# Woldemar Voigt

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Woldemar Voigt
Woldemar Voigt (1850–1919)
Born2 September 1850
Died13 December 1919 (aged 69)
NationalityGerman
Alma mater University of Königsberg
Known for
Scientific career
Fields Physicist
Institutions University of Göttingen
Doctoral students Paul Drude

Woldemar Voigt (German:(); 2 September 1850 – 13 December 1919) was a German physicist, who taught at the Georg August University of Göttingen. Voigt eventually went on to head the Mathematical Physics Department at Göttingen and was succeeded in 1914 by Peter Debye, who took charge of the theoretical department of the Physical Institute. In 1921, Debye was succeeded by Max Born.

## Biography

Voigt was born in Leipzig, and died in Göttingen. He was a student of Franz Ernst Neumann. [1] 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 1898. [2] 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 ${\displaystyle v}$ in the ${\displaystyle x}$ direction. However, as Voigt himself said, the transformation was aimed at a specific problem and did not carry with it the idea of a general coordinate transformation, as is the case in relativity theory. [3]

## The Voigt transformation

In modern notation Voigt's transformation was

${\displaystyle x'=x-vt,}$
${\displaystyle y'=y/\gamma ,}$
${\displaystyle z'=z/\gamma ,}$
${\displaystyle t'=t-vx/c^{2},}$

where ${\displaystyle \gamma =1/{\sqrt {1-v^{2}/c^{2}}}}$. If the right-hand sides of his equations are multiplied by ${\displaystyle \gamma }$, they become 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 that 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 ${\displaystyle \Delta t_{\text{Voigt}}=\gamma ^{-2}\Delta t=\gamma ^{-1}\Delta t_{\text{Lorentz}}}$, while stationary clocks indicate an elapsed time ${\displaystyle \Delta t}$.

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.

## Related Research Articles

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz.

In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:

1. The laws of physics are invariant in all inertial frames of reference.
2. The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or observer.

In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur.

The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 1887 by American physicists Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year.

The Kennedy–Thorndike experiment, first conducted in 1932 by Roy J. Kennedy and Edward M. Thorndike, is a modified form of the Michelson–Morley experimental procedure, testing special relativity. The modification is to make one arm of the classical Michelson–Morley (MM) apparatus shorter than the other one. While the Michelson–Morley experiment showed that the speed of light is independent of the orientation of the apparatus, the Kennedy–Thorndike experiment showed that it is also independent of the velocity of the apparatus in different inertial frames. It also served as a test to indirectly verify time dilation – while the negative result of the Michelson–Morley experiment can be explained by length contraction alone, the negative result of the Kennedy–Thorndike experiment requires time dilation in addition to length contraction to explain why no phase shifts will be detected while the Earth moves around the Sun. The first direct confirmation of time dilation was achieved by the Ives–Stilwell experiment. Combining the results of those three experiments, the complete Lorentz transformation can be derived.

In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them or to a difference in gravitational potential between their locations. When unspecified, "time dilation" usually refers to the effect due to velocity.

Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald contraction and is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction in which the body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes, only becoming significant as the object approaches the speed of light relative to the observer.

The Lorentz factor or Lorentz term is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz.

Special relativity is a physical theory that plays a fundamental role in the description of all physical phenomena, as long as gravitation is not significant. Many experiments played an important role in its development and justification. The strength of the theory lies in its unique ability to correctly predict to high precision the outcome of an extremely diverse range of experiments. Repeats of many of those experiments are still being conducted with steadily increased precision, with modern experiments focusing on effects such as at the Planck scale and in the neutrino sector. Their results are consistent with the predictions of special relativity. Collections of various tests were given by Jakob Laub, Zhang, Mattingly, Clifford Will, and Roberts/Schleif.

The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer. A beam of light is split and the two beams are made to follow the same path but in opposite directions. On return to the point of entry the two light beams are allowed to exit the ring and undergo interference. The relative phases of the two exiting beams, and thus the position of the interference fringes, are shifted according to the angular velocity of the apparatus. In other words, when the interferometer is at rest with respect to a nonrotating frame, the light takes the same amount of time to traverse the ring in either direction. However, when the interferometer system is spun, one beam of light has a longer path to travel than the other in order to complete one circuit of the mechanical frame, and so takes longer, resulting in a phase difference between the two beams. This arrangement is also called a Sagnac interferometer. Georges Sagnac set up this experiment to prove the existence of the aether that Einstein's theory of special relativity had discarded.

In the 19th century, the theory of the luminiferous aether as the hypothetical medium for the propagation of light was widely discussed. An important part of this discussion was the question concerning the state of motion of Earth with respect to this medium. The aether drag hypothesis dealt with the question of whether or not the luminiferous aether is dragged by or entrained within moving matter. According to the first variant no relative motion exists between Earth and aether; according to the second one, relative motion exists and thus the speed of light should depend on the speed of this motion, which should be measurable by instruments at rest on Earth's surface. Specific aether models were invented by Augustin-Jean Fresnel who in 1818 proposed that the aether is partially entrained by matter. The other one was proposed by George Stokes in 1845, in which the aether is completely entrained within or in the vicinity of matter.

The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein and subsequent work of Max Planck, Hermann Minkowski and others.

In physics, the Thomas precession, named after Llewellyn Thomas, is a relativistic correction that applies to the spin of an elementary particle or the rotation of a macroscopic gyroscope and relates the angular velocity of the spin of a particle following a curvilinear orbit to the angular velocity of the orbital motion.

What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century.

The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval and the Minkowski inner product .

The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water. Fizeau used a special interferometer arrangement to measure the effect of movement of a medium upon the speed of light.

Emil Georg Cohn, was a German physicist.

Test theories of special relativity give a mathematical framework for analyzing results of experiments to verify special relativity.

When using the term 'the speed of light' it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed from the source to the detector and back again. Albert Einstein chose a synchronization convention that made the one-way speed equal to the two-way speed. The constancy of the one-way speed in any given inertial frame is the basis of his special theory of relativity, although all experimentally verifiable predictions of this theory do not depend on that convention.

There are many ways to derive the Lorentz transformations utilizing a variety of physical principles, ranging from Maxwell's equations to Einstein's postulates of special relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions, to linear algebra and group theory.

## References

Primary Sources
1. Olesko, Kahryn M. (1991), Physics as a Calling: Discipline and Practice in the Königsberg Seminar for Physics, Cornell University Press
2. Woldemar Voigt, Die fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung [The fundamental physical properties of crystals in an elementary presentation] (Leipzig, Germany: Veit & Co., 1898), p. 20. From page 20: "Wir wollen uns deshalb nur darauf stützen, dass Zustände der geschilderten Art bei Spannungen und Dehnungen nicht starrer Körper auftreten, und sie deshalb tensorielle, die für sie charakteristischen physikalischen Grössen aber Tensoren nennen." (We therefore want [our presentation] to be based only on [the assumption that] conditions of the type described occur during stresses and strains of non-rigid bodies, and therefore call them "tensorial" but call the characteristic physical quantities for them "tensors".)
3. Voigt, W. (1887), "Ueber das Doppler'sche Princip (On the Principle of Doppler)", Göttinger Nachrichten (7): 41–51; Reprinted with additional comments by Voigt in Physikalische ZeitschriftXVI, 381–386 (1915).
• Voigt, W. (1887), "Theorie des Lichts für bewegte Medien", Göttinger Nachrichten (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 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).
• Voigt, W. (1888), "Theorie des Lichts für bewegte Medien", Annalen der Physik, 35 (10): 370–396, 524–551, Bibcode:1888AnP...271..370V, doi:10.1002/andp.18882711011 ; 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.
• Bucherer, A. H. (1908), "Messungen an Becquerelstrahlen. Die experimentelle Bestätigung der Lorentz-Einsteinschen Theorie", Physikalische Zeitschrift, 9 (22): 755–762; For Minkowski's statement see p. 762.
• Lorentz, H.A (1916), The theory of electrons, Leipzig & Berlin: B.G. Teubner; See p. 198.
• Lorentz 1904, Electromagnetic phenomena in a system moving with any velocity smaller than that of light
Secondary sources