

0,1

1

10

100

0,01

Dynamic Universe standard rod

Standard model

DU

4

1

s

zr R zθ +=

( )( )

( )( )22

0F

0 0 0

1

1 1 1 2s H

q zr R q z q q z

θ +=

+ − − + +

Angular size of standard rod & expanding objects / redshift

0 4r Rθ


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0,01 0,1 1 10 100


Dynamic Universe expanding objects

(e.g. galaxies)

Redshift

q0=0

q0=0,5

0,1

1

10

100

0 4r Rθ

0,01

Standard model

DU

4

1

s

zr R zθ +=

DU

4

1

sr R zθ

=

( )( )

( )( )22

0F

0 0 0

1

1 1 1 2s H

q zr R q z q q z

θ +=

+ − − + +




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0,01 0,1 1 10 100


Dynamic Universe expanding objects

(e.g. galaxies)

Redshift

0,1

1

10

100

0,01

DU

4

1

s

zr R zθ +=

DU

4

1

sr R zθ

=

0 4r Rθ


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Angular size /redshift in radio sources (expanding objects)

A. Sandage: The Deep Universe:Fig. 4.4. Kapahi’s (1987, Fig.7) data for the median angular sizes (arcsec) and redshift for his radio-source sample compared with the predictions of the standard model for various q0values (without evolution).

q0 = 0

Steady state

Tired light

DU / Euclidean

q0 = 0.5 (Einstein-deSitter)

Median angular size[arcsec]

redshift0.1 1

10

100

Red curves and observations:

Blue curve: The DU prediction.


Apparent magnitude of standard candle / redshift

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( )

( )2 1e

obs

FF

z z=

+

( )0 5 log 2.5 log 1z zμ μ= + + +

Distance modulus vs. redshift for Riess et al’s gold dataset and the data from the HST. The triangles represent data obtained via ground based observations, and the circles represent data obtained by the HST. The optimum fit for the standard cosmology equations is shown in red, and the optimum fit for the equation μ = μ0 + 5 log( z) + 2.5 log (z + 1) is shown, slightly below, in blue.


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Radioactive dating

-15 -10 -5 0

time ( x 109 years )

-15 -10 -5 0

DU

Q/Q(0)

Q/Q(0)

1

1

0

0

DU

linear decay

linear decay

The effect of the declining rest energy on the geological age estimate based on radioactive dating


Background radiation: 360° light path

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( )

( )( )

( )

2 6444 0

4 00

4 0

2

26 10 light years535.5

2 750000 years3

1 534.5

RR R e

Rt

c

z e

π

π

−= ≈ ≈ ⋅

= ≈

= − =


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ACKNOWLEDGEMENTS

The presentation of this paper in the symposium “The Nature of Light: What is a Photon?” in SPIE 2005 conference in San Diego 2005 has been supported by the Foundation of the Finnish Society of Electronics Engineers. The author expresses his gratefulness to the Foundation and the Society.

Acknowledgement is also due to Bob Day for his detailed analysis of the magnitude versus redshift data of supernova observations.

Theoretical Basis of the D

ynamic U

niverse Tuom

o Suntola

http://www.sci.fi/~suntola/

http://www.amazon.com/

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1. Space is spherically closed through the fourth dimension.

2. There is a zero-energy balance between the total energies of motion and gravitation in the structure. The zero-energy balance is conserved in all interactions in space.

3. Initially space is at rest with infinite dimensions, i.e. the energies of motion and gravitation are zero. Initially mass, as the substance for the expression energy, is unstructured and uniformly distributed in space.

Basic assumptions


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1. The inherent energy of gravitation is defined in “exclusive space” space as

2. The inherent energy of motion is defined as the energy equivalence of inherent momentumin “environment at rest” as

3. Force is defined as a the negative of the gradient of energy − as the measure of “a natural trend towards minimum potential energy”

Basic definitions

( )g iGmME

r= −

( ) ( )m i iE v= p

ˆdEdr

= −F r

=“Vis viva” ( “living force”, Leibniz 1695)


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Energy of gravitation

Energy of motion

Time

−

Contraction Expansion

∞ ∞

∞

−∞From emptiness at infinity in the past … … to emptiness at infinity in the future.

The cycle of physical existence


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R4

0c

m

M

0 cosc c φ=

ffv

φ

M”M”

( ) 00,mE c mcδ =( ) ( )4 2

00,0 ffmE c mc p= +


37


R4

0c

m

M

0 cosc c φ=

ffv

φ

M”M”

( ) 00,mE c mcδ =

( ) ( ) ( ) ( )0 04

" 1 cosg g gGM m GMmE E E

R Rδ δ φ⎡ ⎤

= − − = − =⎢ ⎥⎣ ⎦

42"

MR GMRM Rc

δ = =

( )0gE

( ) ( )4 200,0 ffmE c mc p= +


Observations support spherically closed dynamic space ... SPIE San Diego, 5866-… · SPIE Conference 5866, THE NATURE OF LIGHT: WHAT IS A PHOTON? San Diego, August 1-2, 2005 Tuomo

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