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arXiv:1905.02711 · Expositiones Mathematicae

Classical dynamics, arrow of time, and genesis of the Heisenberg commutation relations

Detlev Buchholz A, Klaus Fredenhagen

Published Jun 1, 2020• 7 citations
arXivHTMLPDF
DOI
10.1016/j.exmath.2020.06.002

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We derive a direct, non-linear relation between the internal phase time per radian , the macroscopically observable coordinate time , and the relative energy fluctuation . Through rigorous differentiation and integration of these phase relations, we demonstrate that for topologically synchronized systems, the product of energy and observable time constitutes a strict dynamic process invariant: . Moving beyond phenomenological interpretations, we deduce the classical Heisenberg uncertainty relation without invoking independent quantum postulates, showing it to be a special boundary limit governing a single elementary phase cycle () under critical fluctuation. Finally, we bridge the gap between microscopic quantum reversibility and the macroscopic thermodynamic arrow of time by analyzing the dynamics of synchronization breakdown and phase slippage ().
In order to describe the quantum electrodynamic measurement process in a relativistic observer-participant manner, an operator symmetry of "microscopic observer-participation" called Measurement Color (MC) is incorporated into the field theoretic structure of Quantum Electrodynamics (QED) in the Heisenberg Picture. It is found that the resultant Measurement Color Quantum Electrodynamics (MC-QED) contains a microscopic quantum electrodynamic arrow of time that emerges dynamically, independent of any thermodynamic or cosmological assumptions. This occurs because the photon has a negative time parity in MC-QED. This causes a spontaneous breaking of the T and CPT symmetry to be generated by the physical requirement that a stable vacuum state exists in the MC-QED formalimm. This dynamically selects operator solutions containing a causal, retarded, quantum electrodynamic arrow of time due in the Heisenberg operator equations of motion. In support of the validity of this idea we show that a classic nonlinear optics experiment in the scientific literature, which involves a Michelson interferometer using combinations of ordinary mirrors and phase conjugate mirrors, contains experimental results which support the idea that the photon has a negative parity under Wigner time reversal and thus carries the arrow of time in the universe.