Accelerated Particle Detectors with Modified Dispersion Relations

TL;DR

This paper investigates how a pixelated spacetime with modified dispersion relations affects the response of an accelerating particle detector, revealing that the thermal nature of detection persists under certain Lorentz-violating conditions.

Contribution

It introduces a calculation of detector response in a discretized spacetime using modified dispersion relations from DSR and Hořava-Lifshitz gravity, exploring implications for quantum gravity models.

Findings

Detector response remains Planckian with superluminal dispersion

Lorentz violation influences the thermal properties of the detector response

Thermal response likely persists in more complete Lorentz-invariant theories

Abstract

There is increasing interest in discrete or "pixelated" spacetime models as a foundation for a satisfactory theory of quantum gravity. If spacetime possesses a cellular structure, there should be observable consequences: for example, the vacuum becomes a dispersive medium. Of obvious interest are the implications for the thermodynamic properties of quantum black holes. As a first step to investigating that topic, we present here a calculation of the response of a uniformly accelerating particle detector in the (modified) quantum vacuum of a background pixelated spacetime, which is well known to mimic some features of the Hawking effect. To investigate the detector response we use the standard DeWitt treatment, with a two-point function modified to incorporate the dispersion. We use dispersion relations taken from the so-called doubly special relativity (DSR) and Ho\v{r}ava-Lifshitz gravity. We find that the correction terms retain the Planckian nature of particle detection, but only for propagation faster than the speed of light, a possibility that arises in this treatment because the dispersion relations violate Lorentz invariance. A fully Lorentz-invariant theory requires additional features; however, we believe the thermal response will be preserved in the more elaborate treatment.