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

Research on time-varying media has recently enjoyed renewed interest, especially in photonics. Despite the large amount of research done in this field in the past few years, the attention has been focused on electromagnetic waves solely, while a comprehensive framework describing how wave phenomena in general are influenced by time-varying media has not been fully developed yet. To this aim, 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 that 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 mate-rial 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 demon-strate two example solutions. We conclude with some remarks on the role of the accelerating wave equation in the context of the arrow of time.

Automated summary

Research on time-varying media, particularly in photonics, has gained renewed interest recently. However, previous research has mainly focused on electromagnetic waves and a comprehensive framework describing the influence of time-varying media on wave phenomena has not been fully developed yet. This study investigates the implications of time-varying wave mechanics and modifies the standard wave equation to account for non-constant wave speed. It demonstrates that waves experiencing longitudinal acceleration exhibit relativistic properties and only propagate forward in time. The research also addresses the Abraham-Minkowski controversy in electromagnetic waves, showing that it is caused by relativistic effects and confirming the conservation of light momentum between different media. Furthermore, it presents examples of accelerating waves that conserve energy when moving along geodesics.