Sounds Like Light: Einstein’s Special Theory of Relativity and Mach’s Work in Acoustics and Aerodynamics

Introduction—Mach le bon mécanicien

It is well known that Einstein did not regard his special theory of relativity as revolutionary, but, as he put it, as ‘simply a systematic development’ of electrodynamics Einstein (1919). Pais writes that he considered it ‘the natural completion’ of earlier physicists’ work, and part of an ‘orderly transition’ (1982, p. 30). This was not a matter of modesty on Einstein’s part; for, as Pais also points out, he did not shrink from describing another paper he published that year as ‘very

Mach in Einstein’s Early Scientific Milieu

Before delving into Mach’s work on these two specific topics, I want to fill in the personal historical picture to show that Mach was part of Einstein’s general scientific milieu during his adolescent years. A neglect of Mach’s scientific work may account for why Einstein scholars have not generally been as appreciative of Mach as Einstein appears to have been, and have, I think, often regarded his respect for Mach as due in part to a sentimental attachment to an adolescent hero, and not on a

Some Themes in Einstein’s 1905 Special Relativity Paper

First, a review of some points made in ‘On the Electrodynamics of Moving Bodies’, (hereafter called the 1905 special relativity paper) to have in thought, before going on to examine Mach’s contributions to the explanation of the Doppler effect and supersonic head waves. What follows is not meant to be a summary of that paper—it is its own best summary—but a selection of points I will refer to later.

The paper opens with the remark: ‘It is known that Maxwell’s electrodynamics—as usually

Motion With Respect to a Medium for Signal Transmission

Some readers may feel that the significance that relativity of simultaneity holds in special relativity has been underplayed in the preceding discussion, and that it is this feature, rather than the equivalence of uniformly moving reference frames for observable phenomena due to propagation of waves in empty space, that is the logically prior insight. Certainly it is the relativity of simultaneity that allowed Einstein to show that the two principles he raised to the level of postulates could

4. Mach Against ‘The Law of Conservation of the Period of Oscillation’ —The Doppler Effect for Sound¹⁹

Whereas Einstein’s two principles are about things that remain invariant (e.g. the velocity of light, the laws by which the states of physical systems undergo change), the insight he had about how to show their compatibility was instead about something that did vary between inertial reference frames: simultaneity of events, or, more generally, the time interval between two events not in the neighbourhood of the observer. In his popular account of special relativity, in which, he said, he ‘has

Mach for the Constancy of the Velocity of Light—The Doppler Effect for Light

Years passed, and in 1873, Mach published his three papers on the Doppler effect in a booklet. In 1878, he published on the Doppler effect again, specifically discussing the extension of the acoustical Doppler effect to optics.²⁵

Mach for the Constancy of the Velocity of Sound—Supersonic Shock Waves

The story of Mach shock waves is similar to that of the Doppler effect in that it is inspired by a comparison between analogous phenomena for light and sound, is performed in the laboratory for sound, and is later shown to apply to light. However, Mach’s own work covers only the first two parts of the story for shock waves. It would provide a happy ending to this story were it true that, as for the Doppler effect, for which Einstein’s derivation of the relativistic expression for the Doppler

Optical Analogues of Supersonic Shock Waves

The conceptual return journey from sound (sonic booms) to light (Cerenkov radiation) was not taken for many years after Mach published his work on shock waves. But in the Nobel Lecture Igor’ Tamm gave in accepting his prize for work in developing the theoretical interpretation of the radiation of electrons moving through matter faster than light, he opens with a statement explaining, as Mach did for shock waves, that the principle is not new:

‘The mechanism of radiation of light by a system

Philosophers and Mechanicians

The philosopher in me has been taught to shrink from having any association with the scepticism of Mach’s empiricism. But the mechanician in me has to grant the excellence of thought arising from the type of scepticism Mach actually employed in his scientific investigations. He saw value in rendering things palpable to the senses, and doing so often required summoning deep analogies in science. In turn, the search for analogies required an informed scepticism in jettisoning the right

Acknowledgements

Special thanks to John Norton, without whose initial encouragement I doubt I would have written down my observations. This paper has been enriched by his stimulating suggestions. Thanks also to Rob Clifton for suggestions and for being especially helpful as a sounding board during later stages of the paper’s development, and to Nuel Belnap, Clark Glymour, Adolf Grünbaum, Laura Ruetsche, Gereon Wolters, and two anonymous referees for Studies in History and Philosophy of Modern Physics.

Thanks to