# Does the spacelike character of the Minkowski four-momentum show up in analog gravity?

## TL;DR

This paper explains recent analog gravity experiments through classical electrodynamics, highlighting the spacelike nature of Minkowski four-momentum and its relation to superluminal phenomena and the anomalous Doppler effect.

## Contribution

It demonstrates that the observed effects in analog gravity experiments can be understood via the spacelike character of Minkowski four-momentum, linking classical electrodynamics to superluminal phenomena.

## Key findings

- The experiment reflects the spacelike character of Minkowski four-momentum.
- A Gedanken experiment illustrates the transition from subluminal to superluminal effects.
- The spacelike Minkowski momentum is closely related to the anomalous Doppler effect.

## Abstract

In analog gravity the recent experiment of Drori {\it et al.} [Phys. Rev. Lett. {\bf 122}, 010404 (2019)] is impressive, as it shows how the emission of two Hawking quanta emitted in opposite directions lead to measurable consequences in the medium's rest system in a straightforward way. This result raises however the following problem: how can this experiment be explained in terms of classical electrodynamics? There must necessarily exist such an explanation (the experiment is after all classical); otherwise classical electrodynamics would be an incomplete theory. This is the main topic of the present paper. We propose that the measured effect is a demonstration of the spacelike character of the Minkowski four-momentum. Moreover, we extend the discussion by analyzing a Gedanken experiment (making use of the Kerr effect as a formal agency), to illustrate the transition from subluminal to superluminal phenomena in a straightforward way. Finally, we emphasize the close relationship that exists between the spacelike Minkowski momentum and the anomalous Doppler effect.