Mid- and far-field deviations from causality in spontaneous light emission by atomic Hydrogen

TL;DR

This paper examines the spacetime behavior of the electromagnetic field emitted by atomic hydrogen during the 2p-1s transition, revealing non-zero wave functions outside the lightcone due to electron position uncertainty.

Contribution

It provides a detailed analysis of causality deviations in spontaneous emission, highlighting the role of electron position uncertainty and characterizing the emitted field in different regions.

Findings

Glauber's wave function is nonzero outside the lightcone after emission begins.

Electron position uncertainty causes deviations from naive causality.

Analytical and numerical methods elucidate the emitted field in mid- and far-field regions.

Abstract

We investigate, in the case of the $2\mathrm{p}-1\mathrm{s}$ transition in atomic Hydrogen, the behaviour of the spontaneously emitted electromagnetic field in spacetime. We focus on Glauber's wave function for the emitted photon, a quantity which we find is nonzero outside the lightcone at all times after the start of the emission. We identify the uncertainty on the position of the decaying electron as a source of departure from causality in the naive sense of the term. We carry out a detailed study of the emitted electric field in the mid- and far-field regions, through analytical and numerical computations as well as asymptotic arguments.