Michelson–Morley experiment

The Michelson -Morley experiment was a physics experiment, which was carried out by the German - American physicist Albert Abraham Michelson 1881 in Potsdam and in a more refined form of it and the American chemist Edward Morley 1887 in Cleveland, Ohio.

The Michelson - Morley experiment had expressed the objective of demonstrating the speed of the earth relative to the aether in its orbit around the sun, or otherwise, the speed of the ether relative to the Earth ( "ether wind "). When light ether it was a hypothetical medium in which light waves should propagate analogous to water waves and sound waves. The experiment resulted in an upper limit for this relative speed of 5-8 km / s, which showed that the " motion relative to the ether " had no effect on the speed of light, since this value was too small to keep up with the sought-after " ether wind to be " associated. The Michelson - Morley experiment, together with other experiments such as the Fizeau experiment or the Trouton -Noble experiment pointed to the problems of ether physics of the 19th century in all clarity. This problem could only be solved by the special theory of relativity, is in no need for a preferred reference system as the ether. That is why it is considered one of the most important experiments in the history of physics - a " Experimentum Crucis ".

Since then, the experiment was repeated with different techniques and significantly increased accuracy. Here, within the measurement accuracy Zero results were obtained, thus confirming the conclusions from the original experiment. Such relative deviation of the speed of light by the value of the speed of light constant could be excluded in the range of 10-17. For further experiments, see tests of special relativity.

• 3.1 Lorentz contraction and Lorentz transformation
• 3.2 Special Theory of Relativity
• 3.3 Refuted alternatives

• 5.1 Optical tests
• 5.2 resonator experiments

• 6.1 Background and history
• 6.2 Preparation and implementation

Overview

To determine the relative velocity of earth and ether, a beam of light through a semitransparent mirror was separated in two different ways, reflected and brought together again at the end, so that an interference pattern of standing light waves formed ( Michelson interferometer ). Due to the movement of the earth in ether is obtained, that the light beam in the moving direction slightly longer than required, the beam perpendicular to it. Since the apparatus as part of the rotation of the earth moved around the sun relative to the presumed ether, was expected shifts of the interference fringes when the apparatus were rotated. Albert Abraham Michelson led the experiment, which was not easy because of c relative to the speed of light low path velocity v of the earth, first in 1881 by, but this was not sufficient accuracy, because Michelson had in his calculations, the change in the light path perpendicular to the direction of motion does not included. In 1887 he repeated and Edward Williams Morley experiment with sufficient accuracy. Although the result was not completely negative ( between 5-8 km / s), it was much too low, according to Michelson and the other physicists of that time to have something to do with the expected aether wind. The insignificance of Michelson's result appears even more clearly when not only the relative velocity of the Earth to the Sun of 30 km / s is taken into account, but also the rotation speed of the solar system around the galactic center of about 220 km / s, and the relative velocity between the solar system and the rest frame of the cosmic background radiation of about 377 km / s In addition, later, up to the present time, measurements made have the original method of Michelson further refined and delivered actually within the measurement accuracy full zero results.

George Francis FitzGerald (1889 ) and Hendrik Antoon Lorentz (1892 ) provided with the Lorentz contraction initially an ad hoc explanation was assuming that the interferometer relatively shrinks in the direction of movement to the ether, whereby the different light travel times are equalized. Subsequently developing the Lorentz transformation which contains the change in the timings of moving bodies, the time dilation, was. The builds on it Lorentz ether theory, however, was considered to be very unlikely because of the ether the one hand, the basis of all physical phenomena, on the other hand, however, should be completely undetectable here. The result of the Michelson -Morley experiment was fully understood only by Albert Einstein's special theory of relativity of 1905, which also contains a length contraction, but dispenses with the ether hypothesis and as a central postulates the principle of relativity and the constancy of the speed of light in any speed moving against each reference systems contains.

The Michelson - Morley experiment is on the one hand, the most important affirmation of the principle of relativity, according to which the physical laws of nature for all uniformly moving observers are identical. It is namely that the speed of light is independent of the orientation relative to a reference system, such as the preferred ether. But it shall not in itself constitute no direct evidence for the universal constancy of the speed of light, as is sometimes assumed:

• The null result is also compatible with models in which the speed of light is variable. Example, it was sometimes assumed that the ether is completely retained on the surface. Another possibility would be an emission theory that the speed of light depends on the source speed and in all inertial frames is constant relative to the light source. Both models are ruled out, however, as they have been experimentally refuted many times, so that the theory of relativity remains the only theory that can explain all experiments.
• Also, the presence of an ether wind is not fully excluded by this experiment. Had the interferometer at rest that is different lengths, would be in relation to the preferred reference system despite a positive effect of length contraction occur during speed changes of the apparatus. Therefore, a further experiment must be taken into account, the Kennedy - Thorndike experiment that tests exactly this dependence of the apparatus speed, and its negative result can only be explained by a combination of length and time changes. For the accurate determination of these quantities in turn, an experiment is needed that measures the time dilation directly, such as the Ives - Stilwell experiment. The combination of these three experiments can be accurately determined indeed the Lorentz transformation.

The experiment

The starting point for Michelson and Morley was to measure the relative speed with which the earth moves through an assumed to be stationary ether. As with an airplane moves through the air, here would be a detectable " aether wind " to be expected since the Earth moves in its orbit around the sun at about v = 30 km / s = 3.104 m / s (always still relatively small compared to the light velocity c of about 3,108 m / s).

To measure this effect, Michelson (1881 ) constructed an interferometer with two perpendicular arms. The movement of the interferometer in the ether can either be described from the perspective of a stationary observer in the ether, or a co-moving with the interferometer observer.

In ether observer at rest

Movement direction: The light emitted from the light source and propagates at the speed of light, while the mirror starts to be taken in the distance and moves with the velocity relative to the ether. On the way up the beam hits at the time when a mirror and puts it back to the path. Until then, the at -starting mirror has traveled the distance. Thus, and thus it results in the runtime. The same considerations arise for the way the context and runtime. The total running time is given by:

This would exploit the fact that very small (order of magnitude ) when would be used for the movement speed of the earth and for the speed of light.

Perpendicular to the direction of motion: Again, the beam propagates with constant out, hits at the time when a mirror, and covers the path. Since the beam is aligned in the rest frame of the interferometer so that it moves vertically upward, it will be slightly inclined in the rest frame of the ether when using the Galilean transformation or taking into account the conservation of momentum. Meanwhile, the moving mirror with it has come the track where he is hit by the beam. Consequently, the path of the beam in the y- direction and in the x- direction, and with the Pythagorean theorem there is a path from. So it is the context given, and thus the running time, which is also identical to the term for the way back. ( This effect corresponds to the schema of a light clock or the aberration of light ). The total running time is given by:

The term perpendicular to the movement direction is thus less than in the direction of movement.

Comoving observers

This result is described from the perspective of a comoving observer, then the effect of the ether wind on light waves according to the ideas of classical physics as well as the impact of a strong current of a river ( speed) on a float only at a constant speed between two points upriver and then moves downstream.

In this image, the second point would be directly upstream of the first, the float would first slowed by the flow and are then accelerated to the way back, and it turns out above maturities of.

Verliefe the route between the start and end point perpendicular to the flow direction, the float would have to compensate for this by oblique floating in a small angle to its destination. Its speed is reduced to and it turns out above maturities of.

Similarly, the effect of the ether wind on a beam of light ( velocity c ) would be perpendicular to the wind direction slightly lower than for a beam of light verliefe parallel to the ether wind.

Time difference

The time difference between the two paths is

Thus, the greater the longer L. Substituting L = 1 m would be to the abovementioned value v of the motion of the earth is a time difference of a second result from the ether, as compared with a period of oscillation in the range of visible light from about seconds. The difference would be in the range of 3 percent, which would have been detectable with the improved apparatus of Michelson and Morley.

In their experiment of 1887, Michelson and Morley tried, so far as possible eliminate the effects of shocks to which their measuring apparatus responded very sensitive. The optical setup consisted of a monochromatic Sodiumlichtquelle ( yellow light) for the adjustment, and a white light from a lamp for the actual measurement. The light beam is split at right angles to each other through a part -silvered mirror into two beams. After leaving the beam splitter the two beams were each reflected by a mirror and brought together on an observation screen again. Where they produced a stripe pattern of constructive and destructive interference, which is extremely sensitive to changes in the difference of the optical paths of the two light beams. It was expected that these optical paths would be influenced by the movement of the earth in the ether, so that the interference pattern would have to move during the rotation of the apparatus carrying stone slab.

Turning the experiment, for example, 90 degrees, reversed the above formulas for the terms of and, we obtain a time difference of

This results in a delay difference of the starting experiment. This corresponds to an optical path length of

If, as in the experiment of 1887 an effective arm length of the interferometer of L = 11 m is chosen. The relative displacement of the interference pattern is obtained with, for example a wavelength as

The average of six measurements that were performed on 8, 9 and 11 July 1887 was held 0.44 but certainly less than 0.02 (or maybe even less than 0.01), which corresponds to a speed of 8 km / s (or 5 km / s) correspond. Although the result was not entirely negative, however, it was widely interpreted as a null result because of the expected, much larger value.

Explanation

Lorentz contraction and Lorentz transformation

The first step to formally correct explanation of the null result was made by George Francis FitzGerald (1889 ) and Hendrik Antoon Lorentz (1892 ) by introducing the Lorentz contraction hypothesis or contraction. To equalize the run times and to save the idea of ​​a stationary ether, they speculated that the length of the experimental arrangement is shortened relative to the direction of movement to the airwaves to where it is called the Lorentz factor. Lorentz used before 1904 but not exactly this value, but only second order in v / c approximations. The term in this direction is shortened as well and is now equal in length perpendicular to the direction of motion, so the negative result is explainable. If you were to multiply in the above formula for the distance traveled by the length L by this factor, we have:

When length contraction, however, is only a special case of the possible explanations. Generally only needs to be assumed to be in the moving state, the transverse length ratio is greater than the longitudinal length, which may be achieved in various ways. If the moving longitudinal length and transverse moving is length and the rest length, then there is the general context:

Is a scale factor which can be chosen arbitrarily, so there are endless combinations of contractions and dilations to the null result to explain. For example, would in the ordinary length contraction occur, however, when would remain unchanged, whereas would be increased. In the period following the contraction hypothesis by Joseph Larmor (1897 ), Lorentz (1904) and Henri Poincaré (1905 ) was further developed by modifications of the time variables for Lorentz transformation to the results of the Trouton -Noble experiment, the experiments of Rayleigh and Brace and to explain the Kaufmann's experiments:

The still undetermined factor was finally set by Lorentz (1904 ) equal to 1. Generally Poincaré (1905) could show that the whole of the Lorentz transformation form only one group. Only then length contraction and time dilation obtain their exact relativistic values ​​. The theory of Lorentz and Poincaré, which is sometimes called Lorentz ether theory, that explains the apparent validity of the principle of relativity and the constancy of the speed of light, but it also leads to the situation that the luminiferous ether, which forms the basis of the theory, outside each experimental verifiability stands. This is a major reason why in spite of the correct mathematical formalism, this theory is considered outdated.

Special Theory of Relativity

The ad hoc nature of the ether -based contraction hypothesis ( and continuing throughout the Lorentz between ether theory ), however, was soon criticized. Lorentz himself spoke vaguely of an influence of the ether as a cause and as an analogy led the observable behavior in electrostatic fields that are contracted in the direction of motion with a velocity-dependent factor. It is believed that the binding forces in the material of electric nature, this may explain the contraction. However, Lorentz himself admitted that such an assumption is by no means necessary.

A solution to this unsatisfactory situation, Albert Einstein in 1905 with special relativity theory (SRT ), which he derived based on two postulates, namely the principle of relativity and the constancy of the speed of light. He interpreted in contrast to Lorentz and Poincaré this as a transformation between equal space and time coordinates (ie no distinction between "true " and " apparent" coordinates) and thus showed that the ether hypothesis is superfluous. Although the explanation of the negative output of the experiment corresponds to a purely formal statement of the Lorentz ether theory, however, the assumption of an ether is no longer necessary in the SRT, and the Lorentz contraction arises as a logical consequence of the underlying postulates. In a moving with v reference system in which the interferometer is at rest, the running times are the same. If we consider a reference system in which the interferometer with velocity v moves and the speed of light is still unchanged, is explained as the result, as described above, with the Lorentz contraction. This statement is regarded as the currently valid. Although in many descriptions of this experiment is described as starting point of the theory to the development of SRT, Einstein himself has denied a direct impact of the experiment on his ideas.

Later, Howard Percy Robertson showed, and others ( see Test theories of special relativity ) that it is possible to derive the entire Lorentz transformation from the combination of three experiments. The Michelson -Morley experiment shows that the speed of light is independent of the orientation of the apparatus, and it determines the relationship between the longitudinal () and transverse () lengths. It was found, however, that the use of different rest lengths of the interferometer arms should occur a positive result when the apparatus changes its speed relative to a preferred frame of reference. The zero result of the Kennedy Thorndike experiment with which this connection has been tested, then, indicates that the speed of light is independent of the speed of the apparatus, and determines the relationship between the time changes () and longitudinal () lengths. Thus the two experiments yield only these relations, not the individual values ​​of, ,. This uncertainty corresponds to the above-defined factor - this was indeed set in the context of group theory to 1, however, an experimental confirmation of this theoretical result would be desirable. This is a direct measurement of one of the three sizes is required. This was performed by the Ives - Stilwell experiment, was measured by the in accordance with the time dilation. With Kennedy - Thorndike can now be identified with the length contraction, and hence by the Michelson-Morley set equal to zero. Thus, all quantities are given which form the basis of the Lorentz transformation.

Refuted alternatives

In theory, the full Äthermitführung, which goes back to George Gabriel Stokes ( 1845), the ether would not rest, but also follow the movement of the earth from the surface up to a certain distance. This may explain the null result, since in this case rests the ether relative to the Earth's surface. However, as Lorentz (1886 ) pointed out, the problems of this theory, especially in the context of the aberration of starlight and the Fizeau experiment were too big, so this statement could not be considered. Michelson himself believed after his first experiment in 1881, that his experiment had confirmed the theory of Stokes. In 1887 he knew but already the objections of Lorentz and rejected this theory.

Also compatible with the null result is this originally by Isaac Newton and later by Walter Ritz (1908 ) advocated emission theory, which denies the existence of the ether and a constant speed of light postulated relative to the light source. When changing the reference systems of the Galilean transformation is used, so that the theory satisfies the classical principle of relativity. In a reference system, in which the interferometer arrangement rests, the speed of light in relation to the stationary interferometer is constant, and there is a similar time of flight in each direction. Seen from a movable relative to the v system gets the light, the speed of the interferometer (which functions here as a light source ) is added as a projectile and thus moves with c ± v. The speed of light relative to the light source but remains constant, and there are in turn, the same maturities. However, this theory is in part due to the Sagnac effect and the observed motions of double stars as disproved.

Further experiments

Experiments of the Michelson -Morley type were performed multiple times with increased accuracy, with most ( Kennedy, Illingworth, Joos ) zero results were within the error limits. Exceptions such as the results of about 10 km / s by Dayton Miller ( 1921-26 ) could not be confirmed with modern analyzes were able to show various sources of error. Miller pointed out that in all other experiments the interferometer around a strong shielding shell has been used, which had carried the airwaves, while this was not the case with him. However, this was refuted by the Hammar experiment ( 1935), where one arm of the interferometer was enclosed in a lead sheath, the other not. According to Miller here a positive result should have been made, but it was negative, so Miller's theory was disproved. Furthermore, it must be added that in the earlier experiments, usually only the relative speed of 30 km / s is taken into account, but not the much larger rotational speed of the solar system around the galactic nucleus of about 220 km / s, or the relative motion between the solar system and the hypothetical rest frame of the background radiation of about 368 km / s, thus the insignificance of the results is still more apparent.

Modern experiments

Optical tests

Optical tests of the isotropy of the speed of light are now routinely performed. The accuracy of the interference experiments was increased by use of laser, maser, cryogenic optical resonators, etc. considerably. This experimental setups were used that differ in part from the classical scheme of the MM experiment. (Set in the following table only food ( 1955), Jaseja et al. (1964 ) and Shamir / Fox ( 1969) experiments of the Michelson -Morley type is, ie, it will be orthogonal beams compared. Use the other experiments different methods. )

Resonator experiments

In recent years, there was an increased interest in the implementation of high-precision tests of Lorentz invariance - including those of the Michelson - Morley - type by means of optical resonators. These experiments were induced by possible violations of Lorentz invariance in various versions of quantum gravity. An example of this was the experiment by Brillet and Hall (1979), wherein a frequency stabilized laser, was to a rotating -optical Fabry-Perot resonator analyzed. In this case, a maximum anisotropy of the light from DELTA.c / c ≈ 10-15 showed where DELTA.c is the difference between the speed of light in the x and y directions.

By 2009, optical and microwave resonators have this limit increased to DELTA.c / c ≈ 10-17. These experiments are conducted with stationary part and to the rotating assemblies, which are often combined with the principle of the Kennedy Thorndike experiment. In the evaluation of the experiments while the relative velocity is used for the rest frame of the cosmic background radiation of about 377 km / s. ( Isotropieexperimente, where a similar accuracy is achieved, are Hughes - Drever experiments, although nucleons are tested. For more modern experiments Modern tests of Lorentz invariance see. )

History

Background and history

At the time when the first experiment (1881 ) was carried out, there are two competing theories ether.

• Augustin Jean Fresnel (1819 ) assumed that the ether near the body does not, and only in the bodies themselves will carried. The speed of light in a moving speed of the medium resulted in this theory as the osmotic drag coefficient, the refractive index is.
• George Gabriel Stokes (1845 ) assumed, however, that the ether will completely entrained in and near the body.

An important decision between the theories provided the Fizeau experiment of Armand Hippolyte Louis Fizeau ( 1851). He used an interferometer arrangement with which the speed of light was measured in the water. The results spoke for a partial entrainment of the ether within the meaning of Fresnel and could be agreed with Stokes theory with only circumstantial auxiliary hypotheses. Similarly, the existence of the aberration of light was better to bring with Fresnel as with Stokes theory consistent. Finally, Lorentz published in 1886 a font that was shown in that the auxiliary hypotheses of Stokes contradict itself. Therefore, finally, the modified Lorentz theory of Fresnel was preferred.

Fresnel entrainment coefficient with the result that in ether drift experiments were to expect any good results in the order of, where V is the relative speed of the earth - ether, and c is the speed of light. However, it should in experiments, which were able to show effects in the order of, necessarily lead to positive results. The Michelson - Morley experiment was the first experiment of this kind

Preparation and implementation

Michelson had 1879 resulted from a letter from James Clerk Maxwell to DP Todd, the head of the Nautical Almanac Office, where he worked as a young Marineinstrukteur and measurements of the speed of light, heard of the possibility of experimental verification of the motion of the earth through the ether. Maxwell mentioned it first to the possible review by observing the blackout periods of Jupiter's moons, an effect first order, then, but too hard to watch, and then that in experiments on Earth a relative accuracy of would be required ( 2nd order effect ), which would, in his view beyond the measurable time. Michelson undertook the experiment first in April 1881 in the basement of the main building of the observatory on the Telegrafenberg in Potsdam (which was not completed until 1879) by, while he was on a scholarship from Bell 1880 to 1882 in Berlin, he was ( encouraged here by the director Hermann von Helmholtz ). Try it before the Physical Institute in Berlin -Mitte, Wilhelmstrasse. Perform 67a failed due to vibrations caused by heavy traffic. Although Michelson received a zero result, but the accuracy was not very high ( he used a rotatable brass frame with arm lengths of about 1 m. ): Expected a displacement of 0.04 fringes, if the Fresnel ether hypothesis was correct, and the margin of error was 0.02. Above all, he did not consider the influence of ether motion on the propagation of light in the arm perpendicular to the direction of motion, ie, the light here is spreading tilted and not straight forward as Michelson had assumed. Michelson's experiment was then at once (1884 and 1886) criticized by Lorentz, who had meanwhile developed its own ether theory. He was able to show that correction of the running time for the transverse arm of the expected effect was only half as large, and also takes into account the Fresnel osmotic drag coefficient, the failure result could ( though just barely ) are explained, which this experiment was taken his validity.

Michelson began in 1885 a collaboration with chemistry professor Edward Morley at the Case Western Reserve University in Cleveland (Ohio ). They conducted a series of measurements for various purposes, with the psychological stress during this precision measurements was apparently so high that Michelson 1885 a nervous breakdown from which he had recovered after several months: They confirmed the result of the Fizeau experiment with higher accuracy ( 1886) and tried the wavelength of light as the new standard length increase ( 1887, 1889).

However, was its repetition (1887 ) of the Michelson experiment of 1881 at the urging of, among others, Rayleigh and Kelvin, which represents the actual Michelson - Morley experiment of greater importance. Here they related improvements such as multiple reflection on the extension of the light path at 11 m instead of 1.2 m in Potsdam, better shock absorption, a floating in a mercury bath and thus easily rotating test platform and a heavy stone table. To minimize vibrations, the traffic was spaciously. The expected during validity of the Fresnel ether hypothesis shift was now 0.4, however, the observed was certainly less than 0.02, and possibly below 0.01. Since the shift was proportional to the square of the speed, this corresponds to a velocity of Michelson according to less than a quarter ( approximately 8 km / sec ) and a sixth ( approximately 5 km / s ) of the ground speed of 30 km / s This was too low for Michelson and his contemporaries to be seriously considered as a positive result, and it was thus the most famous experiment with zero result. Instead show the speed relative to the stationary ether, it did not show the expected effects, such as exists at all is not the " aether wind ". Relative movement between the earth and the ether could not be detected. The experiment itself was carried out from 8 to 12 July 1887 which was measured at a total of 36 turns. On the country's goals of repetitions at different seasons (and thus different relative velocities of the earth against the "ether" ) both waived.

After that Michelson other research turned to and used his interferometer for length measurements. [Footnote 1 ] A further improved experiment was conducted in 1904 by Morley and Dayton Miller, again by extension of the light path, this time at about 32 m. [Footnote 2 ] Even Michelson led the experiment several times in a more refined form of after Miller, who experimented at a higher altitude at Mount Wilson Observatory in California, had claimed in 1925, but have not yet achieved a positive result. Again Michelson's results were negative. Michelson himself was just as Morley never convinced until his death in 1931 completely from the non-existence of an ether. 1930 Georg Joos could increase the ratio to expected 0.75 of the fringe width and an observed upper limit of 0.002. The experiments of Joos and KK Illingworth took place at Zeiss Jena from 1927 to 1930 and used an effective arm length of 30 m. Improved experiments of the Michelson -Morley type to be carried out today ( see "Further experiments").