Observing ghost entanglement beyond scattering amplitudes in quantum electrodynamics

TL;DR

This paper challenges the traditional view that only transverse electromagnetic modes are real by demonstrating that scalar modes can be observed through entanglement with charges, impacting our understanding of quantum electrodynamics.

Contribution

It provides an experimental proposal to observe entanglement involving scalar modes, showing these modes are physically real and detectable, contrary to common assumptions.

Findings

Scalar modes can be entangled with charges

Scalar photons influence charge behavior

Limits on superpositions of large charges

Abstract

A fully local quantum account of the interactions experienced between charges requires us to use all the four modes of the electromagnetic vector potential, in the Lorenz gauge. However, it is frequently stated that only the two transverse modes of the vector potential are ``real" in that they contain photons that can actually be detected. The photons present in the other two modes, the scalar and the longitudinal, are considered unobservable, and are referred to as ``virtual particles" or ``ghosts". Here we argue that this view is erroneous and that even these modes can, in fact, be observed. We present an experiment which is designed to measure the entanglement generated between a charge and the scalar modes. This entanglement is a direct function of the number of photons present in the scalar field. Our conclusion therefore is that the scalar quantum variables are as ``real" as the transverse ones, where reality is defined by their ability to affect the charge. A striking consequence of this is that we cannot detect by local means a superposition of a charge bigger than that containing 137 electrons.