Who has seen a free photon?

TL;DR

This paper explores the concept of photon position and momentum in media, resolving longstanding debates by introducing the idea of an effective mass for photons due to matter interactions, with implications for quantum optics and solid-state physics.

Contribution

It proposes a new interpretation of photon position and momentum by incorporating effective mass, clarifying the Minkowski-Abraham controversy in media.

Findings

Photon position operator cannot be defined for massless particles with finite spin.

Effective mass due to matter interaction allows a meaningful photon position concept.

Reconciliation of Minkowski and Abraham momentum definitions in media.

Abstract

While the notion of the position of photons is indispensable in the quantum optical situations, it has been known in mathematical physics that any position operator cannot be defined for a massless free particle with a non-zero finite spin. This dilemma is resolved by introducing the "effective mass" of a photon due to the interaction with matter. The validity of this interpretation is confirmed in reference to the picture of "polariton", a basic notion in optical and solid physics. In this connection, we discuss the long-standing controversy between Minkowski's and Abraham's definitions of the momenta of a photon in media from the general viewpoint adopted in the appendix.