Two-slit diffraction with highly charged particles: Niels Bohr's consistency argument that the electromagnetic field must be quantized

TL;DR

This paper examines Bohr's argument that the electromagnetic field must be quantized based on a two-slit experiment with charged particles, contrasting it with the non-quantization of gravity, and discusses implications for quantum mechanics.

Contribution

It provides a detailed analysis of Bohr's consistency argument for electromagnetic field quantization using a two-slit experiment with highly charged particles.

Findings

Electromagnetic radiation carries phase information, implying quantization.

Gravitational field measurement does not necessitate quantization.

Interference patterns are suppressed when Coulomb or gravitational fields are measured.

Abstract

We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles that argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances; under these conditions the interference pattern must be suppressed. The key is that as the particle's trajectory is bent in diffraction by the slits it must radiate and the radiation must carry away phase information. Thus the radiation field must be a quantized dynamical degree of freedom. On the other hand, if one similarly tries to determine the path of a massive particle through an inferometer by measuring the Newtonian gravitational potential the particle produces, the interference pattern would have to be finer than the Planck length and thus undiscernable. Unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized.