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

We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles which 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. However, 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 indiscernible. Unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized.