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Historical use of
the Voigt transformation equations.
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Woldemar Voigt's 1887 equation is challenged x' = x - vt |
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In two papers of 1888 and 1889, Oliver Heaviside calculated the deformations of electric and magnetic fields surrounding a moving charge, as well as the effects of it entering a denser medium. This included a prediction of what is now known as Cherenkov radiation, and inspired Fitzgerald to suggest what now is known as the Lorentz-Fitzgerald contraction. | |
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derived from Voigt's equation the square root of 1 - ( v2 - c2 ) |
The contraction of a moving body in the direction of its motion. In 1892 George F. FitzGerald and Hendrik Antoon Lorentz proposed independently that the failure of the Michelson-Morley experiment to detect an absolute motion of the Earth in space arose from a physical contraction of the interferometer in the direction of the Earth's motion. According to this hypothesis, as formulated more exactly by Albert Einstein in the special theory of relativity, a body in motion with speed v is contracted by a factor (as seen on left) in the direction of motion, where c is the speed of light. . |
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 (where x* = x - vt) |
Early approximations of the transformation were published by Voigt 1887 and Hendrik Antoon Lorentz (1895). |
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(where x* = x - vt)
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His final transformations were completed by Joseph Larmor (1897, 1900) |
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x* must be replaced by x - vt |
and Lorentz (1899, 1904) and were brought into their modern form by Jules Henri Poincaré (1905) |
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Albert Einstein 1905 Contrary to Lorentz, who considered "local time" only as a mathematical stipulation, Einstein showed that the "effective" coordinates given by the Lorentz transformation were in fact the inertial coordinates of relatively moving frames of reference. This was in some respect also done by Poincaré who, however, continued to distinguish between "true" and "apparent" time. Einstein's version was identical to Poincaré's (Einstein didn't set the speed of light to unity): |