Particle detectors, geodesic motion, and the equivalence principle

TL;DR

Quantum particle detectors cannot reliably distinguish inertial from non-inertial motion in general spacetimes, challenging their use as probes of spacetime structure and raising questions about the formulation of the equivalence principle.

Contribution

The paper demonstrates the limitations of particle detectors in detecting spacetime features and clarifies the conditions under which the response function vanishes, impacting the understanding of the equivalence principle.

Findings

Detectors fail to distinguish inertial and non-inertial motion in general spacetimes.

In static asymptotically flat spacetimes, all rotating detectors are excited in the static vacuum.

The static vacuum appears associated with a non-rotating frame in certain cases.

Abstract

It is shown that quantum particle detectors are not reliable probes of spacetime structure. In particular, they fail to distinguish between inertial and non-inertial motion in a general spacetime. To prove this, we consider detectors undergoing circular motion in an arbitrary static spherically symmetric spacetime, and give a necessary and sufficient condition for the response function to vanish when the field is in the static vacuum state. By examining two particular cases, we show that there is no relation, in general, between the vanishing of the response function and the fact that the detector motion is, or is not, geodesic. In static asymptotically flat spacetimes, however, all rotating detectors are excited in the static vacuum. Thus, in this particular case the static vacuum appears to be associated with a non-rotating frame. The implications of these results for the equivalence principle are considered. In particular, we discuss how to properly formulate the principle for particle detectors, and show that it is satisfied.