Fizeau-Experiment
The Fizeau experiment was carried out by Hippolyte Fizeau in 1851 to measure the relative velocities of light in moving water. This enabled the " Fresnel entrainment coefficient ", after which the speed of light is modified in media through their movement, are confirmed. Indirectly, this coefficient was also confirmed by other experiments, such as the Hoek experiment. According to the testimony of Albert Einstein, the Fizeau experiment was crucial to the development of special relativity (see tests of special relativity ). [S 1] [ S 2] [ S 3]
Fresnel's entrainment coefficient
The experiment was designed to verify the prediction of Augustin Jean Fresnel (1818 ), after which a moving dispersive medium will cause a slight change in the speed of light, a light beam. This hypothesis was introduced by him to the explanation of Arago's experiment for the aberration of light in moving media (see relative movement between ether and matter ). Physically based Fresnel this by saying that the hypothetical luminiferous ether ( which was used by former performances as a medium for the propagation of light) would benefit from moving matter partly carried. The " Fresnel entrainment coefficient " is given by: [S 4]
Wherein the speed of light is given by N in the material with the refractive index. The speed of light in a moving medium would, therefore, according to Fresnel:
This formula was extended by Lorentz in 1895, which added an additional term taking into account dispersion: [S 5]
Fizeau experiment
Fizeau (1851 ) is now conducted by the following test: [P 1] [ P 2] A emitted by the source S, the light beam is reflected by the glass plate G and carried in parallel by the lens L.. After passing through the slits O1 and O2 results in two light beams which are divided by the channels A1 and A2, wherein the channels are passed through by a flow of water in the opposite direction. The mirror m at the focus of the lens L ' directed by hurrying rays finally in such a way that one of the other always propagates against the direction of the flowing water always in the direction and. After each beam has rushed through the path twice, the two beams are ' united in S, where they produce interference fringes.
As long as the water was at rest, no fringe shift was observed. However, with flow along the water channels, a positive result must occur ( a shift of about 0.46 ) according to the Fresnel osmotic drag coefficient, since the speed of light in the media differs with each direction of movement of the water. In accordance with Fresnel's a shift in osmotic drag coefficient of 0.40 due to the different durations and velocities was actually observed in the same long stretch of Fizeau.
Repetitions
A similar experiment was performed with increased precision by Albert Abraham Michelson and Edward Morley ( 1886). From the light source a light falls to a half-silvered surface b, where it is divided. A beam follows now bcdefbg of the way and who opposed bfedcbg by two traversed by water tubes. Analogous to the Fizeau experiment was in pouring water, a fringe shift determined in accordance with the Fresnel osmotic drag coefficient due to the different light travel times. [P 3]
1914 could also confirm the predicted Lorentz dispersion term Pieter Zeeman. [ 4 P ] [P 5]
1910 Franz Harress tried to prove the Fresnel osmotic drag coefficient with a rotating experiment. He succeeded, but it still exhibited an additional effect, which was interpreted by him as a " systematic error ". In fact, these were to the Sagnac effect, which has to be considered here together with the osmotic drag coefficient. [S 5]
Since then, this entrainment coefficient has been demonstrated in a number of other experiments, often in combination with the Sagnac effect. [S 6 ] For example, with ring lasers and rotating disks, [P 6] [ P7 ] [ P8 ] [ P9 ] or in Neutroneninterferometer experiments. [ 10 P ] [ P 11 ] [ P 12 ] also, a transverse Mitführungseffekt was measured when the medium is moved at right angles to the original direction of the incident light. [ 13 P ] [ P 14 ]
Hoek experiment
An indirect confirmation of the osmotic drag coefficient was provided by Martin Hoek (1868 ). [ P 15 ] [ S 7] resembled his apparatus to that of Fizeau, but an area with ( stationary ) has only one arm filled water while the opposite arm only air contained. From the perspective of an observer at rest in the ether, the earth, including apparatus and thus the water moves in a certain direction. Hoek calculated from the following propagation times for light rays that pass through the apparatus in the opposite direction (see picture):
It follows that the running times are not equal, what would cause a fringe shift in the interferometer. If the view of the ether system, however, the entrainment coefficient applied to the water, the speed of the light rays are modified such that the different maturities are compensated ( for quantities of the first order in v / c). In fact, the experiment produced a null result, and thus confirmed the Fresnel osmotic drag coefficient. ( For a similar experiment, but with the shield of the wind ether was excluded, see the Hammar experiment. )
Explanations
For the former ether theories following consequences were considered: [S 4] [ S 2] The aberration of light contradicted a complete entrainment of the ether by matter and was in accordance with a largely stationary ether. Similarly, the Fresnel entrainment coefficient was equated with an only partial Äthermitführung. Therefore, the theory of the largely stationary aether with partial Äthermitführung was supported by the majority of physicists preferred, and the full Äthermitführung refuted considered (see relative movement between ether and matter ).
But while Fresnel's formula had proven, resulting from the partial Äthermitführung a function of the coefficient of the frequency or the color of the light, which could not be right. Finally, Fresnel was refuted largely dormant or only partially entrained aether directly by the negative result of the Michelson - Morley experiment (1887 ). It resulted in a contradictory for the then ether theories situation: on the one hand, the aberration of light and the Fizeau experiment showed ( and the repetition by Michelson and Morley (1886 ) ) that the ether is apparently at rest or is only partially carried. On the other hand, was the Michelson - Morley experiment (1887 ) contrary to the stationary ether and apparently confirmed the complete Äthermitführung.
Hendrik Antoon Lorentz was held in a series of works 1892-1904 a formal way out of this dilemma. Thus he was able in 1892 to derive the coefficients on the basis of Maxwell's electromagnetic theory of light, be required to adopt any entrainment of the ether. By interaction of the electrons with the light, a portion of the electromagnetic waves modified or entrained in the movement of material, the end result with the Fresnel Mitführungkoeffizieten matches. Consequential, however, was that this Lorentz used as a mathematical tool for sizes first order v / c is a variable for different time relative to the ether moving systems, the so-called local time. 1895 Lorentz went a step further and used only the local time as an explanation, without referring to the interaction of light and matter. However, Lorentz 's theory had the same problem as Fresnel's - it was contrary to the Michelson - Morley experiment (1887 ). That's why he had to introduce the contraction hypothesis that moved in the etheric body can be shortened in the direction of movement. This all culminated in the development of the Lorentz transformation ( 1904).
This could be significantly simplified and deepened physically after Albert Einstein ( 1905) had derived the relativistic Geschwindigkeitsadditionstheorem as part of his special theory of relativity from the Lorentz transformation. The mechanical ether was superfluous and reinterprets the traditional concepts of space and time. Could Based on Max von Laue in 1907 with the help of this theorem to derive the correct entrainment for all sizes to v / c, where the Fresnel coefficient approximated at low speeds revealed. The experiment therefore also represents an acknowledgment of the special theory of relativity
Einstein emphasized so later, again and again the importance of the Fizeau experiment for the development of special relativity, since this experiment at an early stage indicating a deviation from the classical velocity addition. For example, reports Robert S. Shankland of the following statement Einstein: [S 8]
" He continued to say the experimental results Which Influenced had 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 ] continued that the experimental results that had influenced him the most, the observations of stellar aberration and Fizeau's measurements were the speed of light in moving water. "These were sufficient ," he said. "
Relativistically correct derivation of the osmotic drag coefficient
According to the special theory of relativity the speed of light can not be exceeded in a vacuum. That is, the vacuum can not as an ordinary light material medium ( "ether" ) can be considered, the motion state would have an effect on the speed of light. However, the speed of light in the material is always less than the vacuum speed of light. Here, it is in accordance with the theory of relativity thus allowing the ( respective ) light speed is affected by the movement of the medium as long as the resulting velocity does not exceed the vacuum speed of light. To make this possible, the resulting velocity can not be determined by a simple addition of medium speed and the speed of light, but only with the help of the addition theorem for relativistic speeds. It arises here is that the Fresnel entrainment coefficient can be derived solely from the relativistic addition theorem. Any assumptions about the nature of light propagation in a moving medium are not required. When the direction of the velocities coincide, is the addition theorem:
If one uses for the speed of light in the medium, and identified with the velocity of the medium, we obtain for the sum of both velocities in the laboratory frame:
For small velocities provides Taylor expansion after the first order approximation:
This is in accordance with the Fresnel's result. [ 16 P ]