Photon conservation in trans-luminal metamaterials

TL;DR

This paper explores photon conservation in trans-luminal metamaterials, revealing how energy is added by increasing photon frequency without creating or destroying photons, with implications for black hole models.

Contribution

It provides both classical and quantum proofs of photon number conservation in these structures, highlighting conditions involving negative frequencies.

Findings

Energy accumulates at singular points in the structure.

Photon number remains conserved during energy increase.

Connections to black hole physics and Hawking radiation.

Abstract

Structures which appear to move at or near the velocity of light contain singular points. Energy generated by the motion accumulates at these points into ever-narrowing peaks. In this paper we show that energy is generated by a curious process that conserves the number of photons, adding energy by forcing photons already present to climb a ladder of increasing frequency. We present both a classical proof based on conservation of lines of force, and a more formal QED proof demonstrating the absence of unpaired creation and annihilation operators. Exceptions to this rule are found when negative frequencies make an appearance. Finally we make a connection to laboratory-based models of black holes and Hawking radiation.