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We analyze Niels Bohr's proposed two-slit interference experiment with highlycharged particles that argues that the consistency of elementary quantummechanics requires that the electromagnetic field must be quantized. In theexperiment a particle's path through the slits is determined by measuring theCoulomb field that it produces at large distances; under these conditions theinterference pattern must be suppressed. The key is that as the particle'strajectory is bent in diffraction by the slits it must radiate and theradiation must carry away phase information. Thus the radiation field must be aquantized dynamical degree of freedom. On the other hand, if one similarlytries to determine the path of a massive particle through an inferometer bymeasuring the Newtonian gravitational potential the particle produces, theinterference pattern would have to be finer than the Planck length and thusundiscernable. Unlike for the electromagnetic field, Bohr's argument does notimply that the gravitational field must be quantized.

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