Indefinite temporal order without gravity

TL;DR

This paper explores how quantum effects combined with gravity can lead to events with indefinite temporal order, and demonstrates that similar violations can occur without gravity, highlighting ambiguities in testing such phenomena.

Contribution

It constructs a non-gravitational scenario showing violation of temporal Bell inequalities, revealing ambiguities in their interpretation as tests of indefinite temporal order.

Findings

Violations of temporal Bell inequalities can occur without gravity.

Ambiguity exists in using these inequalities as definitive tests.

Quantum-gravity effects can produce indefinite temporal order phenomena.

Abstract

According to the general theory of relativity, time can flow at different rates depending on the configuration of massive objects, affecting the temporal order of events. Recent research has shown that, combined with quantum theory, this gravitational effect can result in events with an indefinite temporal order, which can be tested through the violation of Bell-type inequalities. According to Einstein, we shall assume physical equivalence of a uniform gravitational field and a corresponding acceleration of a reference system. Here we construct a non-gravitational scenario where accelerating particles interacting with optical cavities result in a violation of the temporal Bell inequalities analogous to the gravitational case. However, we find that the inequalities can also be violated by time-like events, exposing an ambiguity in their use as a theory-independent test of indefinite temporal order.