Sound clocks and sonic relativity

TL;DR

This paper explores how sound clocks in certain condensed matter systems can simulate relativistic effects like length contraction and time dilation, despite the systems being fundamentally non-relativistic.

Contribution

It introduces a thought experiment demonstrating that acoustic observers with sound clocks perceive relativistic phenomena, providing insights into analogue models of relativity.

Findings

Sound clocks can simulate relativistic effects such as length contraction.

Observers using sound clocks perceive phenomena consistent with special relativity.

The universe perceived through sound clocks appears relativistic despite a preferred frame.

Abstract

Sound propagation within certain non-relativistic condensed matter models obeys a relativistic wave equation despite such systems admitting entirely non-relativistic descriptions. A natural question that arises upon consideration of this is, "do devices exist that will experience the relativity in these systems?" We describe a thought experiment in which 'acoustic observers' possess devices called sound clocks that can be connected to form chains. Careful investigation shows that appropriately constructed chains of stationary and moving sound clocks are perceived by observers on the other chain as undergoing the relativistic phenomena of length contraction and time dilation by the Lorentz factor, with c the speed of sound. Sound clocks within moving chains actually tick less frequently than stationary ones and must be separated by a shorter distance than when stationary to satisfy simultaneity conditions. Stationary sound clocks appear to be length contracted and time dilated to moving observers due to their misunderstanding of their own state of motion with respect to the laboratory. Observers restricted to using sound clocks describe a universe kinematically consistent with the theory of special relativity, despite the preferred frame of their universe in the laboratory. Such devices show promise in further probing analogue relativity models, for example in investigating phenomena that require careful consideration of the proper time elapsed for observers.