Interference in quantum field theory: detecting ghosts with phases

TL;DR

This paper explores how interference experiments can reveal gauge degrees of freedom, specifically ghost modes, in quantum field theory, challenging the notion that these modes are unphysical and highlighting their measurable nature.

Contribution

It demonstrates that detecting phases or entanglement in interference experiments makes ghost modes in gauge theories physically observable, linking locality, gauge invariance, and measurement.

Findings

Ghost modes are measurable via interference experiments.

Detecting phases reveals gauge degrees of freedom.

Implications for quantum gravity and non-classicality tests.

Abstract

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.