CPT and DECOHERENCE in QUANTUM GRAVITY

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

Violation (CPTV) : Violation (CPTV) : (i)(i) Lorentz violation (LV): Lorentz violation (LV):

microscopic & cosmologicalmicroscopic & cosmological

BrieflyBriefly

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

This talk This talk

Towards microscopic models from Towards microscopic models from (non-critical) (non-critical) strings &strings &

Order of magnitude estimates of expected Order of magnitude estimates of expected effects effects

This talkThis talk

TeV photon astrophysics LV testsTeV photon astrophysics LV tests

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

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

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


OUTLINE OUTLINE Theoretical motivation for CPT Theoretical motivation for CPT

Violation (CPTV) : Violation (CPTV) : (i)(i) Lorentz violation (LV): Lorentz violation (LV):

microscopic & cosmologicalmicroscopic & cosmological

BrieflyBriefly

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

This talk This talk

Towards microscopic models from Towards microscopic models from (non-critical) (non-critical) strings &strings &

Order of magnitude estimates of expected Order of magnitude estimates of expected effects effects

This talkThis talk

TeV photon astrophysics LV testsTeV photon astrophysics LV tests

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

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

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…


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 )

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…


CPT THEOREMCPT THEOREM



10-35 m

J.A. Wheeler

Space-time Foam


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


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%)


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










Global (Cosmological FRW solution)Global (Cosmological FRW solution)










Cosmological (global) deSitter horizon: Cosmological (global) deSitter horizon:

Global (Cosmological FRW solution)Global (Cosmological FRW solution)


Space-Time Foam & Intrinsic CPT ViolationSpace-Time Foam & Intrinsic CPT Violation


CPT symmetry without CPT invariance ? CPT symmetry without CPT invariance ?


Stochastic Light-Cone FluctuationsStochastic Light-Cone Fluctuations

CPT may also be violatedin such stochastic models


Caution on CPTV & Lorentz ViolationCaution 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 ViolationCaution on CPTV & Lorentz Violation





CAUTION: LV does not necessarily imply CPTV

e.g. Standard

Model Extension,

Non-commutative

Geometry field theories


STANDARD MODEL EXTENSIONSTANDARD MODEL EXTENSION


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)


STANDARD MODEL EXTENSIONSTANDARD MODEL EXTENSION


Lorentz Violation & Anti-HydrogenLorentz Violation & Anti-Hydrogen 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


Tests of Lorentz Violation in Neutral KaonsTests of Lorentz Violation in Neutral Kaons


EXPERIMENTAL BOUNDSEXPERIMENTAL BOUNDS


Neutral Mesons: K, B, (unique (?) 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)DETECTING CPT VIOLATION (CPTV)

Complex PhenomenologyNo single figure of merit

4


Order of Magnitude Estimates Order of Magnitude Estimates


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

(b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γγ : : Decoherence damping Decoherence damping exp (-D t),exp (-D t), D = D = γγ ((ΔΔmm22)/E)/E










Adler-Horwitz decoherent evolution modelAdler-Horwitz decoherent evolution model


D-particle Foam Models D-particle Foam Models

Bulk closed

string

ELLIS, NM, WESTMUCKETTELLIS, NM, WESTMUCKETT


D-particle Recoil & LIV modelsD-particle Recoil & LIV models

i

edLimiXXXXuV

Xiin

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i

edLimiXXXXuV

Xiin

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String World-sheetString World-sheet torn aparttorn apart non-conformal Process, Liouville stringnon-conformal Process, Liouville string



i

edLimiXXXXuV

Xiin

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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






Ellis, NMNanopoulos


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) : :



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

Decoherence damping Decoherence damping exp (-D t),exp (-D t), D = D = γγ ((ΔΔmm22)/E)/E

The parameters The parameters σσ and and γγ depend on microscopic model and are suppressed depend on microscopic model and are suppressed

by (powers of) the string scale Mby (powers of) the string scale MStringString


Complex Phenomenology of CPTVComplex Phenomenology of CPTV




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

CPT Operator ill defined (Wald), intrinsic violation, modified concept 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)






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


Multi-messenger observations of the CosmosMulti-messenger observations of the Cosmos

cosmicaccelerator

photons: Absorbed by dust & radiation field (CMB)

gammas ( z < 1 )

Us

neutrinos

neutrinos: Difficult to detect

⇒ Three “astronomies” possible...

protons E>1019 eV ( 10 Mpc )

protons E<1019 eV

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

DeNaurois 2008


VHE Experimental World TodayVHE Experimental World Today

STACEECACTUS

MILAGRO

TIBET ARRAYARGO-YBJ

PACT

GRAPES

TACTIC

MAGIC

HESSCANGAROO

TIBETMILAGRO

STACEE

TACTIC

Canary Islands

M. MARTINEZ


The MAGIC Collaboration The MAGIC Collaboration ((MMajor ajor AAtmospheric tmospheric GGamma-ray amma-ray IImagingmaging

CCherenkov Telescope )herenkov Telescope )

Observation ofFlares from AGNMk 501

Red-shift: z=0.034


The MAGIC ``Effect’’The MAGIC ``Effect’’


Possible InterpetationsPossible Interpetations

Delays of more energetic photons are a result of AGN source Physics (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….


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):


MAGIC Results (ECF Method):MAGIC Results (ECF Method):

LinearLinear QuadraticQuadratic

95% CL95% CL


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


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….

Ellis, NM, NanopoulosEllis, NM, Nanopoulos arXiv:0804.3566arXiv:0804.3566


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


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 + … + …

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










(perturbatively) modified EPR correlations) this talkthis talk Ultracold Neutrons Neutrinos (highest sensitivity) Light-Cone fluctuations (GRB,


QUANTUM GRAVITY QUANTUM GRAVITY DECOHERENCE & CPTVDECOHERENCE & CPTV

NEUTRAL MESON PHENOMENOLOGY


QG DECOHERENCE IN NEUTRAL KAONS: SINGLE STATESQG DECOHERENCE IN NEUTRAL KAONS: SINGLE STATES


Decoherence vs CPTV in QMDecoherence vs CPTV in QM


Neutral Kaon AsymmetriesNeutral Kaon Asymmetries



Effects of α, β, γ decoherence parameters


Decoherence vs QM effectsDecoherence vs QM effects


Indicative Bounds Indicative Bounds


Neutral Kaon Entangled StatesNeutral Kaon Entangled States

Complete Positivity Different parametrization of Decoherence matrix (Benatti-Floreanini)


Entangled States:Entangled States:CPT & EPR correlationsCPT & EPR correlations

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)


CPTV & EPR-correlations modificationCPTV & EPR-correlations modification


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….



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…..


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



CP parameter CPTV parameter (QM)


EquaL-Sign di-lepton charge asymmetry Δt dependenceEquaL-Sign di-lepton charge asymmetry Δt dependence

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

ALVAREZ, BERNABEU, NEBOT


ΔΔt observablet observableExpt.Expt.









CURRENT EXPERIMENTAL LIMITS


D-particle Foam & Entangled StatesD-particle Foam & Entangled States

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

ΦΦ KSKL KSKL


EPR Modifications & D-particle FoamEPR Modifications & D-particle Foam

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



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)



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 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


KSKL

Neutral mesons no longer indistinguishable particles, initial entangled state:




ΦΦ KSKL

KKSSKKSS , ,

KKLLKKLL

KKSSKKSS , ,

KKLLKKLL


KSKL



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…


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)


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






(I) D-foam:



no ω-effect



PRECISION T, CP & CPT TESTS PRECISION T, CP & CPT TESTS WITH CHARGED KAONSWITH CHARGED KAONS

QG DECOHERENCE & NEUTRINOSQG DECOHERENCE & NEUTRINOS


QG Decoherence & Neutrinos QG Decoherence & Neutrinos

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

Quantum Gravitational MSW effect Quantum Gravitational MSW effect

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


Stochastic QG metric fluctuationsStochastic QG metric fluctuations

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


Stochastic QG metric fluctuationsStochastic QG metric fluctuationsOscillation Oscillation ProbabilityProbability

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

NM, Sarkar , Alexandre, NM, Sarkar , Alexandre, Farakos, PasipoularidesFarakos, Pasipoularides


Stochastic QG metric fluctuationsStochastic QG metric fluctuationsOscillation Oscillation ProbabilityProbability

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


Quantum Gravitational MSW Effect Quantum Gravitational MSW Effect

ncbh Black Hole density in foam

Neutrino density matrix evolution is of Lindblad decoherence type: Neutrino density matrix evolution is of Lindblad decoherence type:

Barenboim, NM, Sarkar, Waldron-LaudaBarenboim, NM, Sarkar, Waldron-Lauda



ncbh Black Hole density in foam

Neutrino density matrix evolution is of Lindblad decoherence type: Neutrino density matrix evolution is of Lindblad decoherence type:

CPT Violating (time irreversible,CP symmetric)



OSCILLATION PROBABILITY: OSCILLATION PROBABILITY:

Damping suppressed by neutrino-flavour MSW-coupling differencesDamping suppressed by neutrino-flavour MSW-coupling differences


Current Experimental BoundsCurrent Experimental BoundsFogli, Lisi, Marrone, Montanino, PalazzoLindblad-type decoherence Damping:Lindblad-type decoherence Damping:

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

Including LSND & KamLand Data:


Beyond Lindblad: stochastic metricBeyond Lindblad: stochastic metricFluctuations damping: Fluctuations damping:

Best fits


Current Experimental BoundsCurrent Experimental BoundsFogli, Lisi, Marrone, Montanino, PalazzoLindblad-type decoherence Damping:Lindblad-type decoherence Damping:


Including LSND & KamLand Data:


Beyond Lindblad: stochastic metricBeyond Lindblad: stochastic metricFluctuations damping: Fluctuations damping:

Best fits

SOME EXPONENTS SOME EXPONENTS NON ZERO, NOT ALL…NON ZERO, NOT ALL…


Current Experimental BoundsCurrent Experimental Bounds


Including LSND & KamLand Data:Barenboim, NM, Sarkar, Waldron-LaudaBarenboim, NM, Sarkar, Waldron-Lauda

Beyond Lindblad: stochastic metricBeyond Lindblad: stochastic metricFluctuations damping (Best Fits):Fluctuations damping (Best Fits):




Including LSND & KamLand Data:Including LSND & KamLand Data: Barenboim, NM, Sarkar, Waldron-LaudaBarenboim, NM, Sarkar, Waldron-Lauda


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




Including LSND & KamLand Data:Including LSND & KamLand Data: Barenboim, NM, Sarkar, Waldron-LaudaBarenboim, NM, Sarkar, Waldron-Lauda


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


NM, Sakharov, Meregaglia, Rubbia, SarkarNM, Sakharov, Meregaglia, Rubbia, Sarkar

Look into the future: Potential of J-PARC, CNGS

JPARCJPARC

CNGS


Look into the future: Potential of J-PARC, CNGS


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 …)

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



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

Farzan, Smirnov, Schwetz,Farzan, Smirnov, Schwetz,

Morgan, Winstanley, Anchordoqui, Goldberg, Hooper, Subir Sarkar, Weiler, Halzen…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 GRBAt redshifts z > 1 are observed …)

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



Microscopic QG models ? Microscopic QG models ?

GlobalBest Fit



Much higher sensitivities from high energy neutrinos

AMANDA, ICE CUBE, ASTROPHYSICAL/COSMOLOGICAL NEUTRINOS(e.g. if neutrinos with energies close to 1020 eV from GRBAt redshifts z > 1 are observed …)

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



Microscopic QG models ? Microscopic QG models ?

GlobalBest Fit

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


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…


QG Decoherence & LHC Black HolesQG Decoherence & LHC Black Holes

Models of Decoherence: Models of Decoherence:

(i) (i) Parameters = O(EParameters = O(E22/M/MQGQG)) (e.g. D-particle recoil LV foam ) (e.g. D-particle recoil LV foam )

current bounds: Kaons Mcurrent bounds: Kaons MQG QG > 10> 1019 19 GeV GeV

Photons MPhotons MQG QG > 10> 1018 18 GeV, Neutrinos MGeV, Neutrinos MQGQG > 10 > 102626 GeV GeV

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….


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 …

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

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…




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





Further Questions…Further Questions…

CPT and DECOHERENCE in QUANTUM GRAVITY

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