Universal quantum modifications to general relativistic time dilation in delocalised clocks

Abstract

The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all ``good'' quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures – a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

“…This result adds to the growing list of quantum reference frame dependent physical properties, such as entanglement [70,72,74], spin [73], classicality [72] or objectivity [79,80] of a subsystem, superpositions [70,72], certain quantum resources [78], measurements [70,76], causal relations [47,83], temporal locality [7,47], and even spacetime singularity resolution [77]. The temporal frame changes may also be employed to extend recent proposals for studying time dilation effects of quantum clocks [45,136,137] (see also [137][138][139][140]). Furthermore, it would be interesting to expand the temporal frame changes to cosmological perturbation theory to study the temporal frame dependence of power spectra [64,65].…”

Autonomous Ticking Clocks from Axiomatic Principles

“…One approach is to attempt to make relativistic versions of the axioms for ticking clocks presented in section 4, by stating how the observable statistics and invariant quantities in these axioms transform relativistically. Another method would be to employ the same approach used in [9] to construct a relativistic quantum stopwatch. In such a semi-classical approach, one would include in the ticking clock set-up an additional kinematic degree of freedom associated with the ticking clock's momentum and position.…”

“…An obvious choice would be to consider "Time variant asymmetric ticking clocks", namely those which do not satisfy condition 1) [eq. (9)]. An example of such a ticking clock channel with a classical register would be eqs.…”

“…To verify that 1) [eq. (9)] holds for all D, first note that tr To verify that eq. (10) in condition 2) holds for all D, one needs to verify that…”

“…In the literature, both devices are often simply referred to as "clocks", e.g. [1][2][3][4][5][6][7][8][9][10][11][12], yet it is worth introducing distinct names due to their different character. A stopwatch is a device which measures the elapsed time between two external events.…”