On the spontaneous emission of electromagnetic radiation in the CSL model

TL;DR

This paper investigates the origin of unphysical terms in the photon emission rate predicted by the CSL model, showing these terms decay over time and are artifacts of perturbative approximations.

Contribution

It provides an exact solution to the electrodynamic equations in the CSL model and clarifies why certain unphysical terms vanish in the long-time limit.

Findings

Unphysical emission terms decay exponentially over time.

Exact solutions show the unphysical term approximates to 1 in first-order perturbation.

The unphysical term is linked to transient exponential decay.

Abstract

Spontaneous photon emission in the Continuous Spontaneous Localization (CSL) model is studied one more time. In the CSL model each particle interacts with a noise field that induces the collapse of its wave function. As a consequence of this interaction, when the particle is electrically charged, it radiates. As discussed in [1], the formula for the emission rate, to first perturbative order, contains two terms: One is proportional to the Fourier component of the noise field at the same frequency as that of the emitted photon and one is proportional to the zero Fourier component of the noise field. As discussed in previous works, this second term seems unphysical. In [1], it was shown that the unphysical term disappears when the noises is confined to a bounded region and the final particle's state is a wave packet. Here we investigate the origin of the unphysical term and why it vanishes according to the previous prescription. For this purpose, the electrodynamic part of the equation of motion is solved exactly while the part due to the noise is treated perturbatively. We show that the unphysical term is connected to exponentially decaying function of time which dies out in the large time limit, however, approximates to 1 in the first perturbative order in the electromagnetic field.