  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.
