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Schema of Fizeau experiment

The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water. Albert Einstein later pointed out the importance of the experiment for special relativity.

[edit] The experiment

Fizeau's test was designed to evaluate the prediction by Augustin Fresnel that a moving dispersive medium should create a partial offset in the speed of any light moving through it, because the refractive index, n, would be dependent on the density of the luminiferous aether, so the Fresnel drag coefficient is

$1 - \frac{1}{n^2}$ .

The velocity of light in a moving medium is therefore:

$V = \frac {c}{n} + v \left(1 - \frac{1}{n^2}\right)$

This was confirmed by Fizeau's experiment in 1851. The experiment sent two beams of light through a pair of tubes filled with flowing water, so that one beam was always travelling in the same direction as the flowing water, and the other was travelling against the flow. The timelag between the two beams was then measured with an interferometer.

It was shown by Hendrik Lorentz (1892, 1895) that the experiment can be explained by the reaction of the moving water upon the interfering waves without the need of any aether entrainment. On this occasion, Lorentz introduced a different time coordinate for moving bodies within the aether, the so called Local time (an early form of the Lorentz transformation for small velocities compared to the speed of light). In 1895, Lorentz went a step further and explained the coefficient by local time alone and without mentioning any interaction of light an matter.

Within special relativity, Lorentz's formalism was simplified with the aid of the velocity addition formula, which was derived by Albert Einstein (1905) from the complete Lorentz transformation. Thus it was shown by Jakob Laub and Max von Laue (1907) that the Fresnel drag coefficient can easily explained by that formula and so the experiment is supporting evidence for the colinear case of Einstein's velocity addition formula. Einstein later emphasized the importance of the experiment for developing and confirming the theory.

Although it is referred to as the Fizeau experiment, Fizeau was an active experimenter who carried out a wide variety of different experiments involving measuring the speed of light in different situations.

Fizeau's result was replicated by Albert Michelson and Edward Morley (1886), and by Pieter Zeeman (1914).

[edit] Derivation in special relativity

The speed of light in immobile water is c/n. From the velocity composition law it follows that the speed of light observed in the laboratory, where water is flowing with speed v (in the same direction as light) is

$V_{LAB}=\frac{\frac{c}{n}+v}{1+\frac{\frac{c}{n}v}{c^2}}=\frac{\frac{c}{n}+v}{1+\frac{v}{cn}}$

Thus the difference in speed is (assuming v is small comparing to c, approximating to the first non-trivial correction)

$V_{LAB}-\frac{c}{n}=\frac{\frac{c}{n}+v}{1+\frac{v}{cn}}-\frac{c}{n}=\frac{\frac{c}{n}+v-\frac{c}{n}(1+\frac{v}{cn})}{1+\frac{v}{cn}}=\frac{v\left(1-\frac{1}{n^2}\right)}{1+\frac{v}{cn}}\approx v\left(1-\frac{1}{n^2}\right)$

[edit] References

Fizeau, H. (1851). "Sur les hypothèses relatives à l’éther lumineux". Comptes Rendus 33: 349–355. http://gallica.bnf.fr/ark:/12148/bpt6k29901/f351.chemindefer.

Fizeau, H. (1859). "Sur les hypothèses relatives à l’éther lumineux". Ann. De Chim. Et de Phys. 57: 385–404. http://gallica.bnf.fr/ark:/12148/bpt6k347981/f381.table.

Michelson, A. A. and Morley, E.W. (1886). "Influence of Motion of the Medium on the Velocity of Light". Am. J. Science 31: 377–386.

Laue, M. (1907). "Die Mitführung des Lichtes durch bewegte Körper nach dem Relativitätsprinzip". Annalen der Physik 23: 989–990. doi:10.1002/andp.19073281015. http://gallica.bnf.fr/ark:/12148/bpt6k153304/f993.chemindefer.

Zeeman, Pieter (1914). "Fresnel's coefficient for light of different colours. (First part)". Proc. Kon. Acad. Van Weten. 17: 445–451. http://www.digitallibrary.nl/proceedings/search/detail.cfm?pubid=1708&view=image&startrow=1.

Zeeman, Pieter (1915). "Fresnel's coefficient for light of different colours. (Second part)". Proc. Kon. Acad. Van Weten. 18: 398–408. http://www.digitallibrary.nl/proceedings/search/detail.cfm?pubid=1847&view=image&startrow=1.

Miller, A.I. (1981). Albert Einstein’s special theory of relativity. Emergence (1905) and early interpretation (1905–1911). Reading: Addison–Wesley. ISBN 0-201-04679-2.

[edit] See also

Contents

[edit] The experiment

[edit] Derivation in special relativity

[edit] References

[edit] See also