Woldemar Voigt

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Woldemar Voigt (September 2, 1850 - December 13, 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 a musician and became known as a Bach expert (see External links).

In 1887 Voigt^[1] formulated a form of the Lorentz transformation between a rest frame of reference and a frame moving with speed $v$ in the $x$ direction. According to Ernst et al. (2001), Voigt stated in this paper the universal speed of light and demonstrated that Maxwell's equations are invariant under his transformation ^[2]. Voigt's work was far ahead of its time and went apparently un-noticed by all those who contributed to the development of special relativity (George FitzGerald and Oliver Heaviside, Joseph Larmor, Hendrik Lorentz, Henri Poincaré and Albert Einstein)^[3]. Lorentz gave generous, but belated, credit to Voigt in his 1909 book on "The theory of electrons" ^[4]. In 1887 Voigt also published a "Theory of light for moving media". His analysis of the Michelson experiment of 1886 led in the years of 1887 and 1888 to a correspondence with H. A. Lorentz.^[5]

1 The Voigt transformation
2 References
3 Footnotes
4 External links

[edit] 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 $\gamma = 1/\sqrt{1 - v^2/c^2}$ . If the right-hand sides of his equations are multiplied by $γ$ they are the modern Lorentz transformation. 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 elpased time $Δ t Voigt = γ - 2 Δ t = γ - 1 Δ t Lorentz$ , while stationary clocks indicate an elapsed time $Δ t$ .

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 settles the issue in favor of the Lorentz transformation.

For a photograph of Woldemar Voigt, see: http://www.theorie.physik.uni-goettingen.de/ueberuns/Geschichte/index.en.html

[edit] References

Ernst, A. and Hsu, J.-P. (2001) “First proposal of the universal speed of light by Voigt 1887”, Chinese Journal of Physics, 39(3), 211-230. (For the interpretation of Voigt's equation (2), see [[1]]).
Ives, H. E. and Stilwell, G. R. (1938), “An experimental study of the rate of a moving clock”, J. Opt. Soc. Am, 28, 215-226.
Kennedy, R. J. and Thorndike, E. M. (1932) “Experimental Establishment of the Relativity of Time”, Physical Review. Series 2, 42, 400-418.
Lorentz, H. A. (1899) "Simplified theory of electrical and optical phnomena in moving systems", Proc. Acad. Science Amsterdam, I, 427-43.
Lorentz, H. A. (1909) Theory of electrons and its applications to the phenomena of light and radiant heat: A course of lectures delivered in Columbia University, New York, in March and April 1906, Teubner, Leipzig. David Nutt, Williams & Northgate, London. G. E. Stechert & Co., New York. QC793.5.E62L671909.
Simonyi, K. (1990) Kulturgeschichte der Physik, Urania Verlag, Leipzig/Jena/Berlin (translated from the Hungarian 1986 edition by Klara Christoph), pp. 403-404.
Voigt, W. (1887) "Ueber das Doppler'sche Princip", Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, No. 2, 41-51; reprinted with additional comments by Voigt in Physikalische Zeitschrift XVI, 381 - 386 (1915). This paper can be downloaded from uni-goettingen.

Voigt, W. (1887) "Theorie des Lichts für bewegte Medien", Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen', No. 8, 177-238. 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 judgement 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 on p. 390, Ann. Physik Chem. 35 (1888), see next reference. According to Voigt's first judgement, 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). Also this paper can be downloaded from uni-goettingen.

Voigt, W. (1888) "Theorie des Lichts für bewegte Medien", Ann. Physik Chem. 35, 370-396, 524-551. In a footnote on p. 390 of this article, Voigt corrects his earlier judgement, made in Göttinger Nachrichten No. 2, 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.

[edit] Footnotes

^ See Ernst and Hsu (2001) for an English translation of Voigt (1887).
^ Lorentz (1909) had a similar interpretation of what Voigt has shown, that the transformation "does not alter the form of the equations for the free ether" (see footnote below).
^ For the contributions of Larmor, Lorentz and Poincaré see Macrossan, M. N. "A note on relativity before Einstein", British Journal for the Philosophy of Science, 37 (1986): 232-234.
^ Lorentz (1909, p. 198) wrote:

'In a paper "Uber das Doppler'sche Princip" published in 1887 (Gött. Nachrichten, p. 41) and which to my regret has escaped my notice all these years, Voigt has applied to equations of the form ... $\nabla^2\psi - \left(1/c^{2}\right)\partial^2\psi/\partial t^2=0$ ... a transformation equivalent to the formulae ... $x^\prime = \gamma\ell\left(x - wt\right),$ $y^\prime = \ell y,$ $z^\prime = \ell z,$ $t^\prime = \gamma\ell\left(t - wx/c^2\right)$ ... The idea of the transformations used above [i.e the Lorentz transformations] might therefore have been borrowed from Voigt and the proof that it does not alter the form of the equations for the free ether is contained in that paper.'

The Lorentz transformations are equations (285), (287) and (288) in Lorentz (1909). Lorentz's factor $\ell$ was an arbitrary function of $w / c .$ For $\ell = \gamma^{-1}$ we have Voigt's transformation. Note that Lorentz (1904) determined that $\ell = 1,$ but also showed some general properties of the transformation for arbitrary $\ell$ .
^ See Ernst and Hsu (2001) for more details on the Lorentz-Voigt correspondence.