The issue of photons in dielectrics: Hamiltonian viewpoint

TL;DR

This paper extends the Hamiltonian framework for defining photons from vacuum to complex dielectric media, revealing persistent fundamental dilemmas about photon momentum-energy characteristics.

Contribution

It introduces a Hamiltonian approach using Gordon's effective metric to analyze photons in moving, nonhomogeneous dielectrics, addressing longstanding conceptual issues.

Findings

Reveals the reemergence of the photon momentum-energy dilemma in dielectrics.

Extends Hamiltonian photon definitions to complex dielectric environments.

Provides a unified geometric perspective on photon behavior in media.

Abstract

The definition of the photon in the vacuum of general relativity provided by Kermack et al. and by Synge is extended to nondispersive, nonhomogeneous, isotropic dielectrics in arbitrary motion by Hamiltonian methods that rely on Gordon's effective metric. By these methods the old dilemma, whether the momentum-energy vector of the photon in dielectrics is timelike or spacelike in character, is shown to reappear under a novel guise.