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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.

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Cpt and decoherence in quantum gravity

CPT and DECOHERENCE inQUANTUM 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


Outline

Theoretical motivation for CPT Violation (CPTV) :

Lorentz violation (LV): microscopic & cosmological

Briefly

(ii) Quantum Gravity Foam (QGF) (Decoherence)

This talk

Towards microscopic models from (non-critical) strings &

Order of magnitude estimates of expected effects

This talk

TeV photon astrophysics LV tests

Precision tests of QGF-CPTV of smoking-gun-evidence type:

neutral mesons factories – entangled states: EPR correlations modified (ω-effect)

Disentangling (i) from (ii)

ω-effect as discriminant of space-time foam models

This talk

Neutrino Tests of QG decoherence Damping factors in flavour Oscillation Probabilities – suppressed though by neutrino mass differences

This talk

OUTLINE

N. E. MAVROMATOS


Outline1

Theoretical motivation for CPT Violation (CPTV) :

Lorentz violation (LV): microscopic & cosmological

Briefly

(ii) Quantum Gravity Foam (QGF) (Decoherence)

This talk

Towards microscopic models from (non-critical) strings &

Order of magnitude estimates of expected effects

This talk

TeV photon astrophysics LV tests

Precision tests of QGF-CPTV of smoking-gun-evidence type:

neutral mesons factories – entangled states: EPR correlations modified (ω-effect)

Disentangling (i) from (ii)

ω-effect as discriminant of space-time foam models

This talk

Neutrino Tests of QG decoherence Damping factors in flavour Oscillation Probabilities – suppressed though by neutrino mass differences

This talk

OUTLINE

IMPORTANT : QUANTUM GRAVITY DECOHERENCE CURRENT BOUNDS &

MICROSCOPIC BLACK HOLES AT LHC

Details of microscopic model matter a lot before concusions are reached in excluding large extra dimensional models by such decoherence studies…

N. E. MAVROMATOS


Generic theory issues
Generic Theory Issues

  • CPT SYMMETRY:

    • (1) Lorentz Invariance, (2) Locality , (3) Unitarity

      • Theorem proven for FLAT space times

        (Jost, Luders, Pauli, Bell, Greenberg )

  • Why CPT Violation?

    • Quantum Gravity (QG) Models violating Lorentz and/or Quantum Coherence:

      (I) Space-time foam: QG as “Environment”

      Decoherence, CPT Ill defined (Wald 1979)

      (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…

N. E. MAVROMATOS


Cpt theorem
CPT THEOREM

N. E. MAVROMATOS


Cpt theorem1
CPT THEOREM

N. E. MAVROMATOS


Cpt theorem2
CPT THEOREM

N. E. MAVROMATOS


Cpt theorem3
CPT THEOREM

N. E. MAVROMATOS


Cpt theorem4
CPT THEOREM

J.A. Wheeler

10-35 m

Space-time Foam

N. E. MAVROMATOS



Cpt and decoherence in quantum gravity

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 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 theories. Worth checking experimentally….  CPTV issues

In general, in space-times

with Horizons (e.g. De Sitter cosmology…)

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

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 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 theories. Worth checking experimentally….  CPTV issues

In general, in space-times

with Horizons (e.g. De Sitter cosmology…)

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

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 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 theories. Worth checking experimentally….  CPTV issues

In general, in space-times

with Horizons (e.g. De Sitter cosmology…)

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

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 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 theories. Worth checking experimentally….  CPTV issues

In general, in space-times

with Horizons (e.g. De Sitter cosmology…)

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

In general, in space-times

with Horizons (e.g. De Sitter cosmology…)

N. E. MAVROMATOS


Cosmological motivation for cpt violation
COSMOLOGICAL MOTIVATION FOR CPT VIOLATION?

Supernova and CMB Data (2006)

Baryon oscillations, Large Galactic

Surveys & other data (2008)

Evidence for :

Dark Matter(23%)

Dark Energy (73%)

Ordinary matter (4%)

N. E. MAVROMATOS


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?

DARK ENERGY& Cosmological CPTV?

N. E. MAVROMATOS


Dark energy cosmological cptv1

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?

DARK ENERGY& Cosmological CPTV?

N. E. MAVROMATOS


Dark energy cosmological cptv2

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?

DARK ENERGY& Cosmological CPTV?

Outer Horizon (live ``inside’’ black hole):

Unstable, indicates expansion

N. E. MAVROMATOS


Dark energy cosmological cptv3

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?

DARK ENERGY& Cosmological CPTV?

Global (Cosmological FRW solution)

N. E. MAVROMATOS


Dark energy cosmological cptv4

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?

DARK ENERGY& Cosmological CPTV?

Global (Cosmological FRW solution)

Cosmological (global) deSitter horizon:

N. E. MAVROMATOS





Stochastic light cone fluctuations
Stochastic Light-Cone Fluctuations

CPT may also be violated

in such stochastic models

N. E. MAVROMATOS


Caution on cptv lorentz violation

CPT Operator well defined but NON-Commuting with Hamiltonian [H , Θ ] 0

Lorentz & CPT Violation in the Hamiltonian

Neutral Mesons & Factories, Atomic Physics, Anti-matter factories, Neutrinos, …

Modified Dispersion Relations (GRB, neutrino oscillations, synchrotron radiation…)

Caution on CPTV & Lorentz Violation

N. E. MAVROMATOS


Caution on cptv lorentz violation1

CPT Operator well defined but NON-Commuting with Hamiltonian [H , Θ ] 0

Lorentz & CPT Violation in the Hamiltonian

Neutral Mesons & Factories, Atomic Physics, Anti-matter factories, Neutrinos, …

Modified Dispersion Relations (GRB, neutrino oscillations, synchrotron radiation…)

CAUTION: LV does not necessarily imply CPTV

e.g. Standard

Model Extension,

Non-commutative

Geometry field theories

Caution on CPTV & Lorentz Violation

N. E. MAVROMATOS


Standard model extension
STANDARD MODEL EXTENSION [H , Θ ] 0

N. E. MAVROMATOS


Non commutative effective field theories
Non-commutative effective field theories [H , Θ ] 0

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)

N. E. MAVROMATOS


Non commutative effective field theories1
Non-commutative effective field theories [H , Θ ] 0

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)

N. E. MAVROMATOS


Standard model extension1
STANDARD MODEL EXTENSION [H , Θ ] 0

N. E. MAVROMATOS


Lorentz violation anti hydrogen
Lorentz Violation & Anti-Hydrogen [H , Θ ] 0

  • Trapped Molecules:

    NB:Sensitivity in b3

    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

N. E. MAVROMATOS


Tests of lorentz violation in neutral kaons
Tests of Lorentz Violation in Neutral Kaons [H , Θ ] 0

N. E. MAVROMATOS


Experimental bounds
EXPERIMENTAL BOUNDS [H , Θ ] 0

N. E. MAVROMATOS


Detecting cpt violation cptv

Neutral Mesons: K, B, ( [H , Θ ] 0unique (?) QG induced decoherence tests) meson-factories entangled states

K ± charged-meson decays

Antihydrogen (precision spectroscopic tests on free & trapped molecules - search for forbidden transitions)

Low-energy atomic Physics Experiments

Ultra – Cold Neutrons

Neutrino Physics

Terrestrial & Extraterrestrial tests of Lorentz Invariance - search for modified dispersion relations of matter probes: GRB, AGN photons, Crab nebula synchrotron radiation, Flares….

DETECTING CPT VIOLATION (CPTV)

Complex Phenomenology

No single figure of merit

N. E. MAVROMATOS


Order of magnitude estimates
Order of Magnitude Estimates [H , Θ ] 0

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Order of magnitude estimates1
Order of Magnitude Estimates [H , Θ ] 0

N. E. MAVROMATOS


Order of magnitude estimates2
Order of Magnitude Estimates [H , Θ ] 0

N. E. MAVROMATOS


Order of magnitude estimates3
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates4
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

Adler-Horwitz decoherent evolution model

N. E. MAVROMATOS


Order of magnitude estimates5
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates6
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates7
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


D particle foam models
D-particle Foam Models [H , Θ ] 0

Bulk closed

string

ELLIS, NM, WESTMUCKETT

N. E. MAVROMATOS


D particle recoil liv models
D-particle Recoil & LIV models [H , Θ ] 0

N. E. MAVROMATOS


D particle recoil liv models1
D-particle Recoil & LIV models [H , Θ ] 0

String World-sheettorn apart

non-conformal Process, Liouville string

N. E. MAVROMATOS


D particle recoil liv models2
D-particle Recoil & LIV models [H , Θ ] 0

N. E. MAVROMATOS


A non critical string theory time arrow

Ellis, NM [H , Θ ] 0

Nanopoulos

A (non-critical) string theory time Arrow

Non-equilibrium Strings

(non-critical), due to

e.g. cosmically catastrophic

events in Early Universe,

for instance brane worlds

collisions:

World-sheet conformal

Invariance is disturbed

Central charge of world-

Sheet theory ``runs’’

To a minimal value

Zamolodchikov’s C-theorem

An H-theorem for CFT

Change in degrees of

Freedom (i.e. entropy)

N. E. MAVROMATOS


A non critical string theory time arrow1

Ellis, NM [H , Θ ] 0

Nanopoulos

A (non-critical) string theory time Arrow

Non-equilibrium Strings

(non-critical), due to

e.g. cosmically catastrophic

events in Early Universe,

for instance brane worlds

collisions:

World-sheet conformal

Invariance is disturbed

Central charge of world-

Sheet theory ``runs’’

To a minimal value

Zamolodchikov’s C-theorem

An H-theorem for CFT

Change in degrees of

Freedom (i.e. entropy)

N. E. MAVROMATOS


A non critical string theory time arrow2

Ellis, NM [H , Θ ] 0

Nanopoulos

A (non-critical) string theory time Arrow

Non-equilibrium Strings

(non-critical), due to

e.g. cosmically catastrophic

events in Early Universe,

for instance brane worlds

collisions:

World-sheet conformal

Invariance is disturbed

Central charge of world-

Sheet theory ``runs’’

To a minimal value

Zamolodchikov’s C-theorem

An H-theorem for CFT

Change in degrees of

Freedom (i.e. entropy)

Time as world-sheet irreversible

Renormalization-Group Flow

N. E. MAVROMATOS


Order of magnitude estimates8
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates9
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates10
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates11
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates12
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates13
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates14
Order of Magnitude Estimates [H , Θ ] 0

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates15
Order of Magnitude Estimates [H , Θ ] 0

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

  • The parameters σ and γ depend on microscopic model and are suppressed by (powers of) the string scale MString

N. E. MAVROMATOS


Complex phenomenology of cptv

CPT Operator [H , Θ ] 0well defined but NON-Commuting with Hamiltonian [H , Θ ] 0

Lorentz & CPT Violation in the Hamiltonian

Neutral Mesons & Factories, Atomic Physics, Anti-matter factories, Neutrinos, …

Modified Dispersion Relations (GRB, neutrino oscillations, synchrotron radiation, TeV AGN…)

CPT Operator ill defined(Wald), intrinsic violation, modifiedconcept of antiparticle

Decoherence CPTV Tests

Neutral Mesons: K, B & factories (novel effects in entangled states :

(perturbatively) modified

EPR correlations)

Ultracold Neutrons

Neutrinos (highest sensitivity)

Light-Cone fluctuations (GRB, Gravity-Wave Interferometers, neutrino oscillations)

Complex Phenomenology of CPTV

N. E. MAVROMATOS


Complex phenomenology of cptv1

CPT Operator [H , Θ ] 0well defined but NON-Commuting with Hamiltonian [H , Θ ] 0

Lorentz & CPT Violation in the Hamiltonian

Neutral Mesons & Factories, Atomic Physics, Anti-matter factories, Neutrinos, …

Modified Dispersion Relations (GRB, neutrino oscillations, synchrotron radiation, TeV AGN…)

Complex Phenomenology of CPTV

N. E. MAVROMATOS


Multi messenger observations of the cosmos
Multi-messenger observations of the Cosmos [H , Θ ] 0

protons E>1019 eV ( 10 Mpc )‏

neutrinos

gammas ( z < 1 )‏

protons E<1019 eV

protons/nuclei:Deviated by magnetic fields, Absorbed by radiation field (GZK)‏

photons:Absorbed by dust & radiation field (CMB)‏

neutrinos:Difficult to detect

cosmicaccelerator

Us

N. E. MAVROMATOS

DeNaurois 2008

⇒ Three “astronomies” possible...


Vhe experimental world today
VHE Experimental World Today [H , Θ ] 0

TIBET

MILAGRO

MAGIC

STACEE

TACTIC

CANGAROO

HESS

TIBET ARRAY

ARGO-YBJ

MILAGRO

STACEE

CACTUS

TACTIC

PACT

Canary Islands

GRAPES

N. E. MAVROMATOS

M. MARTINEZ


The magic collaboration m ajor a tmospheric g amma ray i maging c herenkov telescope
The MAGIC Collaboration [H , Θ ] 0(Major Atmospheric Gamma-ray ImagingCherenkov Telescope )

Observation of

Flares from AGN

Mk 501

Red-shift: z=0.034

N. E. MAVROMATOS


The magic effect
The MAGIC ``Effect’’ [H , Θ ] 0

N. E. MAVROMATOS


Possible interpetations
Possible Interpetations [H , Θ ] 0

  • Delays of more energetic photons are a result of AGN sourcePhysics (SSC mechanism)

    MAGIC Coll. ApJ 669, 862 (2007) : SSC I

    Bednarek & Wagner arXive:0804.0619 : SSCII

  • 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….

N. E. MAVROMATOS


Quantum gravity induced modified dispersion for photons
Quantum-Gravity Induced Modified Dispersion for Photons [H , Θ ] 0

Modified dispersion due to QG induced space-time (metric) distortions (c=1 units):

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

MAGIC Results (ECF Method): [H , Θ ] 0

Quadratic

Linear

95% CL

N. E. MAVROMATOS


A stringy model of space time foam
A Stringy Model of Space -Time Foam [H , Θ ] 0

Ellis, NM, Nanopoulos

Open strings on D3-brane world represent

electrically neutral matter or radiation,

interacting via splitting/capture with D-particles

(electric charge conservation) .

D-particle foam medium transparent to (charged)

Electrons no modified dispersion for them

Photons or electrically neutral probes

feel the effects of D-particle foam

Modified Dispersion for them….

N. E. MAVROMATOS


A stringy model of space time foam1
A Stringy Model of Space -Time Foam [H , Θ ] 0

Ellis, NM, Nanopoulos

Open strings on D3-brane world represent

electrically neutral matter or radiation,

interacting via splitting/capture with D-particles

(electric charge conservation) .

D-particle foam medium transparent to (charged)

Electrons no modified dispersion for them

Photons or electrically neutral probes

feel the effects of D-particle foam

Modified Dispersion for them….

NON-UNIVERSAL ACTION OF

D-PARTICLE FOAM ON MATTER

& RADIATION

N. E. MAVROMATOS


A stringy model of space time foam2
A Stringy Model of Space -Time Foam [H , Θ ] 0

Ellis, NM, Nanopoulos

Open strings on D3-brane world represent

electrically neutral matter or radiation,

interacting via splitting/capture with D-particles

(electric charge conservation) .

D-particle foam medium transparent to (charged)

Electrons no modified dispersion for them

Photons or electrically neutral probes

feel the effects of D-particle foam

Modified Dispersion for them….

NON-UNIVERSAL ACTION OF

D-PARTICLE FOAM ON MATTER

& RADIATION

N. E. MAVROMATOS


Stringy uncertainties the capture process
Stringy Uncertainties & the Capture Process [H , Θ ] 0

Ellis, NM, NanopoulosarXiv:0804.3566

During Capture: intermediate

String stretching between

D-particle and D3-brane is

Created. It acquires N internal

Oscillator excitations &

Grows in size & oscillates from

Zero to a maximum length by

absorbing incident photon

Energy p0 :

Minimise right-hand-size w.r.t. L.

End of intermediate string on D3-brane

Moves with speed of light in vacuo c=1

Hence TIME DELAY(causality) during

Capture:

DELAY IS INDEPENDENT OF

PHOTON POLARIZATION, HENCE

NO BIREFRINGENCE….

N. E. MAVROMATOS


Stringy uncertainties the magic effect
Stringy Uncertainties & the MAGIC Effect [H , Θ ] 0

  • D-foam: transparent to electrons

  • D-foam captures photons & re-emits them

  • Time Delay (Causal) ineach Capture:

  • Independent of photon polarization(no Birefringence)

  • Total Delayfrom emission of photons

    till observation overa distance D(assume n* defects

    per string length):

Effectively modified

Dispersion relation

for photons due to

induced metric

distortion G0i ~ p0

REPRODUCE 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034)

For n* =O(1) & Ms ~ 1018 GeV, consistently with Crab Nebula & other

Astrophysical constraints on modified dispersion relations……

N. E. MAVROMATOS


Stringy uncertainties the magic effect1
Stringy Uncertainties & the MAGIC Effect [H , Θ ] 0

  • D-foam: transparent to electrons

  • D-foam captures photons & re-emits them

  • Time Delay (Causal) ineach Capture:

  • Independent of photon polarization(no Birefringence)

  • Total Delayfrom emission of photons

    till observation overa distance D(assume n* defects

    per string length):

COMPATIBLE WITH STRING UNCERTAINTY PRINCIPLES:

Δt Δx ≥ α’ , Δp Δx ≥ 1 + α’ (Δp )2 + …

(α’ = Regge slope = Square of minimum string length scale)

Effectively modified

Dispersion relation

for photons due to

induced metric

distortion G0i ~ p0

REPRODUCE 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034)

For n* =O(1) & Ms ~ 1018 GeV, consistently with Crab Nebula & other

Astrophysical constraints on modified dispersion relations……

N. E. MAVROMATOS


Complex phenomenology of cptv2

CPT Operator [H , Θ ] 0well defined but NON-Commuting with Hamiltonian [H , Θ ] 0

Lorentz & CPT Violation in the Hamiltonian

Neutral Mesons & Factories, Atomic Physics, Anti-matter factories, Neutrinos, …

Modified Dispersion Relations (GRB, neutrino oscillations, synchrotron radiation…)

CPT Operator ill defined(Wald), intrinsic violation, modifiedconcept of antiparticle

Decoherence CPTV Tests

Neutral Mesons: K, B & factories (novel effects in entangled states :

(perturbatively) modified

EPR correlations)this talk

Ultracold Neutrons

Neutrinos (highest sensitivity)

Light-Cone fluctuations (GRB, Gravity-Wave Interferometers, neutrino oscillations)

Complex Phenomenology of CPTV

N. E. MAVROMATOS


Complex phenomenology of cptv3

CPT Operator [H , Θ ] 0well defined but NON-Commuting with Hamiltonian [H , Θ ] 0

Lorentz & CPT Violation in the Hamiltonian

Neutral Mesons & Factories, Atomic Physics, Anti-matter factories, Neutrinos, …

Modified Dispersion Relations (GRB, neutrino oscillations, synchrotron radiation…)

CPT Operator ill defined(Wald), intrinsic violation, modifiedconcept of antiparticle

Decoherence CPTV Tests

Neutral Mesons: K, B & factories (novel effects in entangled states :

(perturbatively) modified

EPR correlations)this talk

Ultracold Neutrons

Neutrinos (highest sensitivity)

Light-Cone fluctuations (GRB, Gravity-Wave Interferometers, neutrino oscillations)

Complex Phenomenology of CPTV

N. E. MAVROMATOS


Quantum gravity decoherence cptv

QUANTUM GRAVITY DECOHERENCE & CPTV [H , Θ ] 0

NEUTRAL MESON PHENOMENOLOGY



Decoherence vs cptv in qm
Decoherence vs CPTV in QM [H , Θ ] 0

N. E. MAVROMATOS


Neutral kaon asymmetries
Neutral Kaon Asymmetries [H , Θ ] 0

N. E. MAVROMATOS


Neutral kaon asymmetries1
Neutral Kaon Asymmetries [H , Θ ] 0

N. E. MAVROMATOS


Neutral kaon asymmetries2
Neutral Kaon Asymmetries [H , Θ ] 0

Effects of α, β, γ decoherence parameters

N. E. MAVROMATOS


Decoherence vs qm effects
Decoherence vs QM effects [H , Θ ] 0

N. E. MAVROMATOS


Indicative bounds
Indicative Bounds [H , Θ ] 0

N. E. MAVROMATOS


Neutral kaon entangled states
Neutral Kaon Entangled States [H , Θ ] 0

  • Complete Positivity Different parametrization ofDecoherence matrix(Benatti-Floreanini)

N. E. MAVROMATOS


Neutral kaon entangled states1
Neutral Kaon Entangled States [H , Θ ] 0

  • Complete Positivity Different parametrization ofDecoherence matrix(Benatti-Floreanini)

N. E. MAVROMATOS


Order of magnitude estimates16

But recall... [H , Θ ] 0

Order of Magnitude Estimates

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates17

But recall... [H , Θ ] 0

Order of Magnitude Estimates

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates18

But recall... [H , Θ ] 0

Order of Magnitude Estimates

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Order of magnitude estimates19

But recall... [H , Θ ] 0

Order of Magnitude Estimates

  • However there are models with inverse energy dependence, e.g.

  • (i) Adler’s Lindblad model for Energy-driven QG Decoherence in two level systems (hep-th/0005220): decoherence Lindblad operator propotional to Hamiltonian

  • Decoherence damping exp(-D t) ,

  • Decoherence Parameter estimate: D = (Δm2)2/E2MP

  • (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 recoil velocities of populations of D-parfticle defects in space time (Sarkar, NM) :

  • (a) Gaussian D-particle recoil velocity distribution, spread σ:

  • Decoherence damping in oscillations among two-level systems : exp (-D t 2),D = σ2(Δm2)2/E2

  • (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ :

  • Decoherence damping exp (-D t),D = γ(Δm2)/E

N. E. MAVROMATOS


Complex phenomenology of cptv4

CPT Operator [H , Θ ] 0well defined but NON-Commuting with Hamiltonian [H , Θ ] 0

Lorentz & CPT Violation in the Hamiltonian

Neutral Mesons & Factories, Atomic Physics, Anti-matter factories, Neutrinos, …

Modified Dispersion Relations (GRB, neutrino oscillations, synchrotron radiation…)

CPT Operator ill defined(Wald), intrinsic violation, modifiedconcept of antiparticle

Decoherence CPTV Tests

Neutral Mesons: K, B & factories (novel effects in entangled states :

(perturbatively) modified

EPR correlations)this talk

Ultracold Neutrons

Neutrinos (highest sensitivity)

Light-Cone fluctuations (GRB, Gravity-Wave Interferometers, neutrino oscillations)

Complex Phenomenology of CPTV

N. E. MAVROMATOS


Complex phenomenology of cptv5

CPT Operator [H , Θ ] 0well defined but NON-Commuting with Hamiltonian [H , Θ ] 0

Lorentz & CPT Violation in the Hamiltonian

Neutral Mesons & Factories, Atomic Physics, Anti-matter factories, Neutrinos, …

Modified Dispersion Relations (GRB, neutrino oscillations, synchrotron radiation…)

CPT Operator ill defined(Wald), intrinsic violation, modifiedconcept of antiparticle

Decoherence CPTV Tests

Neutral Mesons: K, B & factories (novel effects in entangled states :

(perturbatively) modified

EPR correlations)this talk

Ultracold Neutrons

Neutrinos (highest sensitivity)

Light-Cone fluctuations (GRB, Gravity-Wave Interferometers, neutrino oscillations)

Complex Phenomenology of CPTV

N. E. MAVROMATOS


Entangled states cpt epr correlations
Entangled States: [H , Θ ] 0CPT & EPR correlations

  • Novel (genuine) two body effects:

    • If CPT not-well defined

      modification of EPR correlations (ω-effect)

      Unique effect in Entangled states of mesons !! Characteristic of ill-defined nature of intrinsic CPT

      Violation (e.g. due to decoherence)

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cptv epr correlations modification
CPTV & EPR-correlations modification [H , Θ ] 0

N. E. MAVROMATOS


Cptv epr correlations modification1
CPTV & EPR-correlations modification [H , Θ ] 0

N. E. MAVROMATOS


Cptv epr correlations modification2
CPTV & EPR-correlations modification [H , Θ ] 0

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….

N. E. MAVROMATOS


Cptv epr correlations modification3
CPTV & EPR-correlations modification [H , Θ ] 0

KSKS terms from C=+ background

no dependence on centre-of-mass energy s.

Real part of Breit-Wigner amplitude

Vanishes at top of resonance, Interference

of C=+ with C=-- background, vanishes

at top of the resonance, opposite signature

on either side…..

N. E. MAVROMATOS


Cptv epr correlations modification4
CPTV & EPR-correlations modification [H , Θ ] 0

N. E. MAVROMATOS


Cptv epr correlations modification5
CPTV & EPR-correlations modification [H , Θ ] 0

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


B systems effect demise of flavour tagging
B-systems, [H , Θ ] 0ω-effect & demise of flavour-tagging

Alvarez, Bernabeu NM, Nebot, Papavassiliou

  • 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 statisticsInteresting limits of ω-effects there

  • Flavour tagging: Knowledge that one of the two-mesons in a meson factory decays at a given time through flavour-specific “channel’’

    Unambiguously determine the flavour of the other meson at the same time .

    Not True if intrinsic CPTV – ω-effect present : Theoretical limitation (“demise’’) of flavour tagging

N. E. MAVROMATOS


B systems effect demise of flavour tagging1
B-systems, [H , Θ ] 0ω-effect & demise of flavour-tagging

N. E. MAVROMATOS


B systems effect demise of flavour tagging2
B-systems, [H , Θ ] 0ω-effect & demise of flavour-tagging

CPTV parameter (QM)

CP parameter

N. E. MAVROMATOS


Equal sign di lepton charge asymmetry t dependence
EquaL-Sign di-lepton charge asymmetry Δt dependence [H , Θ ] 0

ALVAREZ, BERNABEU, NEBOT

  • Interesting tests of the ω-effect can be performed by looking at the equal-sign di-lepton decay channels

N. E. MAVROMATOS


Equal sign di lepton charge asymmetry t dependence1
EquaL-Sign di-lepton charge asymmetry Δt dependence [H , Θ ] 0

ALVAREZ, BERNABEU, NEBOT

  • Interesting tests of the ω-effect can be performed by looking at the equal-sign di-lepton decay channels

N. E. MAVROMATOS


Equal sign di lepton charge asymmetry t dependence2
EquaL-Sign di-lepton charge asymmetry Δt dependence [H , Θ ] 0

ALVAREZ, BERNABEU, NEBOT

  • Interesting tests of the ω-effect can be performed by looking at the equal-sign di-lepton decay channels

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cpt and decoherence in quantum gravity

Δ [H , Θ ] 0t observable

Expt.

Δt observable

Expt.

Δt observable

Expt.

Δt observable

Expt.

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

CURRENT EXPERIMENTAL LIMITS [H , Θ ] 0

Δt observable

Expt.

Δt observable

Expt.

Δt observable

Expt.

Δt observable

Expt.

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


D particle foam entangled states
D-particle Foam & Entangled States [H , Θ ] 0

  • If CPT Operator well-defined as operator, even if CPT is broken in the Hamiltonian… (e.g. Lorentz violating models)

Φ

KSKL

KSKL

N. E. MAVROMATOS


Epr modifications d particle foam
EPR Modifications & D-particle Foam [H , Θ ] 0

  • If CPT Operatorill-defined, uniqueconsequences inmodifications of EPRcorrelations of entangled states of neutral mesons in meson factories (Φ-, B-factories)Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar

Φ

KSKL

KSKL

KSKL

IF CPT ILL-DEFINED (e.g. D-particle Foam)

Induced metric due to capture/recoil, stochastic fluctuations, Decoherence

N. E. MAVROMATOS


Epr modifications d particle foam1
EPR Modifications & D-particle Foam [H , Θ ] 0

  • 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 Sarkar

Φ

KSKL

KSKL

KSKL

KSKS ,

KLKL

KSKS ,

KLKL

IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)

Induced metric due to capture/recoil, stochastic fluctuations, Decoherence

Estimates of such D-particle foam effects in neutral mesons complicated

due to strong QCD effects present in such composite neutral particles

N. E. MAVROMATOS


Epr modifications d particle foam2
EPR Modifications & D-particle Foam [H , Θ ] 0

  • 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 Sarkar

Φ

KSKL

KSKL

KSKL

KSKS ,

KLKL

KSKS ,

KLKL

IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)

Induced metric due to capture/recoil, stochastic fluctuations, Decoherence

Estimates of such D-particle foam effects in neutral mesons complicated

due to strong QCD effects present in such composite neutral particles

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

  • Neutral mesons [H , Θ ] 0no longer indistinguishable particles, initial entangled state:

Φ

KSKL

KSKL

KSKS ,

KLKL

KSKS ,

KLKL

IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)

If QCD effects, sub-structure in neutral mesons ignored, and D-foam acts

as if they were structureless particles, then for MQG ~ 1018 GeV (MAGIC)

the estimate for ω: | ω | ~ 10-4 |ζ|, for 1 > |ζ| > 10-2 (natural)

Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

  • Neutral mesons [H , Θ ] 0no longer indistinguishable particles, initial entangled state:

Φ

KSKL

KSKL

KSKS ,

KLKL

KSKS ,

KLKL

IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)

If QCD effects, sub-structure in neutral mesons ignored, and D-foam acts

as if they were structureless particles, then for MQG ~ 1018 GeV (MAGIC)

the estimate for ω: | ω | ~ 10-4 |ζ|, for 1 > |ζ| > 10-2 (natural)

Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

  • Neutral mesons [H , Θ ] 0no longer indistinguishable particles, initial entangled state:

Φ

KSKL

KSKL

KSKS ,

KLKL

KSKS ,

KLKL

IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)

If QCD effects, sub-structure in neutral mesons ignored, and D-foam acts

as if they were structureless particles, then for MQG ~ 1018 GeV (MAGIC)

the estimate for ω: | ω | ~ 10-4 |ζ|, for 1 > |ζ| > 10-2 (natural)

Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2)

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


D particle recoil the flavour problem

NB: direction [H , Θ ] 0

of recoil

dependence

LIV ….+

Stochastically

flct. Environment

Decoherence,

CPTV ill defined…

D-particle Recoil & the “Flavour” Problem

Not all particle speciesinteract the same way with D-particles

e.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 << ui >> = 0, but stochastically fluctuating << ui ui >>  0.

For slow recoiling heavy D-particles the resulting Hamiltonian, expressing interactions of neutrinos (or “flavoured” particles, including oscillating neutral mesons), reads:

N. E. MAVROMATOS


D particle recoil the flavour problem1

NB: direction [H , Θ ] 0

of recoil

dependence

LIV ….+

Stochastically

flct. Environment

Decoherence,

CPTV ill defined…

D-particle Recoil & the “Flavour” Problem

Not all particle speciesinteract the same way with D-particles

e.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 << ui >> = 0, but stochastically fluctuating << ui ui >>  0.

For slow recoiling heavy D-particles the resulting Hamiltonian, expressing interactions of neutrinos (or “flavoured” particles, including oscillating neutral mesons), reads:

N. E. MAVROMATOS


D particle recoil and entangled meson states
D-particle recoil and entangled Meson States [H , Θ ] 0

  • Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

N. E. MAVROMATOS


D particle recoil and entangled meson states1
D-particle recoil and entangled Meson States [H , Θ ] 0

  • Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

N. E. MAVROMATOS


D particle recoil and entangled meson states2
D-particle recoil and entangled Meson States [H , Θ ] 0

  • Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

N. E. MAVROMATOS


D particle recoil and entangled meson states3
D-particle recoil and entangled Meson States [H , Θ ] 0

  • Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

N. E. MAVROMATOS


D particle recoil and entangled meson states4
D-particle recoil and entangled Meson States [H , Θ ] 0

  • Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

the dressed state is obtained by

Similarly for

N. E. MAVROMATOS


D particle recoil and entangled meson states5
D-particle recoil and entangled Meson States [H , Θ ] 0

  • Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

the dressed state is obtained by

Similarly for

N. E. MAVROMATOS


D particle recoil and entangled meson states6
D-particle recoil and entangled Meson States [H , Θ ] 0

  • Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

the dressed state is obtained by

Similarly for

N. E. MAVROMATOS


D particle recoil and entangled meson states7
D-particle recoil and entangled Meson States [H , Θ ] 0

  • Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

the dressed state is obtained by

Similarly for

N. E. MAVROMATOS


D particle recoil and entangled meson states8
D-particle recoil and entangled Meson States [H , Θ ] 0

  • Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

the dressed state is obtained by

Similarly for

Prediction of -like effects in entangled states ….( Bernabeu, NM, Papavassiliou)

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Effect as discriminant of space time foam models
ω-effect as discriminant of space-time foam models [H , Θ ] 0

Bernabeu, NM, Sarben Sarkar

  • ω-effectnot generic,depends ondetailsof foam

    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 symmetry, flavour non conservationnon-trivialω-effect

    (II) Quantum Gravity Foam as “thermal Bath’’ (Garay)

    noω-effect

Bath frequency

“atom’’ (matter) frequency

N. E. MAVROMATOS


Effect as discriminant of space time foam models1
ω-effect as discriminant of space-time foam models [H , Θ ] 0

Bernabeu, NM, Sarben Sarkar

  • ω-effectnot generic,depends ondetailsof foam

    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 symmetry, flavour non conservationnon-trivialω-effect

    (II) Quantum Gravity Foam as “thermal Bath’’ (Garay)

    noω-effect

Bath frequency

“atom’’ (matter) frequency

N. E. MAVROMATOS


Effect as discriminant of space time foam models2
ω-effect as discriminant of space-time foam models [H , Θ ] 0

Bernabeu, NM, Sarben Sarkar

  • ω-effectnot generic,depends ondetailsof foam

    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 symmetry, flavour non conservationnon-trivialω-effect

    (II) Quantum Gravity Foam as “thermal Bath’’ (Garay)

    noω-effect

Bath frequency

“atom’’ (matter) frequency

N. E. MAVROMATOS


Effect as discriminant of space time foam models3
ω-effect as discriminant of space-time foam models [H , Θ ] 0

Bernabeu, NM, Sarben Sarkar

  • ω-effectnot generic,depends ondetailsof foam

    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 symmetry, flavour non conservationnon-trivialω-effect

    (II) Quantum Gravity Foam as “thermal Bath’’ (Garay)

    noω-effect

Bath frequency

“atom’’ (matter) frequency

N. E. MAVROMATOS



Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0


Cpt and decoherence in quantum gravity

N. E. MAVROMATOS [H , Θ ] 0



Qg decoherence neutrinos1
QG Decoherence & Neutrinos [H , Θ ] 0

  • Stochastic (quantum) metric fluctuations in Dirac or Majorana Hamiltonian for neutrinos affect oscillation probabilities by damping exponential factors – characteristic of decoherence

  • Quantum Gravitational MSW effect

  • Precise form of neutrino energy dependence of damping factors linked to specific model of foam

N. E. MAVROMATOS


Qg decoherence neutrinos2
QG Decoherence & Neutrinos [H , Θ ] 0

  • Stochastic (quantum) metric fluctuations in Dirac or Majorana Hamiltonian for neutrinos affect oscillation probabilities by damping exponential factors – characteristic of decoherence

  • Quantum Gravitational MSW effect

  • Precise form of neutrino energy dependence of damping factors linked to specific model of foam

N. E. MAVROMATOS


Qg decoherence neutrinos3
QG Decoherence & Neutrinos [H , Θ ] 0

  • Stochastic (quantum) metric fluctuations in Dirac or Majorana Hamiltonian for neutrinos affect oscillation probabilities by damping exponential factors – characteristic of decoherence

  • Quantum Gravitational MSW effect

  • Precise form of neutrino energy dependence of damping factors linked to specific model of foam

N. E. MAVROMATOS


Stochastic qg metric fluctuations
Stochastic QG metric fluctuations [H , Θ ] 0

Consider Dirac or Majorana (two-flavour) Hamiltonian with mixing , in such a metric background, with equation of motion:

Oscillation

Probability

Flavour states

Mass eigenstates

N. E. MAVROMATOS


Stochastic qg metric fluctuations1
Stochastic QG metric fluctuations [H , Θ ] 0

Oscillation

Probability

Two kinds of foam examined:

(i) Gaussian distributions

NM, Sarkar , Alexandre,

Farakos, Pasipoularides

(ii) Cauchy-Lorentz

In D-particle foam model, hoi n= ui involves recoil velocity distribution of D-particle populations .

NB: damping suppressed by neutrino mass differences

N. E. MAVROMATOS


Stochastic qg metric fluctuations2
Stochastic QG metric fluctuations [H , Θ ] 0

Oscillation

Probability

Two kinds of foam examined:

(i) Gaussian distributions

(ii) Cauchy-Lorentz

In D-particle foam model, hoi n= ui involves recoil velocity distribution of D-particle populations .

NB: damping suppressed by neutrino mass differences

N. E. MAVROMATOS


Quantum gravitational msw effect
Quantum Gravitational MSW Effect [H , Θ ] 0

ncbh Black Hole density in foam

Neutrino density matrix evolution is of Lindblad decoherence type:

Barenboim, NM, Sarkar, Waldron-Lauda

N. E. MAVROMATOS


Quantum gravitational msw effect1
Quantum Gravitational MSW Effect [H , Θ ] 0

ncbh Black Hole density in foam

Neutrino density matrix evolution is of Lindblad decoherence type:

CPT Violating (time irreversible,

CP symmetric)

N. E. MAVROMATOS


Quantum gravitational msw effect2
Quantum Gravitational MSW Effect [H , Θ ] 0

OSCILLATION PROBABILITY:

Damping suppressed by neutrino-flavour MSW-coupling differences

N. E. MAVROMATOS


Quantum gravitational msw effect3
Quantum Gravitational MSW Effect [H , Θ ] 0

OSCILLATION PROBABILITY:

Damping suppressed by neutrino-flavour MSW-coupling differences

N. E. MAVROMATOS


Quantum gravitational msw effect4
Quantum Gravitational MSW Effect [H , Θ ] 0

OSCILLATION PROBABILITY:

Damping suppressed by neutrino-flavour MSW-coupling differences

N. E. MAVROMATOS


Quantum gravitational msw effect5
Quantum Gravitational MSW Effect [H , Θ ] 0

OSCILLATION PROBABILITY:

Damping suppressed by neutrino-flavour MSW-coupling differences

N. E. MAVROMATOS


Current experimental bounds
Current Experimental Bounds [H , Θ ] 0

Lindblad-type decoherence Damping:

Fogli, Lisi, Marrone, Montanino, Palazzo

t = L (Oscillation length, (c=1)

Including LSND & KamLand Data:

Best fits

Beyond Lindblad: stochastic metric

Fluctuations damping:

Barenboim, NM, Sarkar, Waldron-Lauda

N. E. MAVROMATOS


Current experimental bounds1
Current Experimental Bounds [H , Θ ] 0

Lindblad-type decoherence Damping:

Fogli, Lisi, Marrone, Montanino, Palazzo

t = L (Oscillation length, (c=1)

Including LSND & KamLand Data:

Best fits

Beyond Lindblad: stochastic metric

Fluctuations damping:

Barenboim, NM, Sarkar, Waldron-Lauda

SOME EXPONENTS

NON ZERO, NOT ALL…

N. E. MAVROMATOS


Current experimental bounds2
Current Experimental Bounds [H , Θ ] 0

Barenboim, NM, Sarkar, Waldron-Lauda

Including LSND & KamLand Data:

t = L (Oscillation length, (c=1)

Beyond Lindblad: stochastic metric

Fluctuations damping (Best Fits):

N. E. MAVROMATOS


Current experimental bounds3
Current Experimental Bounds [H , Θ ] 0

Including LSND & KamLand Data:

Barenboim, NM, Sarkar, Waldron-Lauda

Lindblad type Decoherence

Beyond Lindblad: stochastic metric

Fluctuations damping (Best Fits):

t = L (Oscillation length, (c=1)

Probably too

Large to be QG

Effect….

NB: Lindblad-type damping

Also induced by uncertainties

in energy of neutrino beams

LSND+ KamLand

Ohlsson, Jacobson

N. E. MAVROMATOS


Current experimental bounds4
Current Experimental Bounds [H , Θ ] 0

Including LSND & KamLand Data:

Barenboim, NM, Sarkar, Waldron-Lauda

Lindblad type Decoherence

Beyond Lindblad: stochastic metric

Fluctuations damping (Best Fits):

t = L (Oscillation length, (c=1)

Probably too

Large to be QG

Effect….

NB: Lindblad-type damping

Also induced by uncertainties

in energy of neutrino beams

LSND+ KamLand

Ohlsson, Jacobson

But in that case

all exponents must be non zero

Hence….still unresolved

N. E. MAVROMATOS


Cpt and decoherence in quantum gravity

Look into the future: Potential of J-PARC, CNGS [H , Θ ] 0

NM, Sakharov, Meregaglia, Rubbia, Sarkar

JPARC

CNGS

N. E. MAVROMATOS



Look into the future high energy neutrinos
Look into the future: High Energy Neutrinos [H , Θ ] 0

Morgan, Winstanley, Anchordoqui, Goldberg, Hooper, Subir Sarkar, Weiler, Halzen…

Much higher sensitivities from high energy neutrinos

AMANDA, ICE CUBE,

ASTROPHYSICAL/COSMOLOGICAL NEUTRINOS

(e.g. if neutrinos with energies close to 1020 eV from GRB

At redshifts z > 1 are observed …)

N. E. MAVROMATOS


Look into the future high energy neutrinos1
Look into the future: High Energy Neutrinos [H , Θ ] 0

Morgan, Winstanley, Anchordoqui, Goldberg, Hooper, Subir Sarkar, Weiler, Halzen…

Much higher sensitivities from high energy neutrinos

AMANDA, ICE CUBE,

ASTROPHYSICAL/COSMOLOGICAL NEUTRINOS

(e.g. if neutrinos with energies close to 1020 eV from GRB

At redshifts z > 1 are observed …)

Recently: Interesting scenarios of Lindblad decoherence with SOME damping exponents

having energy dependence E-4 proposed for reconciling LSND (anti-ν) & MINIBOONE

Farzan, Smirnov, Schwetz,

N. E. MAVROMATOS


Look into the future high energy neutrinos2
Look into the future: High Energy Neutrinos [H , Θ ] 0

Morgan, Winstanley, Anchordoqui, Goldberg, Hooper, Sarkar, Weiler, Halzen…

Much higher sensitivities from high energy neutrinos

AMANDA, ICE CUBE,

ASTROPHYSICAL/COSMOLOGICAL NEUTRINOS

(e.g. if neutrinos with energies close to 1020 eV from GRB

At redshifts z > 1 are observed …)

Global

Best Fit

Recently: Interesting scenarios of Lindblad decoherence with SOME damping exponents

having energy dependence E-4 proposed for reconciling LSND (anti-ν) & MINIBOONE

Farzan, Smirnov, Schwetz,

Microscopic QG models ?

N. E. MAVROMATOS


Look into the future high energy neutrinos3
Look into the future: High Energy Neutrinos [H , Θ ] 0

Morgan, Winstanley, Anchordoqui, Goldberg, Hooper, Sarkar, Weiler, Halzen…

Much higher sensitivities from high energy neutrinos

AMANDA, ICE CUBE,

ASTROPHYSICAL/COSMOLOGICAL NEUTRINOS

(e.g. if neutrinos with energies close to 1020 eV from GRB

At redshifts z > 1 are observed …)

Global

Best Fit

Recently: Interesting scenarios of Lindblad decoherence with SOME damping exponents

having energy dependence E-4 proposed for reconciling LSND (anti-ν) & MINIBOONE

Farzan, Smirnov, Schwetz,

e.g. in our stochastic fluctuating metric models

E-4 scaling is obtained in Gaussian model with σ2 ~ k-2

Microscopic QG models ?

N. E. MAVROMATOS


Qg decoherence lhc black holes
QG Decoherence & LHC Black Holes [H , Θ ] 0

  • In string theory or extra-dimensional models (in general) QG mass scale may not be Planck scale but much smaller : MQG << MPlanck

  • Theoretically MQG could be as low as a few TeV. In such a case, collision of energetic particles at LHC could produce microscopic Black Holes at LHC, which will evaporate quickly.

  • If there is decoherence in such models, then, can the above tests determine the magnitude of MQG beforehand?

  • Highly model dependent issue…

N. E. MAVROMATOS


Qg decoherence lhc black holes1
QG Decoherence & LHC Black Holes [H , Θ ] 0

  • Models of Decoherence:

    (i) Parameters = O(E2/MQG) (e.g. D-particle recoil LV foam )

    current bounds: Kaons MQG > 1019 GeV

    Photons MQG > 1018 GeV, Neutrinos MQG > 1026 GeV

    No low MQG mass scale allowed…

    (ii) Parameters = O((Δm2)2/E2MQG) (e.g. Adler’s model of decoherence, stochastic D-particle LI models…)

    Low MQG mass models (even TeV) allowed by current measurements of decoherence… compatible with LHC BH observations….

N. E. MAVROMATOS


Conclusions
CONCLUSIONS [H , Θ ] 0

  • We know very little about QG so experimental searches & tests of various theoretical models will definitely help in putting us on the right course …

  • (Intrinsic) CPT &/or Lorentz Violation & decoherence might characterise QG models…

  • There may be `smoking-gun’ experiments for intrinsic CPTV & QG Decoherence , unique in entangled states of mesons (ω-effect best signature, if present though…. However, not generic effect, depends on model of QG foam…)

  • The magnitude of such effects is highly model dependent, may not be far from sensitivity of immediate-future facilities.

  • QG Decoherence effects in neutrino oscillations yield damping signatures, but those are suppressed by (powers of) neutrino mass differences. Difficult to detect … Nevertheless future (high energy neutrinos) looks promising…

N. E. MAVROMATOS


Conclusions1
CONCLUSIONS [H , Θ ] 0

  • We know very little about QG so experimental searches & tests of various theoretical models will definitely help in putting us on the right course …

  • (Intrinsic) CPT &/or Lorentz Violation & decoherence might characterise QG models… Microscopic Time Irreversibility….

  • There may be `smoking-gun’ experiments for intrinsic CPTV & QG Decoherence , unique in entangled states of mesons (ω-effect best signature, if present though…. However, not generic effect, depends on model of QG foam…)

  • The magnitude of such effects is highly model dependent, may not be far from sensitivity of immediate-future facilities.

  • QG Decoherence effects in neutrino oscillations yield damping signatures, but those are suppressed by (powers of) neutrino mass differences. Difficult to detect … Nevertheless future (high energy neutrinos) looks promising…

N. E. MAVROMATOS


Conclusions2
CONCLUSIONS [H , Θ ] 0

  • We know very little about QG so experimental searches & tests of various theoretical models will definitely help in putting us on the right course …

  • (Intrinsic) CPT &/or Lorentz Violation & decoherence might characterise QG models… Microscopic Time Irreversibility….

  • There may be `smoking-gun’ experiments for intrinsic CPTV & QG Decoherence , unique in entangled states of mesons (ω-effect best signature, if present though…. However, not generic effect, depends on model of QG foam…)

  • The magnitude of such effects is highly model dependent, may not be far from sensitivity of immediate-future facilities.

  • QG Decoherence effects in neutrino oscillations yield damping signatures, but those are suppressed by (powers of) neutrino mass differences. Difficult to detect … Nevertheless future (high energy neutrinos) looks promising…

N. E. MAVROMATOS


Further questions
Further Questions… [H , Θ ] 0

N. E. MAVROMATOS


Further questions1
Further Questions… [H , Θ ] 0

N. E. MAVROMATOS