Non-Commutative Geometry and Measurements of Polarized Two Photon Coincidence Counts

TL;DR

This paper explores the non-commutative geometry of photon position, deriving quantum operators from Maxwell's equations, and proposes an experiment to observe discrete photon distance spectra via polarized two-photon coincidence measurements.

Contribution

It introduces a quantum geometric framework for photons based on Maxwell's equations and suggests an experiment to detect discrete photon distance spectra.

Findings

Photon position exhibits non-commutative geometry.

Photon distance spectrum is discrete and measurable.

Proposed experiment aims to observe these quantum geometric effects.

Abstract

Employing Maxwell's equations as the field theory of the photon, quantum mechanical operators for spin, chirality, helicity, velocity, momentum, energy and position are derived. The photon ``Zitterbewegung'' along helical paths is explored. The resulting non-commutative geometry of photon position and the quantum version of the Pythagorean theorem is discussed. The distance between two photons in a polarized beam of given helicity is shown to have a discrete spectrum. Such a spectrum should become manifest in measurements of two photon coincidence counts. The proposed experiment is briefly described.