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CPT and DECOHERENCE in QUANTUM GRAVITY N. E. Mavromatos King’s College London Physics Department DISCRETE 08 SYMPOSIUM ON PROSPECTS IN THE PHYSICS OF DISCRETE.

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Presentation on theme: "CPT and DECOHERENCE in QUANTUM GRAVITY N. E. Mavromatos King’s College London Physics Department DISCRETE 08 SYMPOSIUM ON PROSPECTS IN THE PHYSICS OF DISCRETE."— Presentation transcript:

1 CPT and DECOHERENCE in QUANTUM GRAVITY N. E. Mavromatos King’s College London Physics Department DISCRETE 08 SYMPOSIUM ON PROSPECTS IN THE PHYSICS OF DISCRETE SYMMETRIES IFIC – Valencia (Spain), December MRTN-CT

2 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 2 OUTLINE OUTLINE  Theoretical motivation for CPT Violation (CPTV) : (i) Lorentz violation (LV): microscopic & cosmological Briefly Briefly (ii) Quantum Gravity Foam (QGF) (Decoherence) This talk This talk  Towards microscopic models from (non-critical) strings & Order of magnitude estimates of expected effects Order of magnitude estimates of expected effects This talk 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) neutral mesons factories – entangled states: EPR correlations modified (ω- effect) Disentangling (i) from (ii) Disentangling (i) from (ii) ω-effect as discriminant of space-time foam models This talk This talk  Neutrino Tests of QG decoherence Damping factors in flavour Oscillation Probabilities – suppressed though by neutrino mass differences This talk This talk

3 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 3 OUTLINE OUTLINE  Theoretical motivation for CPT Violation (CPTV) : (i) Lorentz violation (LV): microscopic & cosmological Briefly Briefly (ii) Quantum Gravity Foam (QGF) (Decoherence) This talk This talk  Towards microscopic models from (non-critical) strings & Order of magnitude estimates of expected effects Order of magnitude estimates of expected effects This talk 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) neutral mesons factories – entangled states: EPR correlations modified (ω- effect) Disentangling (i) from (ii) Disentangling (i) from (ii) ω-effect as discriminant of space-time foam models This talk This talk  Neutrino Tests of QG decoherence Damping factors in flavour Oscillation Probabilities – suppressed though by neutrino mass differences This talk This talk 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…

4 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 4 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…

5 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 5 CPT THEOREM

6 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 6 CPT THEOREM

7 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 7 CPT THEOREM

8 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 8 CPT THEOREM

9 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 9 CPT THEOREM m J.A. Wheeler Space-time Foam

10 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 10

11 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 11 In general, in space-times with 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 issue 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

12 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 12 In general, in space-times with 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 issue 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

13 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 13 In general, in space-times with 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 issue 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

14 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 14 In general, in space-times with 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 issue 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

15 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 15 In general, in space-times with Horizons (e.g. De Sitter cosmology…)

16 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 16 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%)

17 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 17 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?

18 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 18 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?

19 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 19 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): Unstable, indicates expansion

20 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 20 DARK ENERGY& Cosmological CPTV?  KNOW VERY LITTLE ABOUT IT…  EMBARASSING SITUATION 74% OF THE UNIVERSE BUDGET CONSISTS OF UNKNOWN SUBSTANCE  Could be:  a Cosmological Constant  Quintessence (scalar field relaxing to minimum of its potential)  Something else…Extra dimensions, colliding brane worlds etc.  Certainly of Quantum Gravitational origin  If cosmological constant (de Sitter), then quantization of field theories not fully understood due to cosmic horizon CPT invariance? Global (Cosmological FRW solution)

21 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 21 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? Cosmological (global) deSitter horizon: Global (Cosmological FRW solution)

22 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 22 Space-Time Foam & Intrinsic CPT Violation

23 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 23 CPT symmetry without CPT invariance ?

24 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 24 CPT symmetry without CPT invariance ?

25 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 25 Stochastic Light-Cone Fluctuations CPT may also be violated in such stochastic models

26 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 26 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…)

27 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 27 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: LV does not necessarily imply CPTV e.g. Standard Model Extension, Non-commutative Geometry field theories

28 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 28 STANDARD MODEL EXTENSION

29 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 29 Non-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/ )

30 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 30 Non-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/ )

31 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 31 STANDARD MODEL EXTENSION

32 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 32 Lorentz Violation & Anti-Hydrogen  Trapped Molecules: NB: Sensitivity in b 3 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

33 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 33 Tests of Lorentz Violation in Neutral Kaons

34 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 34 EXPERIMENTAL BOUNDS

35 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 35  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) Complex Phenomenology No single figure of merit

36 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 36 Order of Magnitude Estimates

37 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 37

38 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 38 Order of Magnitude Estimates

39 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 39 Order of Magnitude Estimates

40 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 40 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

41 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 41 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E Adler-Horwitz decoherent evolution model

42 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 42 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

43 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 43 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

44 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 44 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

45 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 45 D-particle Foam Models Bulk closed string ELLIS, NM, WESTMUCKETT

46 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 46 D-particle Recoil & LIV models

47 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 47 D-particle Recoil & LIV models String World-sheettorn apart String World-sheet torn apart non-conformal Process, Liouville string

48 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 48 D-particle Recoil & LIV models

49 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 49 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) Ellis, NM Nanopoulos

50 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 50 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) Ellis, NM Nanopoulos

51 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 51 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) Ellis, NM Nanopoulos

52 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 52 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

53 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 53 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

54 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 54 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

55 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 55 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

56 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 56 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

57 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 57 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

58 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 58 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

59 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 59 Order of Magnitude Estimates (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E The parameters σ and γ depend on microscopic model and are suppressed by (powers of) the string scale M String

60 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 60 Complex Phenomenology of CPTV  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, 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)

61 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 61 Complex Phenomenology of CPTV  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, TeV AGN…)

62 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 62 Multi-messenger observations of the Cosmos cosmic accelerator photons: Absorbed by dust & radiation field (CMB) ‏ gammas ( z < 1 ) ‏ Us neutrinos neutrinos: Difficult to detect ⇒ Three “astronomies” possible... protons E>10 19 eV ( 10 Mpc ) ‏ protons E<10 19 eV protons/nuclei: Deviated by magnetic fields, Absorbed by radiation field (GZK) ‏ DeNaurois 2008

63 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 63 VHE Experimental World Today STACEE CACTUS MILAGRO TIBET ARRAY ARGO-YBJ PACT GRAPES TACTIC MAGIC HESS CANGAROO TIBET MILAGRO STACEE TACTIC Canary Islands M. MARTINEZ

64 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 64 The MAGIC Collaboration (Major Atmospheric Gamma-ray Imaging Cherenkov Telescope ) Observation of Flares from AGN Mk 501 Red-shift: z=0.034

65 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 65 The MAGIC ``Effect’’

66 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 66 Possible 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: : 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: ] (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….

67 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 67 Quantum-Gravity Induced Modified Dispersion for Photons Modified dispersion due to QG induced space-time (metric) distortions (c=1 units):

68 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 68 MAGIC Results (ECF Method): Linear Quadratic 95% CL

69 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 69 A Stringy Model of Space -Time Foam Open strings on D3-brane world represent electrically neutral 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 Ellis, NM, Nanopoulos Photons or electrically neutral probes feel the effects of D-particle foam Modified Dispersion for them….

70 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 70 A Stringy Model of Space -Time Foam Open strings on D3-brane world represent electrically neutral 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 Ellis, NM, Nanopoulos 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

71 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 71 A Stringy Model of Space -Time Foam Open strings on D3-brane world represent electrically neutral 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 Ellis, NM, Nanopoulos 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

72 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 72 Stringy Uncertainties & the Capture Process During Capture: During Capture: intermediate stretching String stretching between D-particle and D3-brane is N internal Created. It acquires N internal Oscillator Oscillator excitations & Grows in size & oscillates Grows in size & oscillates from Zero to a maximum length by incident photon absorbing incident photon p 0 : Energy p 0 : Minimise right-hand-size w.r.t. L. End of intermediate string on D3-brane Moves with speed of light in vacuo c=1 TIME DELAY(causality) Hence TIME DELAY (causality) during Capture: DELAY IS INDEPENDENT OF PHOTON POLARIZATION, HENCE NO BIREFRINGENCE NO BIREFRINGENCE…. Ellis, NM, NanopoulosarXiv: Ellis, NM, Nanopoulos arXiv:

73 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 73 Stringy 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 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034) For n* =O(1) & M s ~ GeV, consistently with Crab Nebula & other Astrophysical constraints on modified dispersion relations…… Effectively modified Dispersion relation for photons due to induced metric distortion G 0i ~ p 0

74 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 74 Stringy 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 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034) For n* =O(1) & M s ~ GeV, consistently with Crab Nebula & other Astrophysical constraints on modified dispersion relations…… Effectively modified Dispersion relation for photons due to induced metric distortion G 0i ~ p 0 COMPATIBLE WITH STRING UNCERTAINTY PRINCIPLES: Δt Δx ≥ α’, Δp Δx ≥ 1 + α’ (Δp ) 2 + … (α’ = Regge slope = Square of minimum string length scale)

75 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 75 Complex Phenomenology of CPTV  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…)  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 this talk EPR correlations) this talk Ultracold Neutrons Neutrinos (highest sensitivity) Light-Cone fluctuations (GRB, Gravity-Wave Interferometers, neutrino oscillations)

76 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 76 Complex Phenomenology of CPTV  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…)  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 this talk EPR correlations) this talk Ultracold Neutrons Neutrinos (highest sensitivity) Light-Cone fluctuations (GRB, Gravity-Wave Interferometers, neutrino oscillations)

77 QUANTUM GRAVITY DECOHERENCE & CPTV NEUTRAL MESON PHENOMENOLOGY

78 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 78 QG DECOHERENCE IN NEUTRAL KAONS: SINGLE STATES

79 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 79 Decoherence vs CPTV in QM

80 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 80 Neutral Kaon Asymmetries

81 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 81 Neutral Kaon Asymmetries

82 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 82 Neutral Kaon Asymmetries Effects of α, β, γ decoherence parameters

83 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 83 Decoherence vs QM effects

84 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 84 Indicative Bounds

85 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 85 Neutral Kaon Entangled States  Complete Positivity Different parametrization of Decoherence matrix (Benatti-Floreanini)

86 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 86 Neutral Kaon Entangled States  Complete Positivity Different parametrization of Decoherence matrix (Benatti-Floreanini)

87 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 87 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

88 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 88 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

89 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 89 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

90 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 90 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/ ): decoherence Lindblad operator propotional to Hamiltonian Decoherence damping exp(-D t), Decoherence Parameter estimate: D = (Δm 2 ) 2 /E 2 M P (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) : 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: (a) Gaussian D-particle recoil velocity distribution, spread σ : Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 Decoherence damping in oscillations among two-level systems : exp (-D t 2 ), D = σ 2 (Δm 2 ) 2 /E 2 (b) Cauchy-Lorentz D-particle recoil velocity distribution, parameter γ : Decoherence damping exp (-D t), D = γ(Δm 2 )/E Decoherence damping exp (-D t), D = γ (Δm 2 )/E

91 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 91 Complex Phenomenology of CPTV  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…)  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 this talk EPR correlations) this talk Ultracold Neutrons Neutrinos (highest sensitivity) Light-Cone fluctuations (GRB, Gravity-Wave Interferometers, neutrino oscillations)

92 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 92 Complex Phenomenology of CPTV  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…)  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 this talk EPR correlations) this talk Ultracold Neutrons Neutrinos (highest sensitivity) Light-Cone fluctuations (GRB, Gravity-Wave Interferometers, neutrino oscillations)

93 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 93 Entangled States:CPT & EPR correlations  Novel (genuine) two body effects:  If CPT not-well defined modification of EPR correlations (ω-effect) 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)

94 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 94

95 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 95

96 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 96 CPTV & EPR-correlations modification

97 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 97 CPTV & EPR-correlations modification

98 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 98 CPTV & EPR-correlations modification CPTV CPTV K L K L, ωK S K S 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….

99 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 99 CPTV & EPR-correlations modification K S K S 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…..

100 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 100 CPTV & EPR-correlations modification

101 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 101 CPTV & EPR-correlations modification

102 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 102

103 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 103

104 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 104

105 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 105 B-systems, ω-effect & demise of flavour-tagging  Kaon systems have increased sensitivity to ω-effects due to the decay channel π + π -. advantage of statistics  B-systems do not have such a “good’’ channel but have the advantage of statistics  Interesting limits of ω-effects there one decays at a given timeflavour-specific  Flavour tagging: Knowledge that one of the two-mesons in a meson factory decays at a given time through flavour-specific “channel’’ determineflavour same time 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 Not True if intrinsic CPTV – ω-effect present : Theoretical limitation (“demise’’) of flavour tagging Alvarez, Bernabeu NM, Nebot, Papavassiliou

106 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 106 B-systems, ω-effect & demise of flavour-tagging

107 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 107 B-systems, ω-effect & demise of flavour-tagging CP parameter CPTV parameter (QM)

108 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 108 EquaL-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

109 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 109 EquaL-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

110 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 110 EquaL-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

111 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 111

112 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 112 Δt observable Expt. Expt. Expt. Expt.

113 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 113 Δt observable Expt. Expt. Expt. Expt. CURRENT EXPERIMENTAL LIMITS

114 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 114

115 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 115

116 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 116 D-particle Foam & Entangled States  If CPT Operator well-defined as operator, even if CPT is broken in the Hamiltonian… (e.g. Lorentz violating models) Φ KSKLKSKL KSKLKSKL

117 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 117 EPR Modifications & D-particle Foam Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar  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 Sarkar Induced metric due to capture/recoil, stochastic fluctuations, Decoherence Φ KSKLKSKL KSKLKSKL IF CPT ILL-DEFINED (e.g. D-particle Foam) KSKLKSKL

118 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 118 EPR Modifications & D-particle Foam Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar  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 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 Φ KSKLKSKL KSKLKSKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL KSKLKSKL IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)

119 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 119 EPR Modifications & D-particle Foam Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar  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 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 Φ KSKLKSKL KSKLKSKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL KSKLKSKL IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam)

120 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 120 If QCD effects, sub-structure in neutral mesons ignored, and D-foam acts as if they were structureless particles, then for M QG ~ GeV (MAGIC) the estimate for ω: | ω | ~ |ζ|, for 1 > |ζ| > (natural) Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2) ΦKSKLKSKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam) KSKLKSKL  Neutral mesons no longer indistinguishable particles, initial entangled state :

121 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 121 If QCD effects, sub-structure in neutral mesons ignored, and D-foam acts as if they were structureless particles, then for M QG ~ GeV (MAGIC) the estimate for ω: | ω | ~ |ζ|, for 1 > |ζ| > (natural) Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2) ΦKSKLKSKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam) KSKLKSKL  Neutral mesons no longer indistinguishable particles, initial entangled state :

122 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 122 If QCD effects, sub-structure in neutral mesons ignored, and D-foam acts as if they were structureless particles, then for M QG ~ GeV (MAGIC) the estimate for ω: | ω | ~ |ζ|, for 1 > |ζ| > (natural) Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2) ΦKSKLKSKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL KSKS,KSKS,KLKLKLKLKSKS,KSKS,KLKLKLKL IF CPT ILL-DEFINED (e.g. flavour violating (FV) D-particle Foam) KSKLKSKL  Neutral mesons no longer indistinguishable particles, initial entangled state :

123 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 123

124 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 124 D-particle Recoil & the “Flavour” Problem Not allspecies same way with D-particles Not all particle species interact 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…. > = 0, >  0. In statistical populations of D-particles, one might have isotropic situations, with > = 0, but stochastically fluctuating >  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 dependence LIV ….+ Stochastically flct. Environment Decoherence, CPTV ill defined…

125 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 125 D-particle Recoil & the “Flavour” Problem Not allspecies same way with D-particles Not all particle species interact 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…. > = 0, >  0. In statistical populations of D-particles, one might have isotropic situations, with > = 0, but stochastically fluctuating >  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 dependence LIV ….+ Stochastically flct. Environment Decoherence, CPTV ill defined…

126 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 126 D-particle recoil and entangled Meson States  Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

127 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 127 D-particle recoil and entangled Meson States  Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

128 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 128 D-particle recoil and entangled Meson States  Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

129 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 129 D-particle recoil and entangled Meson States  Apply non-degenerate perturbation theory to construct “gravitationally dressed’’ states from

130 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 130 D-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

131 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 131 D-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

132 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 132 D-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

133 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 133 D-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

134 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 134 D-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 )

135 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 135

136 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 136

137 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 137

138 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 138 ω-effect as discriminant of space-time foam models not genericdetailsfoam  ω-effect not generic, depends on details of foam Initially dressed states depend on form of interaction Hamiltonian H I (non-degenerate) perturbation theory determine existence of ω-effects (I) D-foam: direction of k violates Lorentz symmetryflavour non conservation features: direction of k violates Lorentz symmetry, flavour non conservation non-trivial ω-effect (II) Quantum Gravity Foam as “thermal Bath’’ (Garay) no ω-effect Bernabeu, NM, Sarben Sarkar Bath frequency “atom’’ (matter) frequency

139 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 139 ω-effect as discriminant of space-time foam models not genericdetailsfoam  ω-effect not generic, depends on details of foam Initially dressed states depend on form of interaction Hamiltonian H I (non-degenerate) perturbation theory determine existence of ω-effects (I) D-foam: direction of k violates Lorentz symmetryflavour non conservation features: direction of k violates Lorentz symmetry, flavour non conservation non-trivial ω-effect (II) Quantum Gravity Foam as “thermal Bath’’ (Garay) no ω-effect Bernabeu, NM, Sarben Sarkar Bath frequency “atom’’ (matter) frequency

140 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 140 ω-effect as discriminant of space-time foam models not genericdetailsfoam  ω-effect not generic, depends on details of foam Initially dressed states depend on form of interaction Hamiltonian H I (non-degenerate) perturbation theory determine existence of ω-effects (I) D-foam: direction of k violates Lorentz symmetryflavour non conservation features: direction of k violates Lorentz symmetry, flavour non conservation non-trivial ω-effect (II) Quantum Gravity Foam as “thermal Bath’’ (Garay) no ω-effect Bernabeu, NM, Sarben Sarkar Bath frequency “atom’’ (matter) frequency

141 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 141 ω-effect as discriminant of space-time foam models not genericdetailsfoam  ω-effect not generic, depends on details of foam Initially dressed states depend on form of interaction Hamiltonian H I (non-degenerate) perturbation theory determine existence of ω-effects (I) D-foam: direction of k violates Lorentz symmetryflavour non conservation features: direction of k violates Lorentz symmetry, flavour non conservation non-trivial ω-effect (II) Quantum Gravity Foam as “thermal Bath’’ (Garay) no ω-effect Bernabeu, NM, Sarben Sarkar Bath frequency “atom’’ (matter) frequency

142 PRECISION T, CP & CPT TESTS WITH CHARGED KAONS

143 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 143

144 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 144

145 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 145

146 QG DECOHERENCE & NEUTRINOS

147 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 147 QG Decoherence & Neutrinos damping exponential factorsdecoherence  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 neutrino energy dependence model of foam  Precise form of neutrino energy dependence of damping factors linked to specific model of foam

148 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 148 QG Decoherence & Neutrinos damping exponential factorsdecoherence  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 neutrino energy dependence model of foam  Precise form of neutrino energy dependence of damping factors linked to specific model of foam

149 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 149 QG Decoherence & Neutrinos damping exponential factorsdecoherence  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 neutrino energy dependence model of foam  Precise form of neutrino energy dependence of damping factors linked to specific model of foam

150 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 150 Stochastic QG metric fluctuations Consider Dirac or Majorana (two-flavour) Hamiltonian with mixing, in such a metric background, with equation of motion: Flavour states Mass eigenstates OscillationProbability

151 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 151 Stochastic QG metric fluctuations OscillationProbability Two kinds of foam examined: (i) Gaussian distributions (ii) Cauchy-Lorentz In D-particle foam model, h oi n= u i involves recoil velocity distribution of D- particle populations In D-particle foam model, h oi n= u i involves recoil velocity distribution of D- particle populations. NB: damping suppressed by neutrino mass differences NM, Sarkar, Alexandre, Farakos, Pasipoularides

152 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 152 Stochastic QG metric fluctuations OscillationProbability Two kinds of foam examined: (i) Gaussian distributions (ii) Cauchy-Lorentz In D-particle foam model, h oi n= u i involves recoil velocity distribution of D- particle populations In D-particle foam model, h oi n= u i involves recoil velocity distribution of D- particle populations. NB: damping suppressed by neutrino mass differences

153 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 153 Quantum Gravitational MSW Effect n c bh Black Hole density in foam Neutrino density matrix evolution is of Lindblad decoherence type: Barenboim, NM, Sarkar, Waldron-Lauda

154 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 154 Quantum Gravitational MSW Effect n c bh Black Hole density in foam Neutrino density matrix evolution is of Lindblad decoherence type: CPT Violating (time irreversible, CP symmetric)

155 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 155 Quantum Gravitational MSW Effect OSCILLATION PROBABILITY: Damping suppressed by neutrino-flavour MSW-coupling differences

156 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 156 Quantum Gravitational MSW Effect OSCILLATION PROBABILITY: Damping suppressed by neutrino-flavour MSW-coupling differences

157 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 157 Quantum Gravitational MSW Effect OSCILLATION PROBABILITY: Damping suppressed by neutrino-flavour MSW-coupling differences

158 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 158 Quantum Gravitational MSW Effect OSCILLATION PROBABILITY: Damping suppressed by neutrino-flavour MSW-coupling differences

159 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 159 Current Experimental Bounds Fogli, Lisi, Marrone, Montanino, Palazzo Lindblad-type decoherence Damping: t = L (Oscillation length, (c=1) Including LSND & KamLand Data: Barenboim, NM, Sarkar, Waldron-Lauda Beyond Lindblad: stochastic metric Fluctuations damping: Best fits

160 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 160 Current Experimental Bounds Fogli, Lisi, Marrone, Montanino, Palazzo Lindblad-type decoherence Damping: t = L (Oscillation length, (c=1) Including LSND & KamLand Data: Barenboim, NM, Sarkar, Waldron-Lauda Beyond Lindblad: stochastic metric Fluctuations damping: Best fits SOME EXPONENTS NON ZERO, NOT ALL…

161 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 161 Current Experimental Bounds t = L (Oscillation length, (c=1) Including LSND & KamLand Data: Barenboim, NM, Sarkar, Waldron-Lauda Beyond Lindblad: stochastic metric Fluctuations damping (Best Fits):

162 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 162 Current Experimental Bounds t = L (Oscillation length, (c=1) Including LSND & KamLand Data: Barenboim, NM, Sarkar, Waldron-Lauda Beyond Lindblad: stochastic metric Fluctuations damping (Best Fits): Lindblad type Decoherence Probably too Large to be QG Effect…. NB: Lindblad-type damping Also induced by uncertainties in energy of neutrino beams LSND+ KamLand Ohlsson, Jacobson

163 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 163 Current Experimental Bounds t = L (Oscillation length, (c=1) Including LSND & KamLand Data: Barenboim, NM, Sarkar, Waldron-Lauda Beyond Lindblad: stochastic metric Fluctuations damping (Best Fits): Lindblad type Decoherence 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

164 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 164 NM, Sakharov, Meregaglia, Rubbia, Sarkar Look into the future: Potential of J-PARC, CNGS JPARC CNGS

165 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 165 Look into the future: Potential of J-PARC, CNGS

166 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 166 Look into the future: High Energy Neutrinos Much higher sensitivities from high energy neutrinos AMANDA, ICE CUBE, ASTROPHYSICAL/COSMOLOGICAL NEUTRINOS (e.g. if neutrinos with energies close to eV from GRB At redshifts z > 1 are observed …) Morgan, Winstanley, Anchordoqui, Goldberg, Hooper, Subir Sarkar, Weiler, Halzen…

167 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 167 Look into the future: High Energy Neutrinos Much higher sensitivities from high energy neutrinos AMANDA, ICE CUBE, ASTROPHYSICAL/COSMOLOGICAL NEUTRINOS (e.g. if neutrinos with energies close to eV from GRB At redshifts z > 1 are observed …) SOME 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, Morgan, Winstanley, Anchordoqui, Goldberg, Hooper, Subir Sarkar, Weiler, Halzen…

168 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 168 Look into the future: High Energy Neutrinos Much higher sensitivities from high energy neutrinos AMANDA, ICE CUBE, ASTROPHYSICAL/COSMOLOGICAL NEUTRINOS (e.g. if neutrinos with energies close to eV from GRB At redshifts z > 1 are observed …) Morgan, Winstanley, Anchordoqui, Goldberg, Hooper, Sarkar, Weiler, Halzen… SOME 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 ? Global Best Fit

169 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 169 Look into the future: High Energy Neutrinos Much higher sensitivities from high energy neutrinos AMANDA, ICE CUBE, ASTROPHYSICAL/COSMOLOGICAL NEUTRINOS (e.g. if neutrinos with energies close to eV from GRB At redshifts z > 1 are observed …) Morgan, Winstanley, Anchordoqui, Goldberg, Hooper, Sarkar, Weiler, Halzen… SOME 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 ? Global Best Fit e.g. in our stochastic fluctuating metric models E -4 scaling is obtained in Gaussian model with σ 2 ~ k -2

170 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 170 QG Decoherence & LHC Black Holes  In string theory or extra-dimensional models (in general) QG mass scale may not be Planck scale but much smaller : M QG << M Planck  Theoretically M QG 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 M QG beforehand?  Highly model dependent issue…

171 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 171 QG Decoherence & LHC Black Holes  Models of Decoherence: (i) Parameters = O(E 2 /M QG ) (e.g. D-particle recoil LV foam ) current bounds: Kaons M QG > GeV Photons M QG > GeV, Neutrinos M QG > GeV No low M QG mass scale allowed… No low M QG mass scale allowed… (ii) Parameters = O((Δm 2 ) 2 /E 2 M QG ) (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…. Low MQG mass models (even TeV) allowed by current measurements of decoherence… compatible with LHC BH observations….

172 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 172 CONCLUSIONS  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 mesonsω-effect best signature, if present though…. However, not generic effect, depends on model of QG foam…  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…

173 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 173 CONCLUSIONS  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 mesonsω-effect best signature, if present though…. However, not generic effect, depends on model of QG foam…  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…

174 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 174 CONCLUSIONS  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 mesonsω-effect best signature, if present though…. However, not generic effect, depends on model of QG foam…  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…

175 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 175 Further Questions…

176 DISCRETE 08, IFIC (Valencia), December 08 N. E. MAVROMATOS 176 Further Questions…


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