Time-varying media, relativity, and the arrow of time

TL;DR

This paper explores how time-varying wave mechanics influence relativistic properties, energy conservation, and the arrow of time, revealing new insights into wave behavior and electromagnetic momentum in media.

Contribution

It introduces a modified wave equation for accelerating waves, clarifies the Abraham-Minkowski controversy, and links wave acceleration to the arrow of time.

Findings

Accelerating waves exhibit relativistic properties with a constant reference speed.

The accelerating wave equation admits only forward-in-time solutions.

Electromagnetic wave momentum is conserved across media, resolving the Abraham-Minkowski controversy.

Abstract

We study the implications of time-varying wave mechanics, and show how the standard wave equation is modified if the speed of a wave is not constant in time. In particular, waves which experience longitudinal acceleration are shown to have clear relativistic properties when a constant reference speed exists. Moreover, the accelerating wave equation admits only solutions propagating forward in time, which are continuous across material interfaces. We then consider the special case of electromagnetic waves, finding that the Abraham-Minkowski controversy is caused by relativistic effects, and the momentum of light is in fact conserved between different media. Furthermore, we show that the accelerating waves conserve energy when the wave is moving along a geodesic and demonstrate two example solutions. We conclude with some remarks on the role of the accelerating wave equation in the context of the arrow of time.