The computational power of time dilation in special relativity

Takeshi Chiba, Shunichiro Kinoshita

A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.

David Z. Albert, Rivka Galchen

Herbert Dingle

Michael R. Emmert‐Buck

Special relativity, general relativity, and de Broglie-Bohm (pilot wave) theory are explanations of fundamental aspects of nature. For the most part, special and general relativity concern observations at large scale, whereas pilot wave theory addresses atomic processes. A feature that is unique to relativity is time dilation, the slowing of time with; a) relative movement in an inertial reference frame, and b) the effect of a gravitational field. At present, time dilation remains a difficult notion to intuitively understand, although it can be derived from general principles and characterized by straightforward mathematics. Canonical pilot wave theory is less well known than relativity and does not address time dilation; however, the theory can be conceptually expanded to cover additional phenomena. Described here is an expanded pilot wave model proposing time dilation does not occur in nature, but rather the slowing of clocks or other objects is due to a mechanical change in atomic efficiency. In other words, atoms, structures composed of atoms, and emergent properties of objects operate more slowly with motion or gravity due to a functional decrease in the effect of pilot waves, but time always elapses at a constant rate for all observers. Idealized pilot wave and standing wave models are used to explain a mechanism for the invariant speed of light and apparent slowing of time due to motion or gravity.

V. G. Rousseau

Abstract The universality of time dilation is sometimes misunderstood, with claims that it applies exclusively to light clocks and not to mechanical clocks or other material objects, including biological entities. This leads to incorrect interpretations of experiments like the Hafele–Keating experiment, which actually confirm relativistic effects through the use of atomic clocks. To address this issue, we propose a thought experiment, inspired by Schrödinger’s cat, involving a ‘Sync-or-Die clock’, a device that combines a light clock and a mechanical stopwatch, with the life of Einstein’s cat, Tiger, depending on their synchronization. A straightforward analysis shows that both clocks experience time dilation equally, reinforcing the fact that time dilation is not limited to clocks based on light propagation but is a universal feature of Special Relativity.

Zhiyong Wang, Cai-Dong Xiong, Bing He