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Journal of Physics Conference Series

Time Dilation contra Hamiltonian Mechanics

Aloysius F. Kracklauer

Published Jun 1, 2019• 0 citations
Publisher

Abstract

It is observed that, the introduction of delayed electromagnetic interaction to account for the finite speed of "light" (actually all electromagnetic interaction) leads to different time variables where non relativistic mechanics has only one. By carefully identifying and taking these various times into account, solutions are found for certain conundrums, including in particular the twin of clock paradox. An important consequence of this analysis is that it leads to a direct generalization of mechanics including special relativistic effects.

DOI
10.1088/1742-6596/1251/1/012026

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It is observed that, the introduction of delayed electromagnetic interaction to account for the finite speed of "light" (actually all electromagnetic interaction) leads to different time variables where non relativistic mechanics has only one. By carefully identifying and taking these various times into account, solutions are found for certain conundrums, including in particular the twin of clock paradox. An important consequence of this analysis is that it leads to a direct generalization of mechanics including special relativistic effects.
The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show that (i) closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii) They can constitute a quantum version of the special-relativistic twin paradox. (iii) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.
The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show that (i) closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii) They can constitute a quantum version of the special-relativistic twin paradox. (iii) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.
One of the concepts of Relativity theory that challenges conventional intuition the most is time dilation and length contraction. Usual approaches for describing relativistic effects in quantum systems merely postulate the consequences of these effects as physical constraints. Here, we propose to rebuild Special Relativity from quantum mechanical considerations. This is done by dropping one of its fundamental postulates: the universality of the speed of light. Lorentz transformations are obtained by a quantum mechanism. We use the fact that quantum states depend on the Galilean reference frame where they are defined. In other words, quantum states outside an observer's Galilean reference frame are distorted. Then, we show in a theorem the existence of time-dependent observables that are sensible to this distortion in such a way that their expectation value is a Lorentz-covariant function of time. We then postulate this mechanism as the source of the phenomena of Special Relativity. As a corollary of the main theorem, we show the existence of a Lorentz covariant momentum and mass operators which yield the relativistic momentum and mass. In this theory, the fundamental limit of the speed of light imposes a transparency condition for faster-than-light particles: they are allowed but they are not observable. The transparency effect could explain dark matter in a more general theory following this quantum formalism.
Abstract In the twin paradox of special relativity, an observer that travels along an accelerated trajectory at a high velocity will experience a smaller amount of elapsed time than an observer that remains at rest. This illustrates the fact that time is relative unlike the situation in classical physics where time is absolute. In a recent paper, Bushev et al (2016 New J. Phys. 18 093050 ) showed that the twin paradox can also be demonstrated using a single electron that functions as a quantum-mechanical clock. The wave function of the electron can travel along two different paths simultaneously, which allows a measurement of the difference in proper times along the two trajectories using a single particle. Quantum interference effects show that time cannot be thought of as a classical parameter even when associated with a single clock or observer.
We propose a novel framework for understanding quantum entanglement as a phenomenon fundamentally dependent on the proper-time histories of entangled particles. Drawing an analogy to the classical twin paradox of special relativity, we hypothesize that entanglement persists only when particle worldlines remain synchronized in their accumulated proper time. When differential aging occurs due to relative velocity or gravitational time dilation, quantum correlations degrade in a predictable, oscillatory manner. This “Entangled Twin Paradox” makes testable predictions that distinguish it from standard quantum mechanics, which treats entanglement as independent of relativistic effects.