michelson–morley experiment

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Figure 1. Michelson and Morley's interferometric setup, mounted on a stone slab that floats in an annular trough of mercury. Michelson–Morley experiment From Wikipedia, the free encyclopedia The Michelson–Morley experiment was performed over the spring and summer of 1887 by Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year. [1] It compared the speed of light in perpendicular directions, in an attempt to detect the relative motion of matter through the stationary luminiferous aether ("aether wind"). The negative results are generally considered to be the first strong evidence against the then-prevalent aether theory, and initiated a line of research that eventually led to special relativity, in which the stationary aether concept has no role. [A 1] The experiment has been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution". [A 2] Michelson–Morley type experiments have been repeated many times with steadily increasing sensitivity. These include experiments from 1902 to 1905, and a series of experiments in the 1920s. In addition, recent resonator experiments have confirmed the absence of any aether wind at the 10 −17 level. [2][3] Together with the Ives– Stilwell and Kennedy–Thorndike experiments, the Michelson–Morley experiment forms one of the fundamental tests of special relativity theory. [A 3] Contents 1 Detecting the aether 2 1881 and 1887 experiments 2.1 Michelson experiment (1881) 2.2 Michelson–Morley experiment (1887) 2.3 Most famous "failed" experiment 3 Light path analysis and consequences 3.1 Observer resting in the aether 3.2 Observer comoving with the interferometer 3.3 Mirror reflection 3.4 Length contraction and Lorentz transformation 3.5 Special relativity 3.6 Incorrect alternatives 4 Subsequent experiments 5 Recent experiments 5.1 Optical tests 5.2 Recent optical resonator experiments 5.3 Other tests of Lorentz invariance 6 See also 7 References 7.1 Experiments 7.2 Notes 7.3 Bibliography ("A" series references) 8 External links

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Michelson–Morley Experiment


Page 1: Michelson–Morley Experiment

Figure 1. Michelson and Morley's interferometricsetup, mounted on a stone slab that floats in anannular trough of mercury.

Michelson–Morley experimentFrom Wikipedia, the free encyclopedia

The Michelson–Morley experiment was performed overthe spring and summer of 1887 by Albert A. Michelsonand Edward W. Morley at what is now Case WesternReserve University in Cleveland, Ohio, and published inNovember of the same year.[1] It compared the speed oflight in perpendicular directions, in an attempt to detect therelative motion of matter through the stationaryluminiferous aether ("aether wind"). The negative resultsare generally considered to be the first strong evidenceagainst the then-prevalent aether theory, and initiated a lineof research that eventually led to special relativity, inwhich the stationary aether concept has no role.[A 1] Theexperiment has been referred to as "the moving-off pointfor the theoretical aspects of the Second ScientificRevolution".[A 2]

Michelson–Morley type experiments have been repeated many times with steadily increasing sensitivity. Theseinclude experiments from 1902 to 1905, and a series of experiments in the 1920s. In addition, recent resonatorexperiments have confirmed the absence of any aether wind at the 10−17 level.[2][3] Together with the Ives–Stilwell and Kennedy–Thorndike experiments, the Michelson–Morley experiment forms one of thefundamental tests of special relativity theory.[A 3]

Contents1 Detecting the aether2 1881 and 1887 experiments

2.1 Michelson experiment (1881)2.2 Michelson–Morley experiment (1887)2.3 Most famous "failed" experiment

3 Light path analysis and consequences3.1 Observer resting in the aether3.2 Observer comoving with the interferometer3.3 Mirror reflection3.4 Length contraction and Lorentz transformation3.5 Special relativity3.6 Incorrect alternatives

4 Subsequent experiments5 Recent experiments

5.1 Optical tests5.2 Recent optical resonator experiments5.3 Other tests of Lorentz invariance

6 See also7 References

7.1 Experiments7.2 Notes7.3 Bibliography ("A" series references)

8 External links

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Figure 2. A depiction of the concept of the "aetherwind"

Detecting the aetherPhysics theories of the late 19th century assumed that just as surface water waves must have a supportingsubstance, i.e. a "medium", to move across (in this case water), and audible sound requires a medium totransmit its wave motions (such as air or water), so light must also require a medium, the "luminiferousaether", to transmit its wave motions. Because light can travel through a vacuum, it was assumed that even avacuum must be filled with aether. Because the speed of light is so large, and because material bodies passthrough the aether without obvious friction or drag, it was assumed to have a highly unusual combination ofproperties. Designing experiments to test the properties of the aether was a high priority of 19th centuryphysics.[A 4]:411ff

Earth orbits around the Sun at a speed of around 30 km/s (18.75 mi/s) or over 108,000 km/h (67,500 mi/hr).The Earth is in motion, so two main possibilities were considered: (1) The aether is stationary and onlypartially dragged by Earth (proposed by Augustin-Jean Fresnel in 1818), or (2) the aether is completelydragged by Earth and thus shares its motion at Earth's surface (proposed by Sir George Stokes, 1st Baronet in1844).[A 5] In addition, James Clerk Maxwell (1865) recognized the electromagnetic nature of light anddeveloped what are now called Maxwell's equations, but these equations were still interpreted as describing themotion of waves through an aether, whose state of motion was unknown. Eventually, Fresnel's idea of an(almost) stationary aether was preferred because it appeared to be confirmed by the Fizeau experiment (1851)and the aberration of star light.[A 5]

According to this hypothesis, Earth and the aether are inrelative motion, implying that a so-called "aether wind"(Fig. 2) should exist. Although it would be possible, intheory, for the Earth's motion to match that of the aether atone moment in time, it was not possible for the Earth toremain at rest with respect to the aether at all times,because of the variation in both the direction and the speedof the motion. At any given point on the Earth's surface,the magnitude and direction of the wind would vary withtime of day and season. By analyzing the return speed oflight in different directions at various different times, itwas thought to be possible to measure the motion of theEarth relative to the aether. The expected relativedifference in the measured speed of light was quite small,given that the velocity of the Earth in its orbit around theSun has a magnitude of about one hundredth of one percentof the speed of light.[A 4]:417ff

During the mid-19th century, measurements of aether wind effects of first order i.e. effects proportional to v/c(v being Earth's velocity, c the speed of light) were thought to be possible, but no direct measurement of thespeed of light was possible with the accuracy required. For instance, the Fizeau–Foucault apparatus couldmeasure the speed of light to perhaps 5% accuracy, which was quite inadequate for measuring directly a first-order 0.01% change in the speed of light. A number of physicists therefore attempted to make measurements ofindirect first-order effects not of the speed of light itself, but of variations in the speed of light (see First orderaether-drift experiments). The Hoek experiment, for example, was intended to detect interferometric fringeshifts due to speed differences of oppositely propagating light waves through water at rest. The results of suchexperiments were all negative.[A 6] This could be explained by using Fresnel's dragging coefficient, accordingto which the aether and thus light are partially dragged by moving matter. Partial aether-dragging would thwartattempts to measure any first order change in the speed of light. As pointed out by Maxwell (1878), only

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Figure 3. Michelson's 1881 interferometer.Although ultimately it proved incapable ofdistinguishing between differing theories of aether-dragging, its construction provided importantlessons for the design of Michelson and Morley's1887 instrument.[note 1]

Wikisource has originaltext related to this article:

The Relative Motion ofthe Earth and theLuminiferous Ether(1881)

Wikisource has originaltext related to this article:

On the Relative Motionof the Earth and theLuminiferous Ether

experimental arrangements capable of measuring second order effects would have any hope of detecting aetherdrift, i.e. effects proportional to v2/c2.[A 7][A 8] Existing experimental setups, however, were not sensitiveenough to measure effects of that size.

1881 and 1887 experiments

Michelson experiment (1881)

Michelson had a solution to the problem of how toconstruct a device sufficiently accurate to detect aetherflow. In 1877, while teaching at his alma mater, the UnitedStates Naval Academy in Annapolis, Michelson conductedhis first known light speed experiments as a part of aclassroom demonstration. In 1881, he left active U.S.Naval service while in Germany concluding his studies. Inthat year, Michelson used a prototype experimental deviceto make several more measurements.

The device he designed, later known as a Michelsoninterferometer, sent yellow light from a sodium flame (foralignment), or white light (for the actual observations),through a half-silvered mirror that was used to split it intotwo beams traveling at right angles to one another. Afterleaving the splitter, the beams traveled out to the ends oflong arms where they were reflected back into the middle by smallmirrors. They then recombined on the far side of the splitter in aneyepiece, producing a pattern of constructive and destructiveinterference whose transverse displacement would depend on therelative time it takes light to transit the longitudinal vs. the transversearms. If the Earth is traveling through an aether medium, a beamreflecting back and forth parallel to the flow of aether would takelonger than a beam reflecting perpendicular to the aether because the time gained from traveling downwind isless than that lost traveling upwind. Michelson expected that the Earth's motion would produce a fringe shiftequal to .04 fringes—that is, of the separation between areas of the same intensity. He did not observe theexpected shift; the greatest average deviation that he measured (in the northwest direction) was only 0.018fringes; most of his measurements were much less. His conclusion was that Fresnel's hypothesis of a stationaryaether with partial aether dragging would have to be rejected, and thus he confirmed Stokes' hypothesis ofcomplete aether dragging.[4]

However, Alfred Potier (and later Hendrik Lorentz) pointed out to Michelson that he had made an error ofcalculation, and that the expected fringe shift should have been only 0.02 fringes. Michelson's apparatus wassubject to experimental errors far too large to say anything conclusive about the aether wind. Definitivemeasurement of the aether wind would require an experiment with greater accuracy and better controls than theoriginal. Nevertheless the prototype was successful in demonstrating that the basic method wasfeasible.[A 5][A 9]

Michelson–Morley experiment (1887)

In 1885, Michelson began a collaboration with Edward Morley,spending considerable time and money to confirm with higher accuracyFizeau's 1851 experiment on Fresnel's drag coefficient,[5] to improve onMichelson's 1881 experiment,[1] and to establish the wavelength of

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Figure 5. This figure illustrates the folded light pathused in the Michelson–Morley interferometer thatenabled a path length of 11 m. a is the light source,an oil lamp. b is a beam splitter. c is a compensatingplate so that both the reflected and transmittedbeams travel through the same amount of glass(important since experiments were run with whitelight which has an extremely short coherence lengthrequiring precise matching of optical path lengthsfor fringes to be visible; monochromatic sodiumlight was used only for initial alignment[4][note 2]).d, d' and e are mirrors. e' is a fine adjustmentmirror. f is a telescope.

Figure 6. Fringe pattern producedwith a Michelson interferometerusing white light. As configured here,the central fringe is white rather thanblack.

light as a standard of length.[6][7] At this time Michelson was professorof physics at the Case School of Applied Science, andMorley was professor of chemistry at Western ReserveUniversity (WRU), which shared a campus with the CaseSchool on the eastern edge of Cleveland. Michelsonsuffered a nervous breakdown in September 1885, fromwhich he recovered by October 1885. Morley ascribed thisbreakdown to the intense work of Michelson during thepreparation of the experiments. In 1886, Michelson andMorley successfully confirmed Fresnel's drag coefficient –this result was also considered as a confirmation of thestationary aether concept.[A 1]

This result strengthened their hope of finding the aetherwind. Michelson and Morley created an improved versionof the Michelson experiment with more than enoughaccuracy to detect this hypothetical effect. The experimentwas performed in several periods of concentratedobservations between April and July 1887, in the basementof Adelbert Dormitory of WRU (later renamed Pierce Hall,demolished in 1962).[A 10][A 11]

As shown in Fig. 5, the light was repeatedly reflected backand forth along the arms of the interferometer, increasingthe path length to 11 m. At this length, the drift would beabout 0.4 fringes. To make that easily detectable, theapparatus was assembled in a closed room in the basementof the heavy stone dormitory, eliminating most thermal andvibrational effects. Vibrations were further reduced bybuilding the apparatus on top of a large block of sandstone(Fig. 1), about a foot thick and five feet square, which wasthen floated in an annular trough of mercury. Theyestimated that effects of about 1/100 of a fringe would bedetectable.

Michelson and Morley and other early experimentalistsusing interferometric techniques in an attempt to measure the propertiesof the luminiferous aether, used (partially) monochromatic light onlyfor initially setting up their equipment, always switching to white lightfor the actual measurements. The reason is that measurements wererecorded visually. Purely monochromatic light would result in auniform fringe pattern. Lacking modern means of environmentaltemperature control, experimentalists struggled with continual fringedrift even though the interferometer might be set up in a basement.Because the fringes would occasionally disappear due to vibrationscaused by passing horse traffic, distant thunderstorms and the like, anobserver could easily "get lost" when the fringes returned to visibility.The advantages of white light, which produced a distinctive coloredfringe pattern, far outweighed the difficulties of aligning the apparatusdue to its low coherence length. As Dayton Miller wrote, "White lightfringes were chosen for the observations because they consist of a smallgroup of fringes having a central, sharply defined black fringe which

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Figure 7. Michelson and Morley's results. Theupper solid line is the curve for their observations atnoon, and the lower solid line is that for theirevening observations. Note that the theoreticalcurves and the observed curves are not plotted atthe same scale: the dotted curves, in fact, representonly one-eighth of the theoretical displacements.

forms a permanent zero reference mark for all readings."[A 12][note 3] Use of partially monochromatic light(yellow sodium light) during initial alignment enabled the researchers to locate the position of equal pathlength, more or less easily, before switching to white light.[note 4]

The mercury trough allowed the device to turn with close to zero friction, so that once having given thesandstone block a single push it would slowly rotate through the entire range of possible angles to the "aetherwind," while measurements were continuously observed by looking through the eyepiece. The hypothesis ofaether drift implies that because one of the arms would inevitably turn into the direction of the wind at thesame time that another arm was turning perpendicularly to the wind, an effect should be noticeable even over aperiod of minutes.

The expectation was that the effect would be graphable as a sine wave with two peaks and two troughs perrotation of the device. This result could have been expected because during each full rotation, each arm wouldbe parallel to the wind twice (facing into and away from the wind giving identical readings) and perpendicularto the wind twice. Additionally, due to the Earth's rotation, the wind would be expected to show periodicchanges in direction and magnitude during the course of a sidereal day.

Because of the motion of the Earth around the Sun, the measured data were also expected to show annualvariations.

Most famous "failed" experiment

After all this thought and preparation, the experimentbecame what has been called the most famous failedexperiment in history.[A 13] Instead of providing insightinto the properties of the aether, Michelson and Morley'sarticle in the American Journal of Science reported themeasurement to be as small as one-fortieth of the expecteddisplacement (Fig. 7), but "since the displacement isproportional to the square of the velocity" they concludedthat the measured velocity was "probably less than one-sixth" of the expected velocity of the Earth's motion inorbit and "certainly less than one-fourth."[1] (Afterward,Michelson and Morley ceased their aether driftmeasurements and started to use their newly developedtechnique to establish the wavelength of light as a standardof length.[6][7]) Although this small "velocity" wasmeasured, it was considered far too small to be used asevidence of speed relative to the aether, and it wasunderstood to be within the range of an experimental error that would allow the speed to actually be zero.[A 1]

For instance, Michelson wrote about the "decidedly negative result" in a letter to Lord Rayleigh in August1887:[A 14]

The Experiments on the relative motion of the earth and ether have been completed and the resultdecidedly negative. The expected deviation of the interference fringes from the zero should havebeen 0.40 of a fringe – the maximum displacement was 0.02 and the average much less than 0.01– and then not in the right place. As displacement is proportional to squares of the relativevelocities it follows that if the ether does slip past the relative velocity is less than one sixth of theearth’s velocity.

— Albert Abraham Michelson, 1887

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Figure 4. Expected differential phase shift betweenlight traveling the longitudinal versus the transversearms of the Michelson–Morley apparatus

From the standpoint of the then current aether models, the experimental results were conflicting. The Fizeauexperiment and its 1886 repetition by Michelson and Morley apparently confirmed the stationary aether withpartial aether dragging, and refuted complete aether dragging. On the other hand, the much more preciseMichelson–Morley experiment (1887) apparently confirmed complete aether dragging and refuted thestationary aether.[A 5] In addition, the Michelson–Morley null result was further substantiated by the nullresults of other second-order experiments of different kind, namely the Trouton–Noble experiment (1903) andthe Experiments of Rayleigh and Brace (1902–1904). These problems and their solution led to thedevelopment of the Lorentz transformation and special relativity.

Light path analysis and consequences

Observer resting in the aether

The beam travel time in the longitudinal direction can bederived as follows:[A 15] Light is sent from the source andpropagates with the speed of light in the aether. It passesthrough the half-silvered mirror at the origin at .The reflecting mirror is at that moment at distance (thelength of the interferometer arm) and is moving withvelocity . The beam hits the mirror at time and thustravels the distance . At this time, the mirror hastraveled the distance . Thus andconsequently the travel time . The sameconsideration applies to the backward journey, with thesign of reversed, resulting in and

. The total travel time is:

Michelson obtained this expression correctly in 1881,however, in transverse direction he obtained the incorrectexpression


because he overlooked that the aether wind also affects the transverse beam travel time. This was corrected byAlfred Potier (1882) and Lorentz (1886). The derivation in the transverse direction can be given as follows(analoguous to the derivation of time dilation using a light clock): The beam is propagating at the speed oflight and hits the mirror at time , traveling the distance . At the same time, the mirror has traveled thedistance in x direction. So in order to hit the mirror, the travel path of the beam is in the y direction(assuming equal-length arms) and in the x direction. This inclined travel path follows from thetransformation from the interferometer rest frame to the aether rest frame. Therefore the Pythagorean theoremgives the actual beam travel distance of . Thus and consequently the travel time

, which is the same for the backward journey. The total travel time is:

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The time difference between Tl and Tt before rotation is given by[A 16]


By multiplying with c, the corresponding length difference before rotation is


and after rotation


Dividing by the wavelength λ, the fringe shift n is found:


Since L≈11 meters and λ≈500 nanometers, the expected fringe shift n was ≈0.44. So the result would be adelay in one of the light beams that could be detected when the beams were recombined through interference.Any slight change in the spent time would then be observed as a shift in the positions of the interferencefringes. The negative result led Michelson to the conclusion that there is no measurable aether drift.[1]

Observer comoving with the interferometer

If the same situation is described from the view of an observer co-moving with the interferometer, then theeffect of aether wind is similar to the effect experienced by a swimmer, who tries to move with velocity against a river flowing with velocity .[A 17]

In the longitudinal direction the swimmer first moves upstream, so his velocity is diminished due to the riverflow to . On his way back moving downstream, his velocity is increased to . This gives the beamtravel times and as mentioned above.

In the transverse direction, the swimmer has to compensate for the river flow by moving at a certain angleagainst the flow direction, in order to sustain his exact transverse direction of motion and to reach the otherside of the river at the correct location. This diminishes his speed to , and gives the beam traveltime as mentioned above.

Mirror reflection

The classical analysis predicted a relative phase shift between the longitudinal and transverse beams which inMichelson and Morley's apparatus should have been readily measurable. What is not often appreciated (sincethere was no means of measuring it), is that motion through the hypothetical aether should also have caused thetwo beams to diverge as they emerged from the interferometer by about 10−8 radians.[A 18]

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For an apparatus in motion, the classical analysis requires that the beam-splitting mirror be slightly offset froman exact 45° if the longitudinal and transverse beams are to emerge from the apparatus exactly superimposed.In the relativistic analysis, Lorentz-contraction of the beam splitter in the direction of motion causes it tobecome more perpendicular by precisely the amount necessary to compensate for the angle discrepancy of thetwo beams.[A 18]

Length contraction and Lorentz transformation

Further information: History of special relativity and History of Lorentz transformations

A first step to explaining the Michelson and Morley experiment's null result was found in the FitzGerald–Lorentz contraction hypothesis, now simply called length contraction or Lorentz contraction, first proposed byGeorge FitzGerald (1889) and Hendrik Lorentz (1892).[A 19] According to this law all objects physicallycontract by along the line of motion (originally thought to be relative to the aether),

being the Lorentz factor. This hypothesis was partly motivated by Oliver Heaviside'sdiscovery in 1888, that electrostatic fields are contracting in the line of motion. But since there was no reasonat that time to assume that binding forces in matter are of electric origin, length contraction of matter in motionwith respect to the aether was considered an Ad hoc hypothesis.[A 9]

If length contraction of is inserted into the above formula for , then the light propagation time in thelongitudinal direction becomes equal to that in the transverse direction:

However, length contraction is only a special case of the more general relation, according to which thetransverse length is larger than the longitudinal length by the ratio . This can be achieved in many ways. If

is the moving longitudinal length and the moving transverse length, being the rest lengths,

then it is given:[A 20]


can be arbitrarily chosen, so there are infinitely many combinations to explain the Michelson–Morley nullresult. For instance, if the relativistic value of length contraction of occurs, but if thenno length contraction but an elongation of occurs. This hypothesis was later extended by Joseph Larmor(1897), Lorentz (1904) and Henri Poincaré (1905), who developed the complete Lorentz transformationincluding time dilation in order to explain the Trouton–Noble experiment, the Experiments of Rayleigh andBrace, and Kaufmann's experiments. It has the form

It remained to define the value of , which was shown by Lorentz (1904) to be unity.[A 20] In general, Poincaré(1905)[A 21] demonstrated that only allows this transformation to form a group, so it is the only choicecompatible with the principle of relativity, i.e. making the stationary aether undetectable. Given this, lengthcontraction and time dilation obtain their exact relativistic values.

Special relativity

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Albert Einstein formulated the theory of special relativity by 1905, deriving the Lorentz transformation andthus length contraction and time dilation from the relativity postulate and the constancy of the speed of light,thus removing the ad hoc character from the contraction hypothesis. Einstein emphasized the kinematicfoundation of the theory and the modification of the notion of space and time, with the stationary aether nolonger playing any role in his theory. He also pointed out the group character of the transformation. Einsteinwas motivated by Maxwell's theory of electromagnetism (in the form as it was given by Lorentz in 1895) andthe lack of evidence for the luminiferous aether.[A 22]

This allows a more elegant and intuitive explanation of the Michelson-Morley null result. In a comoving framethe null result is self-evident, since the apparatus can be considered as at rest in accordance with the relativityprinciple, thus the beam travel times are the same. In a frame relative to which the apparatus is moving, thesame reasoning applies as described above in "Length contraction and Lorentz transformation", except theword "aether" has to be replaced by "non-comoving inertial frame". Einstein wrote in 1916:[A 23]

Although the estimated difference between these two times is exceedingly small, Michelson andMorley performed an experiment involving interference in which this difference should have beenclearly detectable. But the experiment gave a negative result — a fact very perplexing tophysicists. Lorentz and FitzGerald rescued the theory from this difficulty by assuming that themotion of the body relative to the æther produces a contraction of the body in the direction ofmotion, the amount of contraction being just sufficient to compensate for the difference in timementioned above. Comparison with the discussion in Section 11 shows that also from thestandpoint of the theory of relativity this solution of the difficulty was the right one. But on thebasis of the theory of relativity the method of interpretation is incomparably more satisfactory.According to this theory there is no such thing as a "specially favoured" (unique) co-ordinatesystem to occasion the introduction of the æther-idea, and hence there can be no æther-drift, norany experiment with which to demonstrate it. Here the contraction of moving bodies follows fromthe two fundamental principles of the theory, without the introduction of particular hypotheses;and as the prime factor involved in this contraction we find, not the motion in itself, to which wecannot attach any meaning, but the motion with respect to the body of reference chosen in theparticular case in point. Thus for a co-ordinate system moving with the earth the mirror system ofMichelson and Morley is not shortened, but it is shortened for a co-ordinate system which is at restrelatively to the sun.

— Albert Einstein, 1916

The extent to which the null result of the Michelson–Morley experiment influenced Einstein is disputed.Alluding to some statements of Einstein, many historians argue that it played no significant role in his path tospecial relativity,[A 24][A 25] while other statements of Einstein probably suggest that he was influenced byit.[A 26] In any case, the null result of the Michelson–Morley experiment helped the notion of the constancy ofthe speed of light gain widespread and rapid acceptance.[A 24]

It was later shown by Howard Percy Robertson (1949) and others[A 3][A 27] (see Robertson–Mansouri–Sexl testtheory), that it is possible to derive the Lorentz transformation entirely from the combination of threeexperiments. First, the Michelson–Morley experiment showed that the speed of light is independent of theorientation of the apparatus, establishing the relationship between longitudinal (β) and transverse (δ) lengths.Then in 1932, Roy Kennedy and Edward Thorndike modified the Michelson–Morley experiment by makingthe path lengths of the split beam unequal, with one arm being very short.[8] The Kennedy–Thorndikeexperiment took place for many months as the Earth moved around the sun. Their negative result showed thatthe speed of light is independent of the velocity of the apparatus in different inertial frames. In addition itestablished that besides length changes, corresponding time changes must also occur, i.e. it established therelationship between longitudinal lengths (β) and time changes (α). So both experiments do not provide theindividual values of these quantities. This uncertainty corresponds to the undefined factor as described

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above. It was clear due to theoretical reasons (the group character of the Lorentz transformation as required bythe relativity principle) that the individual values of length contraction and time dilation must assume theirexact relativistic form. But a direct measurement of one of these quantities was still desirable to confirm thetheoretical results. This was achieved by the Ives–Stilwell experiment (1938), measuring α in accordance withtime dilation. Combining this value for α with the Kennedy–Thorndike null result shows that β must assumethe value of relativistic length contraction. Combining β with the Michelson–Morley null result shows that δmust be zero. Therefore, the Lorentz transformation with is an unavoidable consequence of thecombination of these three experiments.[A 3]

Special relativity is generally considered the solution to all negative aether drift (or isotropy of the speed oflight) measurements, including the Michelson–Morley null result. Many high precision measurements havebeen conducted as tests of special relativity and modern searches for Lorentz violation in the photon, electron,nucleon, or neutrino sector, all of them confirming relativity.

Incorrect alternatives

As mentioned above, Michelson initially believed that his experiment would confirm Stokes' theory, accordingto which the aether was fully dragged in the vicinity of the earth (see Aether drag hypothesis). However,complete aether drag contradicts the observed aberration of light and was contradicted by other experiments aswell. In addition, Lorentz showed in 1886 that Stokes's attempt to explain aberration is contradictory.[A 5][A 4]

Furthermore, the assumption that the aether is not carried in the vicinity, but only within matter, was veryproblematic as shown by the Hammar experiment (1935). Hammar directed one leg of his interferometerthrough a heavy metal pipe plugged with lead. If aether were dragged by mass, it was theorized that the massof the sealed metal pipe would have been enough to cause a visible effect. Once again, no effect was seen, soaether-drag theories are considered to be disproven.

Walter Ritz's Emission theory (or ballistic theory), was also consistent with the results of the experiment, notrequiring aether. The theory postulates that light has always the same velocity in respect to the source.[A 28]

However de Sitter noted that emitter theory predicted several optical effects that were not seen in observationsof binary stars in which the light from the two stars could be measured in a spectrometer. If emission theorywere correct, the light from the stars should experience unusual fringe shifting due to the velocity of the starsbeing added to the speed of the light, but no such effect could be seen. It was later shown by J. G. Fox that theoriginal de Sitter experiments were flawed due to extinction,[9] but in 1977 Brecher observed X-rays frombinary star systems with similar null results.[10] Also terrestrial tests using particle accelerators have been madethat were inconsistent with source dependence of the speed of light.[11] In addition, Emission theory might failthe Ives–Stilwell experiment, but Fox questioned that as well.

Subsequent experimentsAlthough Michelson and Morley went on to different experiments after their first publication in 1887, bothremained active in the field. Other versions of the experiment were carried out with increasingsophistication.[A 29][A 30] Morley was not convinced of his own results, and went on to conduct additionalexperiments with Dayton Miller from 1902 to 1904. Again, the result was negative within the margins oferror.[12][13]

Miller worked on increasingly larger interferometers, culminating in one with a 32 m (effective) arm lengththat he tried at various sites including on top of a mountain at the Mount Wilson observatory. To avoid thepossibility of the aether wind being blocked by solid walls, his mountaintop observations used a special shedwith thin walls, mainly of canvas. From noisy, irregular data, he consistently extracted a small positive signalthat varied with each rotation of the device, with the sidereal day, and on a yearly basis. His measurements inthe 1920s amounted to approximately 10 km/s instead of the nearly 30 km/s expected from the Earth's orbital

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Figure 8. Simulation of theKennedy/Illingworth refinement of theMichelson–Morley experiment. (a)Michelson–Morley interference pattern inmonochromatic mercury light, with a darkfringe precisely centered on the screen. (b)The fringes have been shifted to the left by1/100 of the fringe spacing. It is extremelydifficult to see any difference between thisfigure and the one above. (c) A small stepin one mirror causes two views of the samefringes to be spaced 1/20 of the fringespacing to the left and to the right of thestep. (d) A telescope has been set to viewonly the central dark band around themirror step. Note the symmetricalbrightening about the center line. (e) Thetwo sets of fringes have been shifted to theleft by 1/100 of the fringe spacing. Anabrupt discontinuity in luminosity isvisible across the step.

motion alone. He remained convinced this was due to partialentrainment or aether dragging, though he did not attempt adetailed explanation. He ignored critiques demonstrating theinconsistency of his results and the refutation by the Hammarexperiment.[A 31][note 5] Miller's findings were consideredimportant at the time, and were discussed by Michelson, Lorentzand others at a meeting reported in 1928.[A 32] There was generalagreement that more experimentation was needed to check Miller'sresults. Miller later built a non-magnetic device to eliminatemagnetostriction, while Michelson built one of non-expandingInvar to eliminate any remaining thermal effects. Otherexperimenters from around the world increased accuracy,eliminated possible side effects, or both. So far, no one has beenable to replicate Miller's results, and modern experimentalaccuracies have ruled them out.[A 33] Roberts (2006) has pointedout that the primitive data reduction techniques used by Miller andother early experimenters, including Michelson and Morley, werecapable of creating apparent periodic signals even when noneexisted in the actual data. After reanalyzing Miller's original datausing modern techniques of quantitative error analysis, Robertsfound Miller's apparent signals to be statisticallyinsignificant.[A 34]

Using a special optical arrangement involving a 1/20 wave step inone mirror, Roy J. Kennedy (1926) and K.K. Illingworth (1927)(Fig. 8) converted the task of detecting fringe shifts from therelatively insensitive one of estimating their lateral displacementsto the considerably more sensitive task of adjusting the lightintensity on both sides of a sharp boundary for equalluminance.[14][15] If they observed unequal illumination on eitherside of the step, such as in Fig. 8e, they would add or removecalibrated weights from the interferometer until both sides of thestep were once again evenly illuminated, as in Fig. 8d. The numberof weights added or removed provided a measure of the fringeshift. Different observers could detect changes as little as 1/300 to 1/1500 of a fringe. Kennedy also carried outan experiment at Mount Wilson, finding only about 1/10 the drift measured by Miller and no seasonaleffects.[A 32]

In 1930, Georg Joos conducted an experiment using an automated interferometer with 21-meter-long armsforged from pressed quartz having very low thermal coefficient of expansion, that took continuousphotographic strip recordings of the fringes through dozens of revolutions of the apparatus. Displacements of1/1000 of a fringe could be measured on the photographic plates. No periodic fringe displacements were found,placing an upper limit to the aether wind of 1.5 km/s.[16]

In the table below, the expected values are related to the relative speed between Earth and Sun of 30 km/s.With respect to the speed of the solar system around the galactic center of about 220 km/s, or the speed of thesolar system relative to the CMB rest frame of about 368 km/s, the null results of those experiments are evenmore obvious.

Page 12: Michelson–Morley Experiment

Name Location YearArm










Michelson[4] Potsdam 1881 1.2 0.04 ≤ 0.02 2 ∼20 km/s 0.02 yes

Michelson andMorley[1] Cleveland 1887 11.0 0.4 < 0.02

or ≤ 0.01 40 ∼ 4–8 km/s 0.01 yes

Morley andMiller[12][13] Cleveland 1902–

1904 32.2 1.13 ≤ 0.015 80 ∼3.5 km/s 0.015 yes

Miller[17] Mt. Wilson 1921 32.0 1.12 ≤ 0.08 15 ∼ 8–10 km/s unclear unclear

Miller[17] Cleveland 1923–1924 32.0 1.12 ≤ 0.03 40 ∼ 5 km/s 0.03 yes

Miller(sunlight)[17] Cleveland 1924 32.0 1.12 ≤ 0.014 80 ∼ 3 km/s 0.014 yes

Tomaschek(star light)[18] Heidelberg 1924 8.6 0.3 ≤ 0.02 15 ∼ 7 km/s 0.02 yes

Miller[17][A 12] Mt. Wilson 1925–1926 32.0 1.12 ≤ 0.088 13 ∼ 8–

10 km/s unclear unclear

Kennedy[14] Pasadena/Mt.Wilson 1926 2.0 0.07 ≤ 0.002 35 ∼ 5 km/s 0.002 yes

Illingworth[15] Pasadena 1927 2.0 0.07 ≤ 0.0004 175 ∼ 2 km/s 0.0004 yesPiccard &Stahel[19]

with aBalloon 1926 2.8 0.13 ≤ 0.006 20 ∼ 7 km/s 0.006 yes

Piccard &Stahel[20] Brussels 1927 2.8 0.13 ≤ 0.0002 185 ∼

2.5 km/s 0.0007 yes

Piccard &Stahel[21] Rigi 1927 2.8 0.13 ≤ 0.0003 185 ∼

2.5 km/s 0.0007 yes

Michelson etal.[22] Mt. Wilson 1929 25.9 0.9 ≤ 0.01 90 ∼ 3 km/s 0.01 yes

Joos[16] Jena 1930 21.0 0.75 ≤ 0.002 375 ∼1.5 km/s 0.002 yes

Recent experiments

Optical tests

Optical tests of the isotropy of the speed of light became commonplace.[A 35] New technologies, including theuse of lasers and masers, have significantly improved measurement precision. (In the following table, onlyEssen (1955), Jaseja (1964), and Shamir/Fox (1969) are experiments of Michelson–Morley type, i.e.comparing two perpendicular beams. The other optical experiments employed different methods.)

Page 13: Michelson–Morley Experiment

Figure 9. Michelson–Morley experimentwith cryogenic optical resonators of a formsuch as was used by Müller et al.(2003).[30]

Author Year Description Upperbounds

Louis Essen[23] 1955 The frequency of a rotating microwave cavity resonator is comparedwith that of a quartz clock ~3 km/s

Cedarholm etal.[24][25] 1958 Two ammonia masers were mounted on a rotating table, and their

beams were directed in opposite directions. ~30 m/s

Mössbauer rotorexperiments


In a series of experiments by different researchers, the frequencies ofgamma rays were observed using the Mössbauer effect. ~3–4 m/s

Jaseja et al.[26] 1964The frequencies of two He–Ne masers, mounted on a rotating table,were compared. Unlike Cedarholm et al., the masers were placedperpendicular to each other.

~30 m/s

Shamir and Fox[27] 1969 Both arms of the interferometer were contained in a transparent solid(plexiglass). The light source was a Helium–neon laser. ~7 km/s

Trimmer etal.[28][29] 1973

They searched for anisotropies of the speed of light behaving as thefirst and third of the Legendre polynomials. They used a triangleinterferometer, with one portion of the path in glass. (In comparison,the Michelson–Morley type experiments test the second Legendrepolynomial)[A 27]

~2.5 cm/s

Recent optical resonator experiments

Over the last several years, there has been a resurgence in interestin performing precise Michelson–Morley type experiments usinglasers, masers, cryogenic optical resonators, etc. This is in largepart due to predictions of quantum gravity that suggest that specialrelativity may be violated at scales accessible to experimentalstudy. The first of these highly accurate experiments wasconducted by Brillet & Hall (1979), in which they analyzed a laserfrequency stabilized to a resonance of a rotating optical Fabry–Pérot cavity. They set a limit on the anisotropy of the speed oflight resulting from the Earth's motions of Δc/c ≈ 10−15, where Δcis the difference between the speed of light in the x- and y-directions.[31]

As of 2009, optical and microwave resonator experiments haveimproved this limit to Δc/c ≈ 10−17. In some of them, the deviceswere rotated or remained stationary, and some were combined with the Kennedy–Thorndike experiment. Inparticular, Earth's direction and velocity (ca. 368 km/s) relative to the CMB rest frame are ordinarily used asreferences in these searches for anisotropies.

Page 14: Michelson–Morley Experiment

Author Year Description Δc/c

Wolf et al.[32] 2003

The frequency of a stationary cryogenic microwave oscillator, consistingof sapphire crystal operating in a whispering gallery mode, is comparedto a hydrogen maser whose frequency was compared to caesium andrubidium atomic fountain clocks. Changes during Earth's rotation havebeen searched for. Data between 2001–2002 was analyzed.

Müller et al.[30] 2003Two optical resonators constructed from crystalline sapphire, controllingthe frequencies of two Nd:YAG lasers, are set at right angles within ahelium cryostat. A frequency comparator measures the beat frequency ofthe combined outputs of the two resonators.

Wolf et al.[33] 2004 See Wolf et al. (2003). An active temperature control was implemented.Data between 2002–2003 was analyzed.

Wolf et al.[34] 2004 See Wolf et al. (2003). Data between 2002–2004 was analyzed.

Antonini et al.[35] 2005 Similar to Müller et al. (2003), though the apparatus itself was set intorotation. Data between 2002–2004 was analyzed.

Stanwix et al.[36] 2005Similar to Wolf et al. (2003). The frequency of two cryogenic oscillatorswas compared. In addition, the apparatus was set into rotation. Databetween 2004–2005 was analyzed.

Herrmann etal.[37] 2005

Similar to Müller et al. (2003). The frequencies of two optical Fabry–Pérot resonators cavities are compared – one cavity was continuouslyrotating while the other one was stationary oriented north–south. Databetween 2004–2005 was analyzed.

Stanwix et al.[38] 2006 See Stanwix et al. (2005). Data between 2004–2006 was analyzed.

Müller et al.[39] 2007

See Herrmann et al. (2005) and Stanwix et al. (2006). Data of bothgroups collected between 2004–2006 are combined and further analyzed.Since the experiments are located at difference continents, at Berlin andPerth respectively, the effects of both the rotation of the devicesthemselves and the rotation of Earth could be studied.

Eisele et al.[2] 2009The frequencies of a pair of orthogonal oriented optical standing wavecavities are compared. The cavities were interrogated by a Nd:YAGlaser. Data between 2007–2008 was analyzed.

Herrmann et al.[3] 2009Similar to Herrmann et al. (2005). The frequencies of a pair of rotating,orthogonal optical Fabry–Pérot resonators are compared. Thefrequencies of two Nd:YAG lasers are stabilized to resonances of theseresonators.

Other tests of Lorentz invariance

Further information: Modern searches for Lorentz violation

Examples of other experiments not based on the Michelson–Morley principle, i.e. non-optical isotropy testsachieving an even higher level of precision, are Clock comparison or Hughes–Drever experiments. In Drever's1961 experiment, 7Li nuclei in the ground state, which has total angular momentum J=3/2, were split into fourequally spaced levels by a magnetic field. Each transition between a pair of adjacent levels should emit aphoton of equal frequency, resulting in a single, sharp spectral line. However, since the nuclear wave functionsfor different MJ have different orientations in space relative to the magnetic field, any orientation dependence,whether from an aether wind or from a dependence on the large-scale distribution of mass in space (see Mach'sprinciple), would perturb the energy spacings between the four levels, resulting in an anomalous broadening orsplitting of the line. No such broadening was observed. Modern repeats of this kind of experiment haveprovided some of the most accurate confirmations of the principle of Lorentz invariance.[A 36]

Page 15: Michelson–Morley Experiment

Figure 10. 7Li-NMR spectrum of LiCl(1M) in D2O. The sharp, unsplit NMRline of this isotope of lithium isevidence for the isotropy of mass andspace.

See alsoMichelson–Morley AwardMoving magnet and conductor problemThe Light (Glass)



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Page 17: Michelson–Morley Experiment

1. Among other lessons was the need to control for vibration. Michelson (1881) wrote: "... owing to the extremesensitiveness of the instrument to vibrations, the work could not be carried on during the day. Next, the experimentwas tried at night. When the mirrors were placed half-way on the arms the fringes were visible, but their positioncould not be measured till after twelve o'clock, and then only at intervals. When the mirrors were moved out to theends of the arms, the fringes were only occasionally visible. It thus appeared that the experiments could not beperformed in Berlin, and the apparatus was accordingly removed to the Astrophysicalisches Observatorium inPotsdam ... Here, the fringes under ordinary circumstances were sufficiently quiet to measure, but so extraordinarilysensitive was the instrument that the stamping of the pavement, about 100 meters from the observatory, made thefringes disappear entirely!"

2. Michelson (1881) wrote: "... a sodium flame placed at a produced at once the interference bands. These could thenbe altered in width, position, or direction, by a slight movement of the plate b, and when they were of convenientwidth and of maximum sharpness, the sodium flame was removed and the lamp again substituted. The screw m wasthen slowly turned till the bands reappeared. They were then of course colored, except the central band, which wasnearly black."

3. If one uses a half-silvered mirror as the beam splitter, the reflected beam will undergo a different number of front-surface reflections than the transmitted beam. At each front-surface reflection, the light will undergo a phaseinversion. Because the two beams undergo a different number of phase inversions, when the path lengths of the twobeams match or differ by an integral number of wavelengths (e.g. 0, 1, 2 ...), there will be destructive interferenceand a weak signal at the detector. If the path lengths of the beams differ by a half-integral number of wavelengths(e.g., 0.5, 1.5, 2.5 ...), constructive interference will yield a strong signal. The results are opposite if a cube beam-splitter is used, because a cube beam-splitter makes no distinction between a front- and rear-surface reflection.

4. Sodium light produces a fringe pattern that displays cycles of fuzziness and sharpness that repeat every severalhundred fringes over a distance of approximately a millimeter. This pattern is due to the yellow sodium D line beingactually a doublet, the individual lines of which have a limited coherence length. After aligning the interferometer todisplay the centermost portion of the sharpest set of fringes, the researcher would switch to white light.

5. Thirring (1926) as well as Lorentz pointed out that Miller's results failed even the most basic criteria required tobelieve in their celestial origin, namely that the azimuth of supposed drift should exhibit daily variations consistentwith the source rotating about the celestial pole. Instead, while Miller's observations showed daily variations, theiroscillations in one set of experiments might center, say, around a northwest–southeast line.


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22. Einstein, A (June 30, 1905). "Zur Elektrodynamik bewegter Körper" (PDF). Annalen der Physik (in German) 17:890–921. Bibcode:1905AnP...322..891E. doi:10.1002/andp.19053221004. Retrieved 2009-11-27. Englishtranslation: Perrett, W; Jeffery, GB (tr.); Walker, J (ed.). "On the Electrodynamics of Moving Bodies". Fourmilab.Retrieved 2009-11-27.

23. Einstein A. (1916), Relativity: The Special and General Theory, New York: H. Holt and Company24. Stachel, John (1982), "Einstein and Michelson: the Context of Discovery and Context of Justification",

Astronomische Nachrichten 303 (1): 47–53, Bibcode:1982AN....303...47S, doi:10.1002/asna.210303011025. Michael Polanyi, Personal Knowledge: Towards a Post-Critical Philosophy, ISBN 0-226-67288-3, footnote

page 10–11: Einstein reports, via Dr N Balzas in response to Polanyi's query, that "The Michelson–Morleyexperiment had no role in the foundation of the theory." and "..the theory of relativity was not founded to explain itsoutcome at all."[1] (http://books.google.com/books?id=0Rtu8kCpvz4C&lpg=PP1&pg=PT19#v=onepage&q=&f=false)

26. Jeroen van Dongen (2009), "On the Role of the Michelson–Morley Experiment: Einstein in Chicago", Archive forHistory of Exact Sciences 63 (6): 655–663, arXiv:0908.1545, doi:10.1007/s00407-009-0050-5

27. Mansouri R., Sexl R.U. (1977). "A test theory of special relativity: III. Second-order tests". General. Relat. Gravit. 8(10): 809–814. Bibcode:1977GReGr...8..809M. doi:10.1007/BF00759585.

28. Norton, John D. (2004). "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905". Archive forHistory of Exact Sciences 59: 45–105. Bibcode:2004AHES...59...45N. doi:10.1007/s00407-004-0085-6.

29. Swenson, Loyd S. (1970). "The Michelson–Morley–Miller Experiments before and after 1905". Journal for theHistory of Astronomy 1 (2): 56–78. Bibcode:1970JHA.....1...56S. doi:10.1177/002182867000100108.

30. Swenson, Loyd S., Jr. (2013) [1972]. The Ethereal Aether: A History of the Michelson-Morley-Miller Aether-driftExperiments, 1880–1930. University of Texas Press. ISBN 978-0-292-75836-0.

31. Thirring, Hans (1926). "Prof. Miller's Ether Drift Experiments". Nature 118 (2959): 81–82.Bibcode:1926Natur.118...81T. doi:10.1038/118081c0.

32. Michelson, A. A.; et al. (1928). "Conference on the Michelson–Morley Experiment Held at Mount Wilson,February, 1927". Astrophysical Journal 68: 341–390. Bibcode:1928ApJ....68..341M. doi:10.1086/143148.

33. Shankland, Robert S.; et al. (1955). "New Analysis of the Interferometer Observations of Dayton C. Miller".Reviews of Modern Physics 27 (2): 167–178. Bibcode:1955RvMP...27..167S. doi:10.1103/RevModPhys.27.167.

34. Roberts, T.J. (2006). "An Explanation of Dayton Miller's Anomalous "Ether Drift" Result". Retrieved 7 May 2012.35. Relativity FAQ (2007): What is the experimental basis of Special Relativity?

(http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html)36. Haugan, Mark P.; Will, Clifford M. (May 1987). "Modern tests of special relativity" (PDF). Physics Today 40 (5):

67–76. Bibcode:1987PhT....40e..69H. doi:10.1063/1.881074. Retrieved 14 July 2012.

External links Media related to Michelson-Morley experiment at Wikimedia Commons Mathematical analysis of the Michelson Morley Experiment at Wikibooks

Roberts, T; Schleif, S; Dlugosz, JM (ed.) (2007). "What is the experimental basis of Special Relativity?".Usenet Physics FAQ. University of California, Riverside.

Page 19: Michelson–Morley Experiment

1. E.W. silversmith "Special Relativity", Nature magazine, vol. 322 [AUG. 1986], P.590: the filed exists, per theUnited States Air Force research, and it measured precisely as Michaelson and Morely predicted.

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