Fizeau experiment

Setup of the Fizeau experiment from 1851

The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative speeds of light in moving water. This confirmed the " Fresnel entrainment coefficient", according to which the speed of light in media is modified by their movement. This coefficient was also indirectly determined by other experiments, e.g. B. the Hoek experiment confirmed. According to Albert Einstein , the Fizeau experiment was groundbreaking for the development of the special theory of relativity (see Tests of the special theory of relativity ).

Fresnel entrainment coefficient

The experiment was designed to check the prediction of Augustin Jean Fresnel (1818) that a moving dispersive medium should cause a slight change in the speed of light of a light beam. This hypothesis was introduced by him to explain François Arago's experiment on the aberration of light in moving media (see relative motion between ether and matter ). Fresnel justified this physically with the fact that the hypothetical light ether (which, according to the ideas of the time, served as a medium for the propagation of light) was partially carried along by the moving matter. This light entrainment is also referred to as correction , the "Fresnel entrainment coefficient" correspondingly as the correction coefficient . It results with:

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

where the speed of light in matter is given by with the refractive index and the speed of light in vacuum . The speed of light in a moving medium would therefore be according to Fresnel: ${\displaystyle c/n}$ ${\displaystyle n}$ ${\displaystyle c}$

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

This formula was expanded by Lorentz in 1895 who added an additional term taking into account dispersion :

${\displaystyle c'={\frac {c}{n}}+v\left(1-{\frac {1}{n^{2}}}-{\frac {\lambda }{n}}\cdot {\frac {\mathrm {d} n}{\mathrm {d} \lambda }}\right)}$

Fizeau experiment

Fizeau (1851) then carried out the following experiment: A light beam emitted by the source S is reflected by the glass plate G and passed on in parallel through the lens L. After crossing the slits O ₁ and O ₂ , two light beams are produced which rush through the channels A ₁ and A ₂ , the channels being traversed by a stream of water in the opposite direction. The mirror m at the focus of the lens L 'finally directs the passing rays in such a way that one always spreads in the direction and the other always against the direction of the flowing water. After each ray has traversed the path twice, the two rays are combined at S 'where they create interference fringes.

The Fizeau experiment of 1851.

No streak shift was observed while the water was still. If the water flowed through the canals, however, a positive result must occur according to the Fresnel entrainment coefficient (a shift of approx. 0.46), since the speed of light in the media varies depending on the direction of movement of the water. In agreement with Fresnel's entrainment coefficient, Fizeau actually observed a shift of approx. 0.40 due to the different transit times or speeds over the same distance.

Repetitions

Improved variant of the experiment by Michelson and Morley (1886).

An analogous experiment was carried out with increased precision by Albert A. Michelson and Edward W. Morley (1886). From the light source a , light falls on a half-silvered surface b , where it is divided. A beam now follows the path bcdefbg and the opposite bfedcbg through two tubes through which water flows. Analogous to the Fizeau experiment, a stripe shift was determined in flowing water due to different light transit times in accordance with the Fresnel entrainment coefficient.

In 1914, Pieter Zeeman was also able to confirm the dispersion term predicted by Lorentz.

In 1910 Franz Harress tried to prove Fresnel's entrainment coefficient with a rotating test arrangement. He succeeded, but an additional effect occurred, which he interpreted as a "systematic error". In fact, it was the Sagnac effect , which must be taken into account here together with the entrainment coefficient.

Since then, this drag coefficient has been demonstrated in a number of other experiments, often in combination with the Sagnac effect. For example with ring lasers and rotating disks, or in neutron interferometer experiments. A transverse entrainment effect was also measured when the medium moves at right angles to the original direction of the incoming light.

Hoek experiment

An indirect confirmation of the drag coefficient was provided by Martin Hoek (1868). His apparatus was similar to that of Fizeau, but only in one arm an area was filled with (resting) water, while the opposite arm only contained air. From the point of view of an observer resting in the ether, the earth and its equipment, and thus the water, are moving in a certain direction. From this, Hoek calculated the following propagation times for light rays crossing the apparatus in the opposite direction (see picture):

Structure of the Hoek experiment

${\displaystyle t_{1}={\frac {AB}{c+v}}+{\frac {DE}{{\frac {c}{n}}-v}}}$

${\displaystyle t_{2}={\frac {AB}{c-v}}+{\frac {DE}{{\frac {c}{n}}+v}}}$

It follows from this that the transit times are not the same, which should cause a fringe shift in the interferometer. If, from the point of view of the ether system, the entrainment coefficient is applied to the water, the speeds of the light rays are modified in such a way that the different transit times (for quantities of the first order in v / c) are compensated. In fact, the experiment gave a zero result , thus confirming the Fresnel drag coefficient. (For a similar experiment, but with which the shielding of the ether wind was excluded, see the Hammar experiment .)

Explanations

See also : History of Special Relativity

For the ether theories of that time the following consequences had to be considered: The aberration of the light contradicted a complete entrainment of the ether through the matter and was in agreement with a largely stationary ether. Likewise, the Fresnel entrainment coefficient was equated with an only partial ether entrainment. That is why the majority of physicists preferred the theory of the largely stationary ether with partial ether entrainment, and the complete ether entrainment was considered refuted (see relative movement between ether and matter ).

But while Fresnel's formula had proven itself, the partial ether entrainment resulted in a dependence of the coefficient on the frequency or the color of the light, which could not be correct. Finally, Fresnel's largely dormant or only partially carried ether was directly refuted by the negative result of the Michelson-Morley experiment (1887). The result was a contradicting situation for the ether theories of that time: On the one hand, the aberration of light and the Fizeau experiment (and the repetition by Michelson and Morley (1886)) showed that the ether is apparently at rest or is only partially carried along. On the other hand, the Michelson-Morley experiment (1887) contradicted the stationary ether and apparently confirmed the complete ether entrainment.

Hendrik Antoon Lorentz found a formal way out of this dilemma in a series of works between 1892 and 1904. In 1892 he was able to derive the coefficient on the basis of Maxwell's electromagnetic light theory without having to assume any transport of the ether. The interaction of the electrons with the light causes part of the electromagnetic waves to be modified or carried along during the movement of the matter, whereby the end result corresponds to the Fresnel coefficient of entrainment. More consequential, however, was that Lorentz used a different time variable for systems moving relative to the ether, the so-called local time , as a mathematical aid for quantities of the first order to v / c . In 1895 Lorentz went one step further and used only local time as an explanation, without referring to the interaction of light and matter. Lorentz's theory, however, had the same problem as Fresnel's - it contradicted the Michelson-Morley experiment (1887). Therefore he had to introduce the contraction hypothesis , according to which bodies moving in the ether are shortened in the direction of movement. All of this ultimately led to the development of the Lorentz Transformation (1904).

This could be considerably simplified and physically deepened after Albert Einstein (1905) had derived the relativistic velocity addition theorem from the Lorentz transformation as part of his special theory of relativity . The mechanical ether became superfluous and the traditional concepts of space and time were reinterpreted. Building on this, Max von Laue was able to derive the correct entrainment for all quantities for v / c with the help of this theorem , whereby the Fresnel coefficient resulted approximately at low speeds. The experiment is therefore also a confirmation of the special theory of relativity.

That is why Einstein later repeatedly emphasized the great importance of the Fizeau experiment for the development of the special theory of relativity, as this experiment indicated a deviation from the classical addition of speed at an early stage. For example, Robert S. Shankland reports the following statement by Einstein:

“He continued to say the experimental results which had influenced him most were the observations of stellar aberration and Fizeau's measurements on the speed of light in moving water. 'They were enough,' he said. "

“He [Einstein] went on to say that the experimental results that had influenced him most were observations of stellar aberration and Fizeau's measurements of the speed of light in moving water. 'These were sufficient,' he said. "

Relativistically correct derivation of the drag coefficient

According to the special theory of relativity, the speed of light in a vacuum cannot be exceeded. This means that the vacuum cannot be understood as an ordinary material medium of light (“ ether ”), the state of which would have an influence on the speed of light. The speed of light in matter is always less than the speed of light in a vacuum. According to the theory of relativity, it is allowed that the (respective) speed of light is influenced by the movement of the respective medium, as long as the resulting speed does not exceed the vacuum speed of light. So that this is possible, the resulting speed cannot be determined by simply adding the speed of the medium and the speed of light, but only with the help of the relativistic addition theorem for speeds . It follows that the Fresnel entrainment coefficient can be derived solely from the relativistic addition theorem. Any assumptions about the nature of light propagation in the moving medium are not required for this. If the direction of the two velocities coincide, the addition theorem reads:

${\displaystyle u={\frac {u'+v}{1+{\frac {u'v}{c^{2}}}}}}$

If,, is substituted for the speed of light in the medium and identified with the speed of the medium, the sum of the two speeds in the laboratory system results : ${\displaystyle u'}$ ${\displaystyle u'=c/n}$ ${\displaystyle v}$ ${\displaystyle u}$

${\displaystyle u={\frac {{\frac {c}{n}}+v}{1+{\frac {v}{nc}}}}={\frac {c}{n}}\cdot {\frac {1+{\frac {vn}{c}}}{1+{\frac {v}{nc}}}}}$

For small velocities supplies Taylor expansion of the first order approximation: ${\displaystyle v\ll c/n}$ ${\displaystyle v}$

${\displaystyle u\approx {\frac {c}{n}}+v\left(1-{\frac {1}{n^{2}}}\right)}$

This roughly agrees with the Fresnel result.

literature

• Eleuthère Mascart : Experience de M. Fizeau . In: Traité d'optique , Volume 3. Paris, Gauthier-Villars 1893, pp. 101-105.

Individual evidence

Secondary sources

1. ^ AI Miller: Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905-1911) . Addison-Wesley, Reading 1981, ISBN 0-201-04679-2 .
2. ↑ ^{a b} Michel Janssen, John Stachel: The Optics and Electrodynamics of Moving Bodies . In: John Stachel (Ed.): Going Critical . Springer, 2010, ISBN 1-4020-1308-6 .
3. ↑ Thierry Lahaye, Pierre Labastie, Renaud Mathevet: Fizeau's "aether-drag" experiment in the undergraduate laboratory . In: American Journal of Physics . 80, No. 6, 2012, p. 497. arxiv : 1201.0501 . doi : 10.1119 / 1.3690117 .
4. ^ ^{A b} Edmund Taylor Whittaker : A History of the theories of aether and electricity , 1st edition. Edition, Longman, Green and Co., Dublin 1910.
5. ^ ^{A b} R. Anderson, HR Bilger, GE Stedman: Sagnac effect: A century of Earth-rotated interferometers . In: Am. J. Phys. . 62, No. 11, 1994, pp. 975-985. bibcode : 1994AmJPh..62..975A . doi : 10.1119 / 1.17656 .
6. ^ GE Stedman: Ring laser tests of fundamental physics and geophysics . In: Reports on Progress in Physics . 60, No. 6, 1997, pp. 615-688. doi : 10.1088 / 0034-4885 / 60/6/001 . ; see pp. 631–634 and sources.
7. ↑ Rafael Ferraro: Hoek's experiment . In: Einstein's Space-Time: An Introduction to Special and General Relativity . Springer, 2007, ISBN 0-387-69946-5 , pp. 33-35.
8. ^ RS Shankland: Conversations with Albert Einstein . In: American Journal of Physics . 31, No. 1, 1963, pp. 47-57. bibcode : 1963AmJPh..31 ... 47S . doi : 10.1119 / 1.1969236 .

Primary sources

1. ^ H. Fizeau: Sur les hypothèses relatives à l'éther lumineux . In: Comptes Rendus . 33, 1851, pp. 349-355.
   • German : H. Fizeau: About the hypotheses of the light ether . In: Annals of Physics . Supplementary Volume 3, 1853, pp. 457-462.
2. ^ H. Fizeau: Sur les hypothèses relatives à l'éther lumineux . In: Ann. de Chim. et de Phys. . 57, 1859, pp. 385-404.
   • English : H. Fizeau: On the Effect of the Motion of a Body upon the Velocity with which it is traversed by Light . In: Philosophical Magazine . 19, 1860, pp. 245-260.
3. ^ AA Michelson, EW Morley: Influence of Motion of the Medium on the Velocity of Light . In: Am. J. Science . 31, 1886, pp. 377-386.
   • German : AA Michelson, EW Morley: Influence of the movement of the medium on the speed of light . In: Repertory of Physics . 23, 1887, pp. 198-208.
4. ^ Pieter Zeeman: Fresnel's coefficient for light of different colors. (First part) . In: Proc. Con. Acad. Van Weten. . 17, 1914, pp. 445-451.
5. ^ Pieter Zeeman: Fresnel's coefficient for light of different colors. (Second part) . In: Proc. Con. Acad. Van Weten. . 18, 1915, pp. 398-408.
6. ^ WM Macek: Measurement of Fresnel Drag with the Ring Laser . In: Journal of Applied Physics . 35, No. 8, 1964, p. 2556. doi : 10.1063 / 1.1702908 .
7. ↑ HR Bilger, AT Zavodny: Fresnel drag in a Ring Laser: Measurement of the Dispersive Term . In: Physical Review A . 5, No. 2, 1972, pp. 591-599. doi : 10.1103 / PhysRevA.5.591 .
8. ↑ HR Bilger, WK Stowell,: Light drag in a ring laser - An improved determination of the drag coefficient . In: Physical Review A . 1, 1977, pp. 313-319. doi : 10.1103 / PhysRevA.16.313 .
9. ↑ GA Sanders, Shaoul Ezekiel: Measurement of Fresnel drag in moving media using a ring-resonator technique . In: Journal of the Optical Society of America B . 5, No. 3, 1988, pp. 674-678. doi : 10.1364 / JOSAB.5.000674 .
10. ↑ AG Small, GI Opat, A. Cimmino, A. Zeilinger, W. Treimer, R. Gähler: Neutron propagation in Moving Matter: The Fizeau experiment with Massive Particles . In: Physical Review Letters . 46, No. 24, 1981, pp. 1551-1554. doi : 10.1103 / PhysRevLett.46.1551 .
11. ↑ U. Bonse, A. Rumpf: Interferometric measurement of neutron Fizeau effect . In: Physical Review Letters . 56, 1986, pp. 2441-2444. doi : 10.1103 / PhysRevLett.56.2441 .
12. ↑ M. Arif, H. Kaiser, R. Clothier, SA Werner, EA Hamilton, A. Cimmino, AG Klein: Observation of a motion-induced phase shift of neutron de Broglie waves passing through matter near a nuclear resonance . In: Physical Review A . 39, No. 3, 1989, pp. 931-937. doi : 10.1103 / PhysRevA.39.931 .
13. ^ RV Jones: 'Fresnel Aether Drag' in a Transversely Moving Medium . In: Proceedings of the Royal Society of London. Series A . 328, No. 1574, 1972, pp. 337-352. doi : 10.1098 / rspa.1972.0081 .
14. ^ RV Jones: "Aether Drag" in a Transversely Moving Medium . In: Proceedings of the Royal Society of London. Series A . 345, No. 1642, 1975, pp. 351-364. doi : 10.1098 / rspa.1975.0141 .
15. ↑ M. Hoek: Determination de la vitesse avec laquelle est entrainée une onde lumineuse traversant un milieu en mouvement . In: Verslagen en mededeelingen . 2, 1868, pp. 189-194.
16. ↑ M. Laue: The entrainment of light through moving bodies according to the principle of relativity . In: Annals of Physics . 23, 1907, pp. 989-990.