# Electromagnetism as Quantum Physics

## TL;DR

This paper explores whether Maxwell's equations can be interpreted as describing a photon's quantum wave function, but finds fundamental issues with this interpretation related to Lorentz invariance, implying the electromagnetic field's primacy.

## Contribution

It critically examines the possibility of a photon wave function derived from Maxwell's equations and demonstrates why this approach is fundamentally flawed.

## Key findings

- Photon wave function approach is limited by Lorentz transformation issues
- Electromagnetic field is more fundamental than the photon
- Quantum interpretation of Maxwell's equations is unsatisfactory

## Abstract

One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon's quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon (following Good, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell's equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon.