CPT and DECOHERENCE CPT and DECOHERENCE in in QUANTUM GRAVITY QUANTUM GRAVITY N. E. Mavromatos N. E. Mavromatos King’s College London King’s College London Physics Department Physics Department ISCRETE 08 SYMPOSIUM ON PROSPECTS IN ISCRETE 08 SYMPOSIUM ON PROSPECTS IN HE PHYSICS OF DISCRETE SYMMETRIES HE PHYSICS OF DISCRETE SYMMETRIES FIC – Valencia (Spain), December 11-16 2008 FIC – Valencia (Spain), December 11-16 2008 MRTN-CT- MRTN-CT- 2006- 2006- 035863 035863
CPT and DECOHERENCE in QUANTUM GRAVITY. MRTN-CT-2006-035863. N. E. Mavromatos King’s College London Physics Department. DISCRETE 08 SYMPOSIUM ON PROSPECTS IN THE PHYSICS OF DISCRETE SYMMETRIES IFIC – Valencia (Spain), December 11-16 2008. - PowerPoint PPT Presentation
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CPT and DECOHERENCE CPT and DECOHERENCE inin
QUANTUM GRAVITY QUANTUM GRAVITY
N. E. MavromatosN. E. Mavromatos
King’s College LondonKing’s College London
Physics DepartmentPhysics Department
DISCRETE 08 SYMPOSIUM ON PROSPECTS IN DISCRETE 08 SYMPOSIUM ON PROSPECTS IN THE PHYSICS OF DISCRETE SYMMETRIES THE PHYSICS OF DISCRETE SYMMETRIES IFIC – Valencia (Spain), December 11-16 2008 IFIC – Valencia (Spain), December 11-16 2008
MRTN-CT-MRTN-CT-2006-0358632006-035863
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 2
OUTLINE OUTLINE Theoretical motivation for CPT Theoretical motivation for CPT
Disentangling (i) from (ii) Disentangling (i) from (ii) ω-effect as discriminant of space-time ω-effect as discriminant of space-time
foam modelsfoam models This talkThis talk
Neutrino Tests of QG decoherence Neutrino Tests of QG decoherence Damping factorsDamping factors in flavour Oscillation in flavour Oscillation Probabilities – Probabilities – suppressedsuppressed though by though by neutrino neutrino mass differencesmass differences
This talkThis talk
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 3
OUTLINE OUTLINE Theoretical motivation for CPT Theoretical motivation for CPT
Disentangling (i) from (ii) Disentangling (i) from (ii) ω-effect as discriminant of space-time ω-effect as discriminant of space-time
foam modelsfoam models This talkThis talk
Neutrino Tests of QG decoherence Neutrino Tests of QG decoherence Damping factorsDamping factors in flavour Oscillation in flavour Oscillation Probabilities – Probabilities – suppressedsuppressed though by though by neutrino neutrino mass differencesmass differences
This talkThis talk
IMPORTANT IMPORTANT : QUANTUM GRAVITY : QUANTUM GRAVITY DECOHERENCE CURRENT BOUNDS & DECOHERENCE CURRENT BOUNDS &
MICROSCOPIC BLACK HOLES AT LHCMICROSCOPIC BLACK HOLES AT LHC
DetailsDetails of microscopic model of microscopic model mattermatter a lot a lot before concusions are reached in before concusions are reached in excluding excluding large extra dimensional models by such large extra dimensional models by such decoherence studies…decoherence studies…
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 4
Generic Theory IssuesGeneric Theory Issues CPT SYMMETRY:
(1) Lorentz Invariance, (2) Locality , (3) Unitarity Theorem proven for FLAT space times (Jost, Luders, Pauli, Bell, Greenberg )
(II) Standard Model Extension: Lorentz Violation in Hamiltonian H:
CPT well defined but non-commuting with H
(III) Loop QG/space-time background independent; Non-linearly Deformed Special Relativities : Quantum version not fully understood…
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 5
CPT THEOREMCPT THEOREM
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 6
CPT THEOREMCPT THEOREM
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 7
CPT THEOREMCPT THEOREM
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 8
CPT THEOREMCPT THEOREM
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 9
CPT THEOREMCPT THEOREM
10-35 m
J.A. Wheeler
Space-time Foam
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 10
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 11
In general, in space-timeswith Horizons (e.g. De Sitter cosmology…)
Arguments in favour of holographic picture Arguments in favour of holographic picture : Path Integral over non-trivial BH topologies decays with time, leaving only trivial (unitary) topology contributions (Maldacena, Hawking) Arguments against resolution of issueArguments against resolution of issue: (i) not rigorous proof though over space-time measure. (ii) Entanglement entropy (Srednicki, Einhorn, Brustein,Yarom ). (iii) Also, Space-time foam may be of different type, e.g. due to stochastic space-time point-like defects crossing brane worlds (D-particle foam) ….(Ellis, NM, Nanopoulos, Sarkar).
Hence possible non-trivial decoherence effects in effective Hence possible non-trivial decoherence effects in effective theories. Worth checking experimentally…. theories. Worth checking experimentally…. CPTV issues CPTV issues
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 12
In general, in space-timeswith Horizons (e.g. De Sitter cosmology…)
Arguments in favour of holographic picture Arguments in favour of holographic picture : Path Integral over non-trivial BH topologies decays with time, leaving only trivial (unitary) topology contributions (Maldacena, Hawking) Arguments against resolution of issueArguments against resolution of issue: (i) not rigorous proof though over space-time measure. (ii) Entanglement entropy (Srednicki, Einhorn, Brustein,Yarom ). (iii) Also, Space-time foam may be of different type, e.g. due to stochastic space-time point-like defects crossing brane worlds (D-particle foam) ….(Ellis, NM, Nanopoulos, Sarkar).
Hence possible non-trivial decoherence effects in effective Hence possible non-trivial decoherence effects in effective theories. Worth checking experimentally…. theories. Worth checking experimentally…. CPTV issues CPTV issues
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 13
In general, in space-timeswith Horizons (e.g. De Sitter cosmology…)
Arguments in favour of holographic picture Arguments in favour of holographic picture : Path Integral over non-trivial BH topologies decays with time, leaving only trivial (unitary) topology contributions (Maldacena, Hawking) Arguments against resolution of issueArguments against resolution of issue: (i) not rigorous proof though over space-time measure. (ii) Entanglement entropy (Srednicki, Einhorn, Brustein,Yarom ). (iii) Also, Space-time foam may be of different type, e.g. due to stochastic space-time point-like defects crossing brane worlds (D-particle foam) ….(Ellis, NM, Nanopoulos, Sarkar).
Hence possible non-trivial decoherence effects in effective Hence possible non-trivial decoherence effects in effective theories. Worth checking experimentally…. theories. Worth checking experimentally…. CPTV issues CPTV issues
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 14
In general, in space-timeswith Horizons (e.g. De Sitter cosmology…)
Arguments in favour of holographic picture Arguments in favour of holographic picture : Path Integral over non-trivial BH topologies decays with time, leaving only trivial (unitary) topology contributions (Maldacena, Hawking) Arguments against resolution of issueArguments against resolution of issue: (i) not rigorous proof though over space-time measure. (ii) Entanglement entropy (Srednicki, Einhorn, Brustein,Yarom ). (iii) Also, Space-time foam may be of different type, e.g. due to stochastic space-time point-like defects crossing brane worlds (D-particle foam) ….(Ellis, NM, Nanopoulos, Sarkar).
Hence possible non-trivial decoherence effects in effective Hence possible non-trivial decoherence effects in effective theories. Worth checking experimentally…. theories. Worth checking experimentally…. CPTV issues CPTV issues
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 15
In general, in space-timeswith Horizons (e.g. De Sitter cosmology…)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 16
COSMOLOGICAL MOTIVATION FOR CPT VIOLATION?COSMOLOGICAL MOTIVATION FOR CPT VIOLATION? Supernova and CMB Data (2006)Supernova and CMB Data (2006)Baryon oscillations, Large GalacticBaryon oscillations, Large GalacticSurveys & other data (2008) Surveys & other data (2008)
Evidence for :Evidence for :Dark Matter(23%)Dark Matter(23%)Dark Energy (73%)Dark Energy (73%)Ordinary matter (4%) Ordinary matter (4%)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 17
DARK ENERGY& Cosmological CPTV?DARK ENERGY& Cosmological CPTV?
KNOW VERY LITTLE ABOUT IT…
EMBARASSING SITUATION 74% OF THE UNIVERSE BUDGET CONSISTS OF UNKNOWN SUBSTANCE
Could be: a Cosmological Constant Quintessence (scalar field
relaxing to minimum of its potential)
Something else…Extra dimensions, colliding brane worlds etc.
Certainly of Quantum Gravitational origin
If cosmological constant (de Sitter), then quantization of field theories not fully understood due to cosmic horizon CPT invariance?
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 18
DARK ENERGY& Cosmological CPTV?DARK ENERGY& Cosmological CPTV?
KNOW VERY LITTLE ABOUT IT…
EMBARASSING SITUATION 74% OF THE UNIVERSE BUDGET CONSISTS OF UNKNOWN SUBSTANCE
Could be: a Cosmological Constant Quintessence (scalar field
relaxing to minimum of its potential)
Something else…Extra dimensions, colliding brane worlds etc.
Certainly of Quantum Gravitational origin
If cosmological constant (de Sitter), then quantization of field theories not fully understood due to cosmic horizon CPT invariance?
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 19
DARK ENERGY& Cosmological CPTV?DARK ENERGY& Cosmological CPTV?
KNOW VERY LITTLE ABOUT IT…
EMBARASSING SITUATION 74% OF THE UNIVERSE BUDGET CONSISTS OF UNKNOWN SUBSTANCE
Could be: a Cosmological Constant Quintessence (scalar field
relaxing to minimum of its potential)
Something else…Extra dimensions, colliding brane worlds etc.
Certainly of Quantum Gravitational origin
If cosmological constant (de Sitter), then quantization of field theories not fully understood due to cosmic horizon CPT invariance?
Outer Horizon (live ``inside’’ black hole):Outer Horizon (live ``inside’’ black hole): /3rUnstable, indicates expansionUnstable, indicates expansion
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 20
DARK ENERGY& Cosmological CPTV?DARK ENERGY& Cosmological CPTV?
KNOW VERY LITTLE ABOUT IT…
EMBARASSING SITUATION 74% OF THE UNIVERSE BUDGET CONSISTS OF UNKNOWN SUBSTANCE
Could be: a Cosmological Constant Quintessence (scalar field
relaxing to minimum of its potential)
Something else…Extra dimensions, colliding brane worlds etc.
Certainly of Quantum Gravitational origin
If cosmological constant (de Sitter), then quantization of field theories not fully understood due to cosmic horizon CPT invariance?
Global (Cosmological FRW solution)Global (Cosmological FRW solution)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 21
DARK ENERGY& Cosmological CPTV?DARK ENERGY& Cosmological CPTV?
KNOW VERY LITTLE ABOUT IT…
EMBARASSING SITUATION 74% OF THE UNIVERSE BUDGET CONSISTS OF UNKNOWN SUBSTANCE
Could be: a Cosmological Constant Quintessence (scalar field
relaxing to minimum of its potential)
Something else…Extra dimensions, colliding brane worlds etc.
Certainly of Quantum Gravitational origin
If cosmological constant (de Sitter), then quantization of field theories not fully understood due to cosmic horizon CPT invariance?
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 28
STANDARD MODEL EXTENSIONSTANDARD MODEL EXTENSION
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 29
Non-commutative effective field theoriesNon-commutative effective field theories
CPT invariant SME type field theory (Q.E.D. ) - only even number of indices appear in effective non-renormalisable terms. (Carroll et al. hep-th/0105082)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 30
Non-commutative effective field theoriesNon-commutative effective field theories
CPT invariant SME type field theory (Q.E.D. ) - only even number of indices appear in effective non-renormalisable terms. (Carroll et al. hep-th/0105082)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 31
STANDARD MODEL EXTENSIONSTANDARD MODEL EXTENSION
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 32
that rivals astrophysical or atomic-physics bounds can only be attained if spectral resolution of 1 mHz is achieved. Not feasible at present in anti-H factories
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 33
Tests of Lorentz Violation in Neutral KaonsTests of Lorentz Violation in Neutral Kaons
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 34
EXPERIMENTAL BOUNDSEXPERIMENTAL BOUNDS
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 35
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 36
Order of Magnitude Estimates Order of Magnitude Estimates
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 37
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 38
Order of Magnitude Estimates Order of Magnitude Estimates
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 39
Order of Magnitude Estimates Order of Magnitude Estimates
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 40
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 41
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
Adler-Horwitz decoherent evolution modelAdler-Horwitz decoherent evolution model
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 42
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 43
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 44
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 48
D-particle Recoil & LIV modelsD-particle Recoil & LIV models
i
edLimiXXXXuV
Xiin
ic
0
0
000Re )(,)(
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 49
A (non-critical) string theory time Arrow A (non-critical) string theory time Arrow
Non-equilibrium StringsNon-equilibrium Strings(non-critical), due to (non-critical), due to e.g. cosmically catastrophice.g. cosmically catastrophicevents in Early Universe,events in Early Universe,for instance brane worldsfor instance brane worldscollisions: collisions:
World-sheet conformal World-sheet conformal Invariance is disturbedInvariance is disturbed
Central charge of world-Central charge of world-Sheet theory ``runs’’ Sheet theory ``runs’’ To a minimal value To a minimal value Zamolodchikov’s C-theoremZamolodchikov’s C-theoremAn H-theorem for CFTAn H-theorem for CFT Change in degrees of Change in degrees of Freedom (i.e. entropy) Freedom (i.e. entropy)
Ellis, NMNanopoulos
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 50
A (non-critical) string theory time Arrow A (non-critical) string theory time Arrow
Non-equilibrium StringsNon-equilibrium Strings(non-critical), due to (non-critical), due to e.g. cosmically catastrophice.g. cosmically catastrophicevents in Early Universe,events in Early Universe,for instance brane worldsfor instance brane worldscollisions: collisions:
World-sheet conformal World-sheet conformal Invariance is disturbedInvariance is disturbed
Central charge of world-Central charge of world-Sheet theory ``runs’’ Sheet theory ``runs’’ To a minimal value To a minimal value Zamolodchikov’s C-theoremZamolodchikov’s C-theoremAn H-theorem for CFTAn H-theorem for CFT Change in degrees of Change in degrees of Freedom (i.e. entropy) Freedom (i.e. entropy)
Ellis, NMNanopoulos
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 51
A (non-critical) string theory time Arrow A (non-critical) string theory time Arrow
Non-equilibrium StringsNon-equilibrium Strings(non-critical), due to (non-critical), due to e.g. cosmically catastrophice.g. cosmically catastrophicevents in Early Universe,events in Early Universe,for instance brane worldsfor instance brane worldscollisions: collisions:
World-sheet conformal World-sheet conformal Invariance is disturbedInvariance is disturbed
Central charge of world-Central charge of world-Sheet theory ``runs’’ Sheet theory ``runs’’ To a minimal value To a minimal value Zamolodchikov’s C-theoremZamolodchikov’s C-theoremAn H-theorem for CFTAn H-theorem for CFT Change in degrees of Change in degrees of Freedom (i.e. entropy) Freedom (i.e. entropy)
Ellis, NMNanopoulos
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 52
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 53
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 54
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 55
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 56
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 57
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 58
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 59
Order of Magnitude Estimates Order of Magnitude Estimates (ii) Stochastic models of foam in brane/string theory (D-particle recoil models (ii) Stochastic models of foam in brane/string theory (D-particle recoil models
(below))(below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, (Sarkar, NM)NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
Delays of more energetic photons occur in propagation due to new fundamental Physics (e.g. refractive index in vacuo due to Quantum Gravity space-time Foam Effects…)
MAGIC Coll & Ellis, NM, Nanopoulos, Sakharov, Sarkisyan [arXive:0708.2889] (individual photon analysis – reconstruct peak of flare by
assuming modified dispersion relations for photons, linearly or quadratically suppressed by the QG scale)
SOURCE MECHANISM BIGGEST THEORETICAL UNCERTAINTY AT PRESENT….
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 67
Quantum-Gravity Induced Modified Dispersion for PhotonsQuantum-Gravity Induced Modified Dispersion for Photons
Modified dispersion due to QG induced space-time (metric) Modified dispersion due to QG induced space-time (metric) distortions (c=1 units):distortions (c=1 units):
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 68
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 69
A Stringy Model of Space -Time FoamA Stringy Model of Space -Time Foam
Open strings on D3-brane world represent electrically neutralelectrically neutral matter or radiation,interacting via splitting/capture with D-particles(electric charge conservation) (electric charge conservation) ..
D-particle foam medium D-particle foam medium transparent transparent to (charged)to (charged)Electrons no modified dispersion for themElectrons no modified dispersion for them
Ellis, NM, NanopoulosEllis, NM, Nanopoulos
Photons or electrically neutral probesfeel the effects of D-particle foamModified Dispersion for them….Modified Dispersion for them….
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 70
A Stringy Model of Space -Time FoamA Stringy Model of Space -Time Foam
Open strings on D3-brane world represent electrically neutralelectrically neutral matter or radiation,interacting via splitting/capture with D-particles(electric charge conservation) (electric charge conservation) ..
D-particle foam medium D-particle foam medium transparent transparent to (charged)to (charged)Electrons no modified dispersion for themElectrons no modified dispersion for them
Ellis, NM, NanopoulosEllis, NM, Nanopoulos
Photons or electrically neutral probesfeel the effects of D-particle foamModified Dispersion for them….Modified Dispersion for them….
NON-UNIVERSAL ACTION OF NON-UNIVERSAL ACTION OF D-PARTICLE FOAM ON MATTER D-PARTICLE FOAM ON MATTER & RADIATION& RADIATION
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 71
A Stringy Model of Space -Time FoamA Stringy Model of Space -Time Foam
Open strings on D3-brane world represent electrically neutralelectrically neutral matter or radiation,interacting via splitting/capture with D-particles(electric charge conservation) (electric charge conservation) ..
D-particle foam medium D-particle foam medium transparent transparent to (charged)to (charged)Electrons no modified dispersion for themElectrons no modified dispersion for them
Ellis, NM, NanopoulosEllis, NM, Nanopoulos
Photons or electrically neutral probesfeel the effects of D-particle foamModified Dispersion for them….Modified Dispersion for them….
NON-UNIVERSAL ACTION OF NON-UNIVERSAL ACTION OF D-PARTICLE FOAM ON MATTER D-PARTICLE FOAM ON MATTER & RADIATION& RADIATION
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 72
Stringy Uncertainties & the Capture ProcessStringy Uncertainties & the Capture Process
During Capture:During Capture: intermediateString stretchingstretching between D-particle and D3-brane is Created. It acquires N internalN internalOscillatorOscillator excitations & Grows in size & oscillatesGrows in size & oscillates from Zero to a maximum length byabsorbing incident photonincident photon Energy pp0 0 ::
Minimise right-hand-size w.r.t. L.End of intermediate string on D3-braneMoves with speed of light in vacuo c=1Hence TIME DELAYTIME DELAY (causality)(causality) during Capture:
DELAY IS INDEPENDENT OF PHOTON POLARIZATION, HENCE NO BIREFRINGENCENO BIREFRINGENCE….
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 73
Stringy Uncertainties & the MAGIC EffectStringy Uncertainties & the MAGIC Effect D-foam: transparent to electrons D-foam captures photons & re-emits them Time Delay (Causal) in each Capture:
Independent of photon polarization (no Birefringence) Total Delay from emission of photons till observation over a distance D (assume n* defects per string length):
REPRODUCE 4REPRODUCE 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034)±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034)For For n* n* =O(1) & M=O(1) & Mss ~ 10 ~ 101818 GeV, consistently with Crab Nebula & other GeV, consistently with Crab Nebula & other
Astrophysical constraints on modified dispersion relations……Astrophysical constraints on modified dispersion relations……
Effectively modifiedEffectively modifiedDispersion relationDispersion relationfor photons due to for photons due to induced metricinduced metricdistortion Gdistortion G0i 0i ~ p~ p00
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 74
Stringy Uncertainties & the MAGIC EffectStringy Uncertainties & the MAGIC Effect D-foam: transparent to electrons D-foam captures photons & re-emits them Time Delay (Causal) in each Capture:
Independent of photon polarization (no Birefringence) Total Delay from emission of photons till observation over a distance D (assume n* defects per string length):
REPRODUCE 4REPRODUCE 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034)±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034)For For n* n* =O(1) & M=O(1) & Mss ~ 10 ~ 101818 GeV, consistently with Crab Nebula & other GeV, consistently with Crab Nebula & other
Astrophysical constraints on modified dispersion relations……Astrophysical constraints on modified dispersion relations……
Effectively modifiedEffectively modifiedDispersion relationDispersion relationfor photons due to for photons due to induced metricinduced metricdistortion Gdistortion G0i 0i ~ p~ p00
COMPATIBLE WITH STRING UNCERTAINTY COMPATIBLE WITH STRING UNCERTAINTY PRINCIPLES:PRINCIPLES:
ΔΔt t ΔΔx ≥ x ≥ αα’ , ’ , ΔΔp p ΔΔx ≥ 1 + x ≥ 1 + αα’ (’ (ΔΔp )p )22 + … + …
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 78
QG DECOHERENCE IN NEUTRAL KAONS: SINGLE STATESQG DECOHERENCE IN NEUTRAL KAONS: SINGLE STATES
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 79
Decoherence vs CPTV in QMDecoherence vs CPTV in QM
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 80
Neutral Kaon AsymmetriesNeutral Kaon Asymmetries
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 81
Neutral Kaon AsymmetriesNeutral Kaon Asymmetries
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 82
Neutral Kaon AsymmetriesNeutral Kaon Asymmetries
Effects of α, β, γ decoherence parameters
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 83
Decoherence vs QM effectsDecoherence vs QM effects
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 84
Indicative Bounds Indicative Bounds
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 85
Neutral Kaon Entangled StatesNeutral Kaon Entangled States
Complete Positivity Different parametrization of Decoherence matrix (Benatti-Floreanini)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 86
Neutral Kaon Entangled StatesNeutral Kaon Entangled States
Complete Positivity Different parametrization of Decoherence matrix (Benatti-Floreanini)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 87
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 88
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 89
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 90
Order of Magnitude Estimates Order of Magnitude Estimates However there are models with inverse energy dependence, e.g. However there are models with inverse energy dependence, e.g. (i) (i) Adler’s Lindblad modelAdler’s Lindblad model for Energy-driven QG Decoherence in two level systems for Energy-driven QG Decoherence in two level systems
(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian(hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian
Decoherence damping exp(-D t) ,Decoherence damping exp(-D t) , Decoherence Parameter estimate: D = (Decoherence Parameter estimate: D = (ΔΔmm22))22/E/E22MMPP
(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below))(ii) Stochastic models of foam in brane/string theory (D-particle recoil models (below)) Decoherence Parameters estimates depend on details of foam, e.g. distribution of Decoherence Parameters estimates depend on details of foam, e.g. distribution of
recoil velocities of populations of D-parfticle defects in space time recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM)(Sarkar, NM) : :
(a) Gaussian D-particle recoil velocity distribution, spread (a) Gaussian D-particle recoil velocity distribution, spread σσ : : Decoherence damping in oscillations among two-level systems : Decoherence damping in oscillations among two-level systems :
exp (-D t exp (-D t 22),), D = D = σσ22((ΔΔmm22))22/E/E2 2
Novel (genuine) two body effects: If CPT not-well defined
modification of EPR correlations (modification of EPR correlations (ω-effect)ω-effect)
Unique effect in Entangled states of mesons !! Unique effect in Entangled states of mesons !! Characteristic of ill-defined nature of intrinsic CPTCharacteristic of ill-defined nature of intrinsic CPT
Violation (e.g. due to decoherence)Violation (e.g. due to decoherence)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 94
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 95
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 96
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 98
CPTV & EPR-correlations modificationCPTV & EPR-correlations modificationCPTV CPTV KLKL, ωKSKS terms originate from Φ-particle , hence same dependence on centre-of-mass energy s. Interference proportional to real part of amplitude,exhibits peak at the resonance….
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 99
KKSSKKS S terms from C=+ terms from C=+ background background
no dependence on centre-of-mass energy s. no dependence on centre-of-mass energy s. Real part of Breit-Wigner amplitudeReal part of Breit-Wigner amplitudeVanishes at top of resonance, Interference Vanishes at top of resonance, Interference of C=+ with C=-- background, vanishes of C=+ with C=-- background, vanishes at top of the resonance, opposite signature at top of the resonance, opposite signature on either side…..on either side…..
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 100
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 102
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 103
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 104
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 105
B-systems, B-systems, ω-effect & demise of flavour-taggingω-effect & demise of flavour-tagging
Kaon systems have increased sensitivity to ω-effects due to the decay channel π+π- .
B-systems do not have such a “good’’ channel but have the advantage of statisticsadvantage of statistics Interesting limits of ω-effects there
Flavour tagging: Knowledge that oneone of the two-mesons in a meson factory decays at a given timedecays at a given time through flavour-specificflavour-specific “channel’’
Unambiguously determinedetermine the flavourflavour of the other meson at the same time same time .
Not True if intrinsic CPTV – Not True if intrinsic CPTV – ω-effect present : ω-effect present : Theoretical Theoretical limitation (“demise’’) of flavour tagginglimitation (“demise’’) of flavour tagging
Alvarez, Bernabeu NM, Nebot, Papavassiliou
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 106
B-systems, B-systems, ω-effect & demise of flavour-taggingω-effect & demise of flavour-tagging
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 107
B-systems, B-systems, ω-effect & demise of flavour-taggingω-effect & demise of flavour-tagging
CP parameter CPTV parameter (QM)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 108
If CPT Operator ill-defined, unique consequences in modifications of EPR correlations of entangled states of neutral mesons in meson factories (Φ-, B-factories) Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben SarkarBernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar
Induced metric due to capture/recoil, stochastic fluctuations, DecoherenceInduced metric due to capture/recoil, stochastic fluctuations, Decoherence
ΦΦ KSKL KSKL
IF CPT ILL-DEFINED IF CPT ILL-DEFINED (e.g. D-particle Foam)(e.g. D-particle Foam)
KSKL
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 118
CPT Operator ill-defined, unique consequences in modifications of EPR correlations of entangled states of neutral mesons in meson factories (Φ-, B-factories) Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben SarkarBernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar
Induced metric due to capture/recoil, stochastic fluctuations, DecoherenceInduced metric due to capture/recoil, stochastic fluctuations, DecoherenceEstimates of such D-particle foam effects in neutral mesons complicated Estimates of such D-particle foam effects in neutral mesons complicated due to strong QCD effects present in such composite neutral particles due to strong QCD effects present in such composite neutral particles
ΦΦ KSKL KSKL
KKSSKKSS , ,
KKLLKKLL
KKSSKKSS , ,
KKLLKKLL
KSKL
IF CPT ILL-DEFINED (e.g. flavour IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)violating (FV) D-particle Foam)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 119
CPT Operator ill-defined, unique consequences in modifications of EPR correlations of entangled states of neutral mesons in meson factories (Φ-, B-factories) Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben SarkarBernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar
Induced metric due to capture/recoil, stochastic fluctuations, DecoherenceInduced metric due to capture/recoil, stochastic fluctuations, DecoherenceEstimates of such D-particle foam effects in neutral mesons complicated Estimates of such D-particle foam effects in neutral mesons complicated due to strong QCD effects present in such composite neutral particles due to strong QCD effects present in such composite neutral particles
ΦΦ KSKL KSKL
KKSSKKSS , ,
KKLLKKLL
KKSSKKSS , ,
KKLLKKLL
KSKL
IF CPT ILL-DEFINED (e.g. flavour IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)violating (FV) D-particle Foam)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 120
If QCD effects, sub-structure in neutral mesons ignored, and D-foam actsIf QCD effects, sub-structure in neutral mesons ignored, and D-foam actsas if they were structureless particles, then for as if they were structureless particles, then for MMQG QG ~ 10~ 101818 GeV (MAGIC) GeV (MAGIC)
the estimate for the estimate for ωω: : | | ωω | | ~ 10~ 10-4 -4 | |ζζ|, for 1 > |, for 1 > ||ζζ| > 10| > 10-2-2 (natural) (natural) Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)
ΦΦ KSKL
KKSSKKSS , ,
KKLLKKLL
KKSSKKSS , ,
KKLLKKLL
IF CPT ILL-DEFINED (e.g. flavour IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)violating (FV) D-particle Foam)
KSKL
Neutral mesons no longer indistinguishable particles, initial entangled state:
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 121
If QCD effects, sub-structure in neutral mesons ignored, and D-foam actsIf QCD effects, sub-structure in neutral mesons ignored, and D-foam actsas if they were structureless particles, then for as if they were structureless particles, then for MMQG QG ~ 10~ 101818 GeV (MAGIC) GeV (MAGIC)
the estimate for the estimate for ωω: : | | ωω | | ~ 10~ 10-4 -4 | |ζζ|, for 1 > |, for 1 > ||ζζ| > 10| > 10-2-2 (natural) (natural) Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)
ΦΦ KSKL
KKSSKKSS , ,
KKLLKKLL
KKSSKKSS , ,
KKLLKKLL
IF CPT ILL-DEFINED (e.g. flavour IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)violating (FV) D-particle Foam)
KSKL
Neutral mesons no longer indistinguishable particles, initial entangled state:
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 122
If QCD effects, sub-structure in neutral mesons ignored, and D-foam actsIf QCD effects, sub-structure in neutral mesons ignored, and D-foam actsas if they were structureless particles, then for as if they were structureless particles, then for MMQG QG ~ 10~ 101818 GeV (MAGIC) GeV (MAGIC)
the estimate for the estimate for ωω: : | | ωω | | ~ 10~ 10-4 -4 | |ζζ|, for 1 > |, for 1 > ||ζζ| > 10| > 10-2-2 (natural) (natural) Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)
ΦΦ KSKL
KKSSKKSS , ,
KKLLKKLL
KKSSKKSS , ,
KKLLKKLL
IF CPT ILL-DEFINED (e.g. flavour IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)violating (FV) D-particle Foam)
KSKL
Neutral mesons no longer indistinguishable particles, initial entangled state:
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 123
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 124
D-particle Recoil & the “Flavour” ProblemD-particle Recoil & the “Flavour” Problem
Not allNot all particle speciesspecies interact the same way with D-particlessame way with D-particlese.g. electric charge symmetries should be preserved, hence electrically-charged excitations cannot split and attach to neutral D-particles…. Neutrinos (or neutral mesons) are good candidates…But there may be flavour oscillations during the capture/recoil process, i.e. wave-function of recoiling string might differ by a phase from incident one….
In statistical populations of D-particles, one might have isotropic situations, with << u<< uii >> = 0, >> = 0, but stochastically fluctuating << u<< uii u ui i >> >> 0 0..For slow recoiling heavy D-particles the resulting Hamiltonian, expressing interactions of neutrinos (or “flavoured” particles, including oscillating neutral mesons), reads:
NB: direction of recoil dependenceLIV ….+ Stochasticallyflct. EnvironmentDecoherence,CPTV ill defined…
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 125
D-particle Recoil & the “Flavour” ProblemD-particle Recoil & the “Flavour” Problem
Not allNot all particle speciesspecies interact the same way with D-particlessame way with D-particlese.g. electric charge symmetries should be preserved, hence electrically-charged excitations cannot split and attach to neutral D-particles…. Neutrinos (or neutral mesons) are good candidates…But there may be flavour oscillations during the capture/recoil process, i.e. wave-function of recoiling string might differ by a phase from incident one….
In statistical populations of D-particles, one might have isotropic situations, with << u<< uii >> = 0, >> = 0, but stochastically fluctuating << u<< uii u ui i >> >> 0 0..For slow recoiling heavy D-particles the resulting Hamiltonian, expressing interactions of neutrinos (or “flavoured” particles, including oscillating neutral mesons), reads:
NB: direction of recoil dependenceLIV ….+ Stochasticallyflct. EnvironmentDecoherence,CPTV ill defined…
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 126
D-particle recoil and entangled Meson StatesD-particle recoil and entangled Meson States
Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 127
D-particle recoil and entangled Meson StatesD-particle recoil and entangled Meson States
Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 128
D-particle recoil and entangled Meson StatesD-particle recoil and entangled Meson States
Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 129
D-particle recoil and entangled Meson StatesD-particle recoil and entangled Meson States
Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 130
D-particle recoil and entangled Meson StatesD-particle recoil and entangled Meson States
Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from
Similarly for the dressed state is obtained by
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 131
D-particle recoil and entangled Meson StatesD-particle recoil and entangled Meson States
Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from
Similarly for the dressed state is obtained by
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 132
D-particle recoil and entangled Meson StatesD-particle recoil and entangled Meson States
Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from
Similarly for the dressed state is obtained by
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 133
D-particle recoil and entangled Meson StatesD-particle recoil and entangled Meson States
Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from
Similarly for the dressed state is obtained by
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 134
D-particle recoil and entangled Meson StatesD-particle recoil and entangled Meson States
Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from
Similarly for the dressed state is obtained by
Prediction of -like effects in entangled states ….( Bernabeu, NM, Papavassiliou)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 135
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 136
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 137
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 138
ω-effect as discriminant of space-time foam modelsω-effect as discriminant of space-time foam models
ω-effect not genericnot generic, depends on detailsdetails of foamfoam
Initially dressed states depend on form
of interaction Hamiltonian HI (non-degenerate) perturbation theory determine existence of ω-effects
(I) D-foam:
features: direction of k violates Lorentz symmetrydirection of k violates Lorentz symmetry, flavour non flavour non conservationconservation non-trivial ω-effect
(II) Quantum Gravity Foam as “thermal Bath’’ (Garay)
no ω-effect
Bernabeu, NM, Sarben Sarkar
Bath frequency“atom’’ (matter) frequency
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 139
ω-effect as discriminant of space-time foam modelsω-effect as discriminant of space-time foam models
ω-effect not genericnot generic, depends on detailsdetails of foamfoam
Initially dressed states depend on form
of interaction Hamiltonian HI (non-degenerate) perturbation theory determine existence of ω-effects
(I) D-foam:
features: direction of k violates Lorentz symmetrydirection of k violates Lorentz symmetry, flavour non flavour non conservationconservation non-trivial ω-effect
(II) Quantum Gravity Foam as “thermal Bath’’ (Garay)
no ω-effect
Bernabeu, NM, Sarben Sarkar
Bath frequency“atom’’ (matter) frequency
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 140
ω-effect as discriminant of space-time foam modelsω-effect as discriminant of space-time foam models
ω-effect not genericnot generic, depends on detailsdetails of foamfoam
Initially dressed states depend on form
of interaction Hamiltonian HI (non-degenerate) perturbation theory determine existence of ω-effects
(I) D-foam:
features: direction of k violates Lorentz symmetrydirection of k violates Lorentz symmetry, flavour non flavour non conservationconservation non-trivial ω-effect
(II) Quantum Gravity Foam as “thermal Bath’’ (Garay)
no ω-effect
Bernabeu, NM, Sarben Sarkar
Bath frequency“atom’’ (matter) frequency
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 141
ω-effect as discriminant of space-time foam modelsω-effect as discriminant of space-time foam models
ω-effect not genericnot generic, depends on detailsdetails of foamfoam
Initially dressed states depend on form
of interaction Hamiltonian HI (non-degenerate) perturbation theory determine existence of ω-effects
(I) D-foam:
features: direction of k violates Lorentz symmetrydirection of k violates Lorentz symmetry, flavour non flavour non conservationconservation non-trivial ω-effect
(II) Quantum Gravity Foam as “thermal Bath’’ (Garay)
Stochastic (quantum) metric fluctuations in Dirac or Majorana Hamiltonian for neutrinos affect oscillation probabilities by damping exponential damping exponential factorsfactors – characteristic of decoherencedecoherence
Stochastic (quantum) metric fluctuations in Dirac or Majorana Hamiltonian for neutrinos affect oscillation probabilities by damping exponential damping exponential factorsfactors – characteristic of decoherencedecoherence
Stochastic (quantum) metric fluctuations in Dirac or Majorana Hamiltonian for neutrinos affect oscillation probabilities by damping exponential damping exponential factorsfactors – characteristic of decoherencedecoherence
Consider Dirac or Majorana (two-flavour) Hamiltonian with mixing , in such Consider Dirac or Majorana (two-flavour) Hamiltonian with mixing , in such a metric background, with equation of motion: a metric background, with equation of motion:
Flavour states Mass eigenstatesOscillation Oscillation ProbabilityProbability
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 151
Two kinds of foam examined:Two kinds of foam examined: (i) Gaussian distributions
(ii) Cauchy-Lorentz
In D-particle foam model, hIn D-particle foam model, hoioi n= u n= uii involves recoil velocity distribution of D- involves recoil velocity distribution of D-
particle populationsparticle populations . NB: damping suppressed by neutrino mass differencesNB: damping suppressed by neutrino mass differences
Two kinds of foam examined:Two kinds of foam examined: (i) Gaussian distributions
(ii) Cauchy-Lorentz
In D-particle foam model, hIn D-particle foam model, hoioi n= u n= uii involves recoil velocity distribution of D- involves recoil velocity distribution of D-
particle populationsparticle populations . NB: damping suppressed by neutrino mass differencesNB: damping suppressed by neutrino mass differences
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 153
Lindblad type DecoherenceLindblad type Decoherence
Probably too Large to be QGEffect….
NB: Lindblad-type dampingNB: Lindblad-type dampingAlso induced by uncertaintiesAlso induced by uncertaintiesin energy of neutrino beamsin energy of neutrino beams
LSND+ KamLand
Ohlsson, JacobsonOhlsson, Jacobson
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 163
Current Experimental BoundsCurrent Experimental Bounds
Lindblad type DecoherenceLindblad type Decoherence
Probably too Large to be QGEffect….
NB: Lindblad-type dampingNB: Lindblad-type dampingAlso induced by uncertaintiesAlso induced by uncertaintiesin energy of neutrino beamsin energy of neutrino beams
LSND+ KamLand
Ohlsson, JacobsonOhlsson, Jacobson
But in that caseall exponents must be non zeroHence….still unresolved
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 164
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 165
Look into the future: Potential of J-PARC, CNGS
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 166
Look into the future: High Energy NeutrinosLook into the future: High Energy Neutrinos
Much higher sensitivities from high energy neutrinosMuch higher sensitivities from high energy neutrinos
AMANDA, ICE CUBE, AMANDA, ICE CUBE, ASTROPHYSICAL/COSMOLOGICAL NEUTRINOSASTROPHYSICAL/COSMOLOGICAL NEUTRINOS(e.g. if neutrinos with energies close to 10(e.g. if neutrinos with energies close to 102020 eV from GRB eV from GRBAt redshifts z > 1 are observed …) At redshifts z > 1 are observed …)
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 167
Look into the future: High Energy NeutrinosLook into the future: High Energy Neutrinos
Much higher sensitivities from high energy neutrinosMuch higher sensitivities from high energy neutrinos
AMANDA, ICE CUBE, AMANDA, ICE CUBE, ASTROPHYSICAL/COSMOLOGICAL NEUTRINOSASTROPHYSICAL/COSMOLOGICAL NEUTRINOS(e.g. if neutrinos with energies close to 10(e.g. if neutrinos with energies close to 102020 eV from GRB eV from GRBAt redshifts z > 1 are observed …) At redshifts z > 1 are observed …)
Recently: Interesting scenarios of Lindblad decoherence with SOMESOME damping exponentshaving energy dependence E-4 proposed for reconciling LSND (anti-ν) & MINIBOONE
Recently: Interesting scenarios of Lindblad decoherence with SOMESOME damping exponentshaving energy dependence E-4 proposed for reconciling LSND (anti-ν) & MINIBOONE
Recently: Interesting scenarios of Lindblad decoherence with SOMESOME damping exponentshaving energy dependence E-4 proposed for reconciling LSND (anti-ν) & MINIBOONE
e.g. in our stochastic fluctuating metric modelse.g. in our stochastic fluctuating metric modelsEE-4 -4 scaling is obtained in Gaussian model with scaling is obtained in Gaussian model with σσ22 ~ k ~ k-2-2
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 170
QG Decoherence & LHC Black Holes QG Decoherence & LHC Black Holes
In string theory or extra-dimensional models (in In string theory or extra-dimensional models (in general) QG mass scale may not be Planck scale but general) QG mass scale may not be Planck scale but much smaller : Mmuch smaller : MQG QG << M << MPlanck Planck
Theoretically MTheoretically MQGQG could be as low as a few TeV. In could be as low as a few TeV. In such a case, collision of energetic particles at LHC such a case, collision of energetic particles at LHC could produce microscopic Black Holes at LHC, could produce microscopic Black Holes at LHC, which will evaporate quickly. which will evaporate quickly.
If there is decoherence in such models, then, can the If there is decoherence in such models, then, can the above tests determine the magnitude of Mabove tests determine the magnitude of MQG QG
beforehand? beforehand? Highly model dependent issue…Highly model dependent issue…
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 171
QG Decoherence & LHC Black HolesQG Decoherence & LHC Black Holes
No low MNo low MQGQG mass scale allowed… mass scale allowed…
(ii) (ii) Parameters = O((Parameters = O((ΔΔmm22))22/E/E22MMQGQG)) (e.g. Adler’s model of (e.g. Adler’s model of decoherence, stochastic D-particle LI models…) decoherence, stochastic D-particle LI models…)
Low MQG mass models (even TeV) allowed by current Low MQG mass models (even TeV) allowed by current
measurements of decoherence… compatible with LHC BH measurements of decoherence… compatible with LHC BH observations….observations….
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 172
CONCLUSIONS CONCLUSIONS We know very little about QG so experimental searches & tests of various We know very little about QG so experimental searches & tests of various
theoretical models will definitely help in putting us on the right course …theoretical models will definitely help in putting us on the right course …
There may be `smoking-gun’ experiments for intrinsic CPTV & QG There may be `smoking-gun’ experiments for intrinsic CPTV & QG Decoherence , unique in entangled states of mesonsDecoherence , unique in entangled states of mesons (ω-effect best signature, if ω-effect best signature, if present though…. present though…. HoweverHowever, not, not generic effect, depends on model of QG foam… generic effect, depends on model of QG foam…)
The magnitude of such effects is highly model dependent, may not be far The magnitude of such effects is highly model dependent, may not be far from sensitivity of immediate-future facilities.from sensitivity of immediate-future facilities.
QG Decoherence effects in neutrino oscillations yield damping signatures, but QG Decoherence effects in neutrino oscillations yield damping signatures, but those are suppressed by (powers of) neutrino mass differences. Difficult to those are suppressed by (powers of) neutrino mass differences. Difficult to detect … Nevertheless future (high energy neutrinos) looks promising…detect … Nevertheless future (high energy neutrinos) looks promising…
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 173
CONCLUSIONS CONCLUSIONS We know very little about QG so experimental searches & tests of various We know very little about QG so experimental searches & tests of various
theoretical models will definitely help in putting us on the right course …theoretical models will definitely help in putting us on the right course …
There may be `smoking-gun’ experiments for intrinsic CPTV & QG There may be `smoking-gun’ experiments for intrinsic CPTV & QG Decoherence , unique in entangled states of mesonsDecoherence , unique in entangled states of mesons (ω-effect best signature, if ω-effect best signature, if present though…. present though…. HoweverHowever, not, not generic effect, depends on model of QG foam… generic effect, depends on model of QG foam…)
The magnitude of such effects is highly model dependent, may not be far The magnitude of such effects is highly model dependent, may not be far from sensitivity of immediate-future facilities.from sensitivity of immediate-future facilities.
QG Decoherence effects in neutrino oscillations yield damping signatures, but QG Decoherence effects in neutrino oscillations yield damping signatures, but those are suppressed by (powers of) neutrino mass differences. Difficult to those are suppressed by (powers of) neutrino mass differences. Difficult to detect … Nevertheless future (high energy neutrinos) looks promising…detect … Nevertheless future (high energy neutrinos) looks promising…
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 174
CONCLUSIONS CONCLUSIONS We know very little about QG so experimental searches & tests of various We know very little about QG so experimental searches & tests of various
theoretical models will definitely help in putting us on the right course …theoretical models will definitely help in putting us on the right course …
There may be `smoking-gun’ experiments for intrinsic CPTV & QG There may be `smoking-gun’ experiments for intrinsic CPTV & QG Decoherence , unique in entangled states of mesonsDecoherence , unique in entangled states of mesons (ω-effect best signature, if ω-effect best signature, if present though…. present though…. HoweverHowever, not, not generic effect, depends on model of QG foam… generic effect, depends on model of QG foam…)
The magnitude of such effects is highly model dependent, may not be far The magnitude of such effects is highly model dependent, may not be far from sensitivity of immediate-future facilities.from sensitivity of immediate-future facilities.
QG Decoherence effects in neutrino oscillations yield damping signatures, but QG Decoherence effects in neutrino oscillations yield damping signatures, but those are suppressed by (powers of) neutrino mass differences. Difficult to those are suppressed by (powers of) neutrino mass differences. Difficult to detect … Nevertheless future (high energy neutrinos) looks promising…detect … Nevertheless future (high energy neutrinos) looks promising…
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 175
Further Questions…Further Questions…
DISCRETE 08, IFIC (Valencia) , December 08 N. E. MAVROMATOS 176