Decoherence of spatial superpositions along stationary worldlines

TL;DR

This paper studies how a particle's spatial superposition decoheres when moving along stationary paths in Minkowski space, considering internal and external degrees of freedom and deriving a master equation for decoherence.

Contribution

It introduces a model combining internal and external degrees of freedom, deriving a master equation for decoherence along stationary worldlines, including effects of time dilation and field spectrum modifications.

Findings

Decoherence rates depend on the particle's trajectory and motion type.

Both internal field response and time dilation contribute to decoherence.

Decoherence exhibits an effectively thermal behavior for stationary trajectories.

Abstract

We analyze the decoherence of a particle's spatial superposition moving along a stationary worldline through the Minkowski vacuum. The particle is modeled via an internal degree of freedom that couples to a scalar field, and an external degree of freedom, i.e., its quantized center-of-mass motion around the stationary worldline. Assuming a separation of time scales between the particle's internal and external dynamics, we first obtain an effective red-shifted polarizability of the particle, characterizing the trajectory-dependent linear response of the internal oscillator to the field. We then derive a quantum Brownian motion master equation for the particle's center of mass, under the Born-Markov approximation, which describes its decoherence in the position basis, as well as, Hamiltonian modifications corresponding to a dispersive potential. The resulting decoherence has two components: (1) arising from a modified field spectrum observed by the particle; and (2) due to a differential time-dilation over the particle's extended spatial wavefunction. For stationary trajectories, both contributions take an effectively thermal form. We evaluate the decoherence rates for two specific cases of hyperbolic and uniform circular motion.