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, gamma , 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.

Highlights

  • The repeated null results from experiments to detect the luminiferous aether towards the end of the nineteenth century—most notably the null result of the MichelsonMorley experiment [1]—culminated with many physicists, most notably George FitzGerald, Hendrik Lorentz, and Henri Poincaré, proposing mechanisms by which the aether was undetectable

  • It has been shown that it is possible for a certain class of inertial observers to deduce the existence of two key phenomena from special relativity—length contraction and time dilation—in condensed-matter systems for which the speed of sound plays an analogous role to the speed of light within our universe

  • It is perhaps not too surprising that stationary observers in these systems infer that moving observers undergo relativistic time dilation and length contraction, but given the presence of a preferred reference frame it may not be immediately obvious that moving observers should see stationary observers subject to these same effects

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Summary

Introduction

The repeated null results from experiments to detect the luminiferous aether towards the end of the nineteenth century—most notably the null result of the MichelsonMorley experiment [1]—culminated with many physicists, most notably George FitzGerald, Hendrik Lorentz, and Henri Poincaré, proposing mechanisms by which the aether was undetectable. Unruh [13] and others (Brout et al (analytically) [14], Corley (analytically) [15,16], and Corley and Jacobson (numerically) [17,18]) were able to show that acoustic black holes should radiate at a temperature as calculated using Hawking’s approach for black holes even when the comparative assumptions in the acoustic black hole model were broken This result demonstrates that the blackbody temperature of black holes as calculated by Hawking will not necessarily break down when the contributions of Planck scale physics are taken into account, providing us with some evidence that our current understanding of black hole thermodynamics could well be correct [9]. Any object constructed from the medium of the analogue universe will inherit the symmetries of the medium, i.e. the Lorentz group Interferometers built this way will possess arms that will shrink in their direction of motion, and without any way to measure velocity relative to their aether, observers who only have access to these devices will come to believe the postulates of relativity via Ockham’s razor. With certain restrictions placed on what type of experiments can be conducted, we show here that sound clocks—the equivalent of light clocks in systems obeying sonic relativity—can be used as appropriate relativistic observers for a medium in which sound obeys a relativistic wave equation

Approach
Simple Sound Clocks
Sound Clock Chains
Calibrating Clock Separation
Synchronisation of Clocks
Relativistic Effects Observed by Stationary Sound Clocks
Time Dilation as Seen by Stationary Observers
Length Contraction as Seen by Stationary Observers
Relativistic Effects Observed by Moving Sound Clocks
Time Dilation as Seen by Moving Observers
Length Contraction as Seen by Moving Observers
Sonic Relativity
Discussion
Conclusion
Full Text
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