Definitions

# Woldemar Voigt

Woldemar Voigt (2 September 185013 December 1919) was a German physicist.

He was born in Leipzig, and died in Göttingen. He was a student of Franz Ernst Neumann. He worked on crystal physics, thermodynamics and electro-optics. His main work was the Lehrbuch der Kristallphysik (textbook on crystal physics), first published in 1910. He discovered the Voigt effect in 1898. The word tensor in its current meaning was introduced by him in 1899. Voigt profile and Voigt notation are named after him. He was also an amateur musician and became known as a Bach expert (see External links).

In 1887 Voigt formulated a form of the Lorentz transformation between a rest frame of reference and a frame moving with speed $v$ in the $x$ direction. However, as Voigt himself declared the transformation was aimed for a specific problem and did not carry with it the ideas of a general coordinate transformation, as is the case in relativity theory.

## The Voigt transformation

In modern notation Voigt's transformation was
$x^prime = x - vt$
$y^prime = y/gamma$
$z^prime = z/gamma$
$t^prime = t - vx/c^2$
where $gamma = 1/sqrt\left\{1 - v^2/c^2\right\}$. If the right-hand sides of his equations are multiplied by $gamma$ they are the modern Lorentz transformation. Hermann Minkowski said in 1908 that the transformations which play the main role in the principle of relativity were first examined by Voigt in 1887. Also Hendrik Lorentz (1909) is on record as saying he could have taken these transformations into his theory of electrodynamics, if only he had known of them, rather than developing his own. It is interesting then to examine the consequences of these transformations from this point of view. Lorentz might then have seen that the transformation introduced relativity of simultaneity, and also time dilation. However, the magnitude of the dilation was greater than the now accepted value in the Lorentz transformations. Moving clocks, obeying Voigt's time transformation, indicate an elapsed time $Delta t_mathrm\left\{Voigt\right\} = gamma^\left\{-2\right\}Delta t = gamma^\left\{-1\right\}Delta t_mathrm\left\{Lorentz\right\}$, while stationary clocks indicate an elapsed time $Delta t$.

If Lorentz had adopted this transformation, it would have been a matter of experiment to decide between them and the modern Lorentz transformation. Since Voigt's transformation preserves the speed of light in all frames, the Michelson-Morley experiment and the Kennedy-Thorndike experiment can not distinguish between the two transformations. The crucial question is the issue of time dilation. The experimental measurement of time dilation by Ives and Stillwell (1938) and others settled the issue in favor of the Lorentz transformation.

## References

Footnotes Primary Sources

• ; Reprinted with additional comments by Voigt in Physikalische Zeitschrift XVI, 381 - 386 (1915).
• ; This article ends with the announcement that in a forthcoming article the principles worked out so far shall be applied to the problems of reflection and refraction. The article contains on p. 235, last paragraph, and on p. 236, 2nd paragraph, a judgment on the Michelson experiment of 1886, which Voigt, after a correspondence with H. A. Lorentz in 1887 and 1888, has partly withdrawn in the article announced, namely in a footnote in Voigt (1888). According to Voigt's first judgment, the Michelson experiment must yield a null result, independently of whether the Earth transports the luminiferous aether with it (Fizeau's 1st aether hypothesis), or whether the Earth moves through an entirely independent, self-consistent universal luminiferous aether (Fizeau's 2nd aether hypothesis).
• ; In a footnote on p. 390 of this article, Voigt corrects his earlier judgment, made in Göttinger Nachrichten No. 8, p. 235 and p. 236 (1887), and states indirectly that, after a correspondence with H. A. Lorentz, he can no longer maintain that in the case of the validity of Fizeau's 2nd aether hypothesis the Michelson experiment must yield a null result too.
• ; For Minkowski's statement see p. 762.
• ; See p. 198.Secondary sources