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Time Symmetric Quantum Mechanics and Causal Classical Physics ?

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Abstract

A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual “near future” macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.

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Notes

  1. Group theoretical both subsystems have the structure of a sub algebra of the Lie algebras \(SU(n_{\mathrm {measured\, subsystem}})\) and \(SU(n_{\mathrm {wittnessing\, subsystem}})\). The combined system \(SU(n_{\mathrm {measured\, subsystem}}+n_{\mathrm {wittnessing\, subsystem}})\) contains among many other elements a U(1) allowing for a arbitrary relative phase between the subsystems which can be transferred to the measured subsystem.

  2. Such an emission and absorption were required in theories in which the photon had no separate reality  [29, 60, 61] A generalization is the “transactional” interpretation [53].

  3. The unity argument follows [61].

  4. No statement is necessary about the observed tiny CP or the related T violation. If attributed to p.e. a CP asymmetric baryon imbalance of vacuum  [33, 62, 63] it has nothing to do with a real time arrow or the CPT structure. The vacuum might evolve or switch on the considered asymmetry.

  5. The description with formally independent evolutions is redundant. It suffices to consider just the wave function \(\phi (t)\) and eliminate the complex conjugate using \(\phi ^*(t)=\phi (T-t)\) where T is the lifetime of the universe and the asterisk is the conjugate. The probability that a state \(\phi (t_1)\) goes to \(\phi (t_2)\) requires a congruence of a transition \(<\phi (t_1)| U(t_1,t_2) |\phi (t_2)>\) in the expanding universe and a transition \(<\phi (T-t_2)| U(T-t_2,T-t_1) |\phi (T-t_1)>\) in the contracting one. It provides a beautiful explanation of bilinear Born probabilities in quantum mechanics.

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Acknowledgements

We thank David Craig, Claus Kiefer and Wolfgang Schleich for help in pointing out relevant literature.

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    Fritz W. Bopp

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Bopp, F.W. Time Symmetric Quantum Mechanics and Causal Classical Physics ?. Found Phys 47, 490–504 (2017). https://doi.org/10.1007/s10701-017-0074-7

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