A review of Voigt's transformations in the framework of special relativityI have posted a lot on the history of special relativity, without saying much about Voigt. He deserves credit for being the first to derive a version of the Lorentz transformations.
In 1887 Woldemar Voigt published the paper "On Doppler's Principle," in which he demanded covariance to the homogeneous wave equation in inertial reference frames, assumed the invariance of the speed of light in these frames, and obtained a set of spacetime transformations different from the Lorentz transformations. Without explicitly mentioning so, Voigt applied the postulates of special relativity to the wave equation. Here, we review the original derivation of Voigt's transformations and comment on their conceptual and historical importance in the context of special relativity. We discuss the relation between the Voigt and Lorentz transformations and derive the former from the conformal covariance of the wave equation.
Unfortunately, no one appreciated the significance of what he had done, including himself.
Voigt's paper did not have much influence on historical development of special relativity by others, but the same could be said of Einstein's 1905 paper. The historical chain of special relativity ideas went from Maxwell to Michelson-Morley to Lorentz to Poincare to Minkowski to textbooks. Voigt, FitzGerald, Larmor, and Einstein were minor players.
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