Are accelerated detectors sensitive to Planck scale changes?

Abstract

One of the foremost concerns in the analysis of quantum gravity is whether the locations of classical horizons are stable under a full quantum analysis. In principle, any classical description, when interpolated to the microscopic level, can become prone to fluctuations. The curious question in that case is if there indeed are such fluctuations at the Planck scale, do they have any significance for physics taking place at scales much away from the Planck scale? In this work, we address the question of small scales and address whether there are definitive signatures of Planck scale shifts in the horizon structure. In a recent work (arXiv:2107.03406), it was suggested that in a nested sequence of Rindler causal wedges, the vacua of preceding Rindler frames appear thermally populated to a shifted Rindler frame. The Bogoliubov analysis relies on the global notion of the quantum field theory and turns out to be insensitive to the local character of these horizon shifts. We investigate this system by means of the Unruh-DeWitt detector and see if this local probe of the quantum field theory is sensitive enough to the shift parameters to reveal any microscopic effects. For the case of infinite-time response, we recover the thermal spectrum, thus reaffirming that the infinite-time response probes the global properties of the field. On the other hand, the finite-time response turns out to be sensitive to the shift parameter in a peculiar way that any detector with energy gap $\Omega c/a \sim 1$ and is operational for timescale $T a/c \sim 1$ has a measurably different response for a macroscopic and microscopic shift of the horizon, giving us a direct probe to the tiniest separation between the Rindler wedges. Thus, this study provides an operational method to identify Planck scale effects that can be generalized to various other interesting gravitational settings.