Entropy & matter T violation anomaly Quantum theory of time Sources of T violation Experimental test The quantum theory of time: from formalism to experimental test tree wind Toshio Croucher Joan Vaccaro leaves on Centre for Quantum Dynamics ground on Griffith University this side Brisbane Australia of tree 1 / 20 Entropy & matter T violation anomaly Quantum theory of time Sources of T violation Experimental test Vaccaro, Proc. R. Soc. A 472, 20150670 (2016) 56,000 9,000 2 / 20 Entropy & & matter matter T violation anomaly Quantum theory of time Sources of T violation Experimental test Entropy & matter anomalies Recall Loschmidt’s paradox: Evolving “upwards” in time: − entropy increases. t y Consider a gas with N, T, P, & V known, x in a container that has a leak. Evolving “downwards” in time: − entropy increases. Symmetry is due to time symmetric dynamical laws. We take entropy increase as evidence of the “direction of time evolution” or “direction of time” for short. 3 / 20 Entropy & & matter matter T violation anomaly Quantum theory of time Sources of T violation Experimental test Empirical evidence: all space and time has a consistent direction of entropy increase: Distant galaxy effects direction direction of of entropy time increase evolution Earth causes 4 / 20 Entropy & & matter matter T violation anomaly Quantum theory of time Sources of T violation Experimental test From Loschmidt’s paradox, expect symmetry in time: high entropy? low entropy high entropy − t time evolution? 0 time evolution t Similarly, expect symmetry in matter and antimatter: antimatter? radiation matter − t 0 t There is no external reference for the direction of time. So the universe must be time symmetric overall. These are the entropy and matter-antimatter anomalies. Proposed resolutions: entropy 2004 Carrol & Chen hep-th/0410270 high low high 2011 Vaccaro Found Phys 41, 1596 − t 0 t 2014 Barbour, Koslowski & Mercati antimatter radiation matter Phys Rev Lett 113 181101 (2014) − t 0 t 2018 Boyle, Finn & Turok Phys Rev Lett 121 251301 (2018) 5 / 20 Entropy & matter TT violation violation anomalyanomaly Quantum theory of time Sources of T violation Experimental test T violation anomaly Recall the discrete symmetries: z x y t t C P 0 0 T − 0 ̅+ � �0 x y z � ̅ P parity inversion C charge conjugation x ↔ −x T time reversal y ↔ −y particle ↔ antiparticle z ↔ −z t ↔ −t History: P violation Lee & Yang 1956 β− decay in 60Co P CP violation Cronin & Fitch 1964 Wu’s experiment 0 K decay ( + 0) + +− →≠ CP= 1 −0 0+ CP=−1 CP=+ 1 T violation BarBar, SLAC 2012 0 B decay T 0 0 � → − ≠ − → � 6 / 20 Entropy & matter TT violation violation anomalyanomaly Quantum theory of time Sources of T violation Experimental test T violation in B0 system weak interaction + Experiment: BarBar Collaboration, SLAC, Stanford University + − J. P. Lees et al., Phys. Rev. Lett. 109, 211801 (2012). Detailed description: 0 0 Bernabeu et al, JETP Lett. 2012, 64 (2012). decay decay� + − Empirical − Hamiltonian 0 0 � 0 * time 0 reversal� operation T violation: different ∆τ Time-reversed Hamiltonian� 0 *0 � 0 e e −1 −�Δ +e��� Δ 0 0 0 �Δ 7 / 20 � � − � − Entropy & matter TT violation violation anomalyanomaly Quantum theory of time Sources of T violation Experimental test T violation implies 2 Hamiltonians and 2 dynamics – one for each direction of time. Physical theory needs to account for both Hamiltonians. Conventional physical theories have a single version of the Hamiltonian and the time evolution it describes (into the future, by default). Phil. Tras. A 376, 20170316 (2018). This is the T violation anomaly Proposed resolution: The quantum theory of time arXiv: 1605.01965 Invited Chapter in book: S. Wuppuluri, G. Ghirardi Eds, "Space, Time and the Limits of Human Understanding" (Springer International, 2016) 185-201 8 / 20 Entropy & matter T violation anomaly QuantumQuantum theorytheory ofof timetime Sources of T violation Experimental test Quantum theory of time worldline of particle Space-time background itself: - space and time are essentially interconvertible = 2 = 2 2 2 2 2 − 2 − 2 − 2 Things on space-time background: − − − Dynamics (relativistic, quantum, classical): - defines translations over time but not space. treat as a Conservation laws (energy, momentum, lepton #,...): phenomenological - apply over time but not over space. e.g. Quantum Mechanics: wave function over space wave function over time ( ) ( ) why not this? mass not conserved 9 / 20 Entropy & matter T violation anomaly QuantumQuantum theorytheory ofof timetime Sources of T violation Experimental test The idea is this: fundamental level phenomenological ( , ) ( , ) phenomenological details no dynamics dynamics emerge Need to look at phenomenology of generators of translations in space and time: • the Hamiltonian generates translations in time C,P,T discrete e e symmetries are −1 � �� � t violated by the • + − the momentum operator generates translations in space Hamiltonian only! e e x +� −� 10 / 20 Entropy & matter T violation anomaly QuantumQuantum theorytheory ofof timetime Sources of T violation Experimental test Four principles Vaccaro, Phil. Trans. Roy. Soc. A 376, 20170316 (2018). 1. States have same construction in time and space Retain the symmetry of the space time background 2. Time evolution is directional , e “forwards” , e−� “backwards” � � ≡ −1 � � ≡ ��� time evolution physical dynamics ≡ causality “backwards” e e “forwards” � −� e e −mathematical� inverses� ≡ rewind 11 / 20 Entropy & matter T violation anomaly QuantumQuantum theorytheory ofof timetime Sources of T violation Experimental test 3. Fundamental resolution limit E.g. Planck scale, or other limit (the actual limit is not important) 4. A state is represented by a quantum path with step sizes below resolutionT symmetry limit = Space: Time: T symmetry = = + = � � � 2 −� e ee e� � � � −� t e e = +� −� | � � x + − | ⟩ ⟩ + random paths = random paths � 2 −� step size = e 2 no dynamics step size − 2 4 mass not ≈conserved,∫ no X dynamics 12 / 20 Entropy & matter T violation anomaly QuantumQuantum theorytheory ofof timetime Sources of T violation Experimental test T violation , = Get interference between different paths to the same point in time. � � � | = + = ⟩ 2 � 2 −�T violation � � = � ≠ � ⋯ ⋯ ⋯ ⋯ e e − | | � −� −⟩ destructive+⟩ interference Schrodinger equations | + ≈ −� + 〉 | dynamics destructive interference − ≈ −� − 〉 13 / 20 Entropy & matter T violation anomaly Quantum theory of time SourcesSources ofof T violation Experimental test Sources of T violation Croucher & Vaccaro, in preparation (2019) weak interaction , , Mesons 0 0 Particle0 and0 antiparticle0 0 mixing: = � 0 � � 1 * Many particles 0 0 � 0 group contraction decay decay� T � harmonic oscillator: 0 *0 Inonu & Wigner P Natl Acad Sci USA 39 510 (1953) ̂− � Arecchi et al Phys Rev A 6 2211 (1972) → �† = 0 ̂+ ( ) → � 1 = , = Branco, Silva & Lavoura CP Violation0 (1999) � ̂ � ̂ � � ̂ ̂ ̂ = + + = † + + ∗ † � � � � � † ∗ † , = � ̂ ̂ � � � � , � � ̂ � � ≫ ≈ � 14 / 20 � ̂ Entropy & matter T violation anomaly Quantum theory of time SourcesSources ofof T violation Experimental test Neutrinos Nunokawa Prog. Part. Nucl. Phys. 60 338 (2008) In rotated Flavour basis: Suspected of violating CP and T symmetries 2D subspace is just like mesons Flavour mixing: ( ) = * = 1 , 1 � * � ( ) � � ≫1 ≈ � = 1 Higgs-like scalar field Branco et� al., Phys Rep., 516, 1 (2012) Spontaneous symmetry breaking: CP & T violation arises in 2 or more doublet models Explicit symmetry breaking in scalar field: = + + + + 2 2 2 2 � zero � = � �+ + ℋ momentum� ∇ � , † ∗ † mode = + + �0 �0�0 �0 �0 † † �0 �0 ≫ � ∗ ≈ 15 / 20 �0 �0�0 �0 �0 Entropy & matter T violation anomaly Quantum theory of time Sources of T violation ExperimentalExperimental testtest Experimental test Vaccaro, in preparation (2019) Spatial distribution – T symmetry case e + e � � = + + e 2 2 = lim − � 2 2 2 − � � � � 2 →∞ + + correlated fluctuations 2 2 2 � �( � ) e 2 2 2 2 = e 2 2e 2 2e 2 2 � +� +� � � � − − − − 2 2 2 2 e + e e + e e + e � � � � � � − − − 2 2 2 independent fluctuations , but no interactions 16 / 20 Entropy & matter T violation anomaly Quantum theory of time Sources of T violation ExperimentalExperimental testtest 1 1 1 1 + + = + + + + + 3 3 3 3 2 2 2 2 2 2 2 � � � � � � � − � � − � � − � ( ) ( ) ( ) ( ) ( ) ( 1 1 1 1 1 1 e � + ⋯ + e � + ⋯ e � −� + e � −� e � −� + e � − 3 − 3 3 − 3 3 − 3 2 2 2 allows interactions allows independent fluctuations One last thing…. The value of needs to adjust locally to maintain minimum uncertainty in independent fluctuations, energy, thus with interactions + + + + 17 / 20 � � � ↦ � � � Entropy & matter T violation anomaly Quantum theory of time Sources of T violation ExperimentalExperimental testtest ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 e � +⋯ + e � +⋯ e � −� + e � −� e � −� + 3 − 3 3 − 3 3 2 2 2 T violation case independent fluctuations, with interactions and local effects 18 / 20 Entropy & matter T violation anomaly Quantum theory of time Sources of T violation ExperimentalExperimental testtest Experimental test Local variation in T violation local variation in clock time = 2 Antineutrinos = , 1 � � 1+ is the ∝ratio ofΛ the2 strengths of the T violation due to the reactor neutrinos andΛ the background processes at 1 m density 1 generated power