  We discuss the implications of the principle of locality for interference in
quantum field theory. As an example, we consider the interaction of two charges
via a mediating quantum field and the resulting interference pattern, in the
Lorenz gauge. Using the Heisenberg picture, we propose that detecting relative
phases or entanglement between two charges in an interference experiment is
equivalent to accessing empirically the gauge degrees of freedom associated
with the so-called ghost (scalar) modes of the field in the Lorenz gauge. These
results imply that ghost modes are measurable and hence physically relevant,
contrary to what is usually thought. They also raise interesting questions
about the relation between the principle of locality and the principle of
gauge-invariance. Our analysis applies also to linearised quantum gravity in
the harmonic gauge, and hence has implications for the recently proposed
entanglement-based witnesses of non-classicality in gravity.
