# Michelson–Morley experiment

Michelson–Morley experiment
Box plots based on data from the Michelson–Morley experiment

The Michelson–Morley experiment was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University in Cleveland, Ohio. Its results are generally considered to be the first strong evidence against the theory of a luminiferous ether and in favor of special relativity. The most immediate effect at the time was to put an end to Lord Kelvin's Vortex theory, which said that atoms were vortices in the ether.[1] The experiment has also been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution".[2] See also Tests of special relativity.

## Measuring ether

A depiction of the concept of the "aether wind"

Physics theories of the late 19th century postulated that, just as water waves must have a medium to move across (water), and audible sound waves require a medium to move through (such as air or water), so also light waves require a medium, the "luminiferous aether". Because light can travel through a vacuum, it was assumed that the vacuum must contain the medium of light. Because the speed of light is so great, designing an experiment to detect the presence and properties of this aether took considerable ingenuity.

Earth travels a tremendous distance in its orbit around the Sun, at a speed of around 30 km/s or over 108,000 km per hour. The Sun itself is travelling about the Galactic Center at even greater speeds, and there are other motions at higher levels of the structure of the universe. Since the Earth is in motion, it was expected that the flow of aether across the Earth should produce a detectable "aether wind". Although it would be possible, in theory, for the Earth's motion to match that of the aether at one moment in time, it was not possible for the Earth to remain at rest with respect to the aether at all times, because of the variation in both the direction and the speed of the motion.

At any given point on the Earth's surface, the magnitude and direction of the wind would vary with time of day and season. By analysing the return speed of light in different directions at various different times, it was thought to be possible to measure the motion of the Earth relative to the aether.

The expected difference in the measured speed of light was quite small, given that the velocity of the Earth in its orbit around the Sun was about one hundredth of one percent of the speed of light. A number of physicists had attempted to make this measurement during the mid-19th century, but the accuracy demanded was simply too great for existing experimental setups. For instance, the Fizeau–Foucault apparatus could measure the speed of light to perhaps 5% accuracy, not nearly enough to make any sort of aether wind measurement.

## The 1881 and 1887 experiments

Michelson had a solution to the problem of how to construct a device sufficiently accurate to detect aether flow. The device he designed, later known as an interferometer, sent a single source of white light through a half-silvered mirror that was used to split it into two beams travelling at right angles to one another. After leaving the splitter, the beams travelled out to the ends of long arms where they were reflected back into the middle on small mirrors. They then recombined on the far side of the splitter in an eyepiece, producing a pattern of constructive and destructive interference based on the spent time to transit the arms. If the Earth is traveling through an ether medium, a beam reflecting back and forth parallel to the flow of ether would take longer than a beam reflecting perpendicular to the ether because the time gained from traveling downwind is less than that lost traveling upwind. The result would be a delay 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 interference fringes. If the aether were stationary relative to the Sun, then the Earth's motion would produce a fringe shift 4% the size of a single fringe.

While teaching at his alma mater in 1877, the U.S. Naval Academy in Annapolis, Michelson conducted his first known successful light speed experiments as a part of a classroom demonstration. He left active U.S. Naval service in 1881, while he was in Germany concluding studies there. In that year and while there, Michelson had used an experimental device to make several more measurements, in which he noticed that the expected shift of 0.04 was not seen, and a smaller shift of (at most) about 0.02 was.[3] However his apparatus was a prototype, and had experimental errors far too large to say anything about the aether wind. For a measurement of the aether wind, a much more accurate and tightly controlled experiment would have to be carried out. The prototype was, however, successful in demonstrating that the basic method was feasible.

Though using a contemporary laser, this Michelson interferometer is the same in principle as those used in the original experiment.

Six years later he collaborated with Edward Morley, spending considerable time and money to create an improved version with more than enough accuracy to detect the drift.[4] At this time Michelson was professor of physics at the Case School of Applied Science, and Morley was professor of chemistry at Western Reserve University, which shared a campus with the Case School on the eastern edge of Cleveland. The experiment was performed in several periods of concentrated observations between April and July 1887, in Adelbert Dormitory of WRU (later renamed Pierce Hall, demolished in 1962).[5][6]

In their experiment, the light was repeatedly reflected back and forth along the arms of the interferometer, increasing the path length to 11 m. At this length, the drift would be about 0.4 fringes. To make that easily detectable, the apparatus was assembled in a closed room in the basement of the heavy stone dormitory, eliminating most thermal and vibrational effects. Vibrations were further reduced by building the apparatus on top of a large block of sandstone, about a foot thick and five feet square, which was then floated in an annular trough of mercury. They calculated that effects of about 1/100th of a fringe would be detectable.

The mercury pool allowed the device to be easily turned, so that given a single steady push it would slowly rotate through the entire range of possible angles to the "aether wind", while measurements were continuously observed by looking through the eyepiece. Even over a period of minutes some sort of effect would be noticed, since one of the arms would inevitably turn into the direction of the wind and the other away. Over longer periods day/night cycles or yearly cycles would also be easily measurable.

During each full rotation of the device, each arm would be parallel to the wind twice (facing into and away from the wind) and perpendicular to the wind twice. This effect would show readings in a sine wave formation with two peaks and two troughs. Additionally, if the wind were only from Earth's orbit around the Sun, the wind would fully change directions east/west during a 12-hour period. In this ideal conceptualization, the sine wave of day/night readings would be of opposing phase.

Because it was assumed that the motion of the Earth around the Sun would cause an additional component to the wind, the yearly cycles would be detectable as an alteration of the magnitude of the wind. An example of this effect is a helicopter flying forward. While hovering, a helicopter's blades would be measured as travelling around typically at 300 mph at the tips. However, if the helicopter is travelling forward at 150 mph, there are points where the tips of the blades are travelling through the air at 150 mph (downwind) and 450 mph (upwind). The same effect would cause the magnitude of an aether wind to decrease and increase on a yearly basis.

## Most famous "failed" experiment

### Subsequent experiments

Interference pattern produced with a Michelson Interferometer using a red laser.

After all this thought and preparation, the experiment became what might be called the most famous failed experiment to date.[7] Instead of providing insight into the properties of the aether, Michelson and Morley's article in the American Journal of Science reported the measurement to be as small as one-fortieth of the expected displacement but "since the displacement is proportional to the square of the velocity" they concluded that the measured velocity was "probably less than one-sixth" of the expected velocity of the Earth's motion in orbit and "certainly less than one-fourth." Although this small "velocity" was measured, it was considered far too small to be used as evidence of speed relative to the aether, and it was later said to be within the range of an experimental error that would allow the speed to actually be zero.

Although Michelson and Morley went on to different experiments after their first publication in 1887, both remained active in the field. Other versions of the experiment were carried out with increasing sophistication. Roy J. Kennedy and K. K. Illingworth both modified the mirrors to include a half-wave "step", eliminating the possibility of some sort of standing wave pattern within the apparatus. Illingworth could detect changes on the order of 1/300th of a fringe, Kennedy up to 1/1500th. Miller later built a non-magnetic device to eliminate magnetostriction, while Michelson built one of non-expanding invar to eliminate any remaining thermal effects. Others from around the world increased accuracy, eliminated possible side effects, or both.

Morley was not convinced of his own results, and went on to conduct additional experiments with Dayton Miller. Miller worked on increasingly large experiments, culminating in one with a 32 m (effective) arm length at an installation at the Mount Wilson observatory. To avoid the possibility of the aether wind being blocked by solid walls, he used a special shed with thin walls, mainly of canvas. He consistently measured a small positive effect that varied with each rotation of the device, the sidereal day and on a yearly basis. His measurements amounted to approximately 10 km/s instead of the nearly 30 km/s expected from the Earth's orbital motion alone. He remained convinced this was due to partial entrainment, though he did not attempt a detailed explanation.

Though Kennedy later also carried out an experiment at Mount Wilson, finding 1/10 the drift measured by Miller, and no seasonal effects, Miller's findings were considered important at the time, and were discussed by Michelson, Lorentz and others at a meeting reported in 1928 (ref below). There was general agreement that more experimentation was needed to check Miller's results. Lorentz recognised that the results, whatever their cause, did not quite tally with either his or Einstein's versions of special relativity. Einstein was not present at the meeting and felt the results could be dismissed as experimental error (see Shankland ref below). To date, no-one has been able to replicate Miller's results, and modern experimental accuracies are considered to have ruled them out.[8]

Also note, that 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 ca. 220 km/s, or the speed of the solar system relative to the CMB rest frame of ca. 368 km/s, the zero results of those experiments are even more obvious.

Name Location Year Arm length (meters) Fringe shift expected Fringe shift measured Ratio Upper Limit on Vaether Experimental Resolution Null result
Michelson[3] Potsdam 1881 1.2 0.04 ≤ 0.02 2 ∼ 20 km/s 0,02 $\approx$ yes
Michelson and Morley[4] Cleveland 1887 11.0 0.4 < 0.02
or ≤ 0,01
40 ∼ 4–8 km/s 0,01 $\approx$ yes
Morley and Miller[9][10] Cleveland 1902–1904 32.2 1.13 ≤ 0.015 80 ∼ 3,5 km/s 0,015 yes
Miller[11] Mt. Wilson 1921 32.0 1.12 ≤ 0.08 15 ∼ 8–10 km/s unclear unclear
Miller[11] Cleveland 1923–1924 32.0 1.12 ≤ 0.03 40 ∼ 5 km/s 0.03 yes
Miller (sunlight)[11] Cleveland 1924 32.0 1.12 ≤ 0.014 80 ∼ 3 km/s 0.014 yes
Tomaschek (star light)[12] Heidelberg 1924 8.6 0.3 ≤ 0.02 15 ∼ 7 km/s 0.02 yes
Miller[11][13] 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 yes
Piccard & Stahel[16] with a Balloon 1926 2.8 0.13 ≤ 0.006 20 ∼ 7 km/s 0.006 yes
Piccard & Stahel[17] Brussels 1927 2.8 0.13 ≤ 0.0002 185 ∼ 2,5 km/s 0.0007 yes
Piccard & Stahel[18] Rigi 1927 2.8 0.13 ≤ 0.0003 185 ∼ 2,5 km/s 0.0007 yes
Michelson et al.[19] Mt. Wilson 1929 25.9 0.9 ≤ 0.01 90 ∼ 3 km/s 0.01 yes
Joos[20] Jena 1930 21.0 0.75 ≤ 0.002 375 ∼ 1,5 km/s 0.002 yes

### Recent experiments

In recent times experiments similar to the Michelson–Morley experiment have become commonplace. Lasers and masers amplify light by repeatedly bouncing it back and forth inside a carefully tuned cavity, thereby inducing high-energy atoms in the cavity to give off more light. The result is an effective path length of kilometers. Better yet, the light emitted in one cavity can be used to start the same cascade in another set at right angles, thereby creating an interferometer of extreme accuracy.[21] The first such experiment was led by Charles H. Townes, one of the co-creators of the first maser. Their 1958 experiment put an upper limit on drift, including any possible experimental errors, of only 30 m/s. In 1974 a repeat with accurate lasers in the triangular Trimmer experiment reduced this to 0.025 m/s, and included tests of entrainment by placing one leg in glass. [22]

The most precise experiments of this kind (using laser, maser, cryogenic optical resonators, etc.) were made in recent years. In some of those experiments, the devices were rotated or remained stationary, and some were combined with the Kennedy–Thorndike experiment. Tests on Lorentz invariance achieving a comparable precision, are the Hughes–Drever experiments.

Author Year Maximum
anisotropy of c
Brillet & Hall[23] 1979
$\lesssim10^{-15}$
Wolf et al.[24] 2003
Müller et al.[25] 2003
Wolf et al.[26] 2004
Wolf et al.[27] 2004
Antonini et al.[28] 2005
$\lesssim10^{-16}$
Stanwix et al.[29] 2005
Herrmann et al.[30] 2005
Stanwix et al.[31] 2006
Müller et al.[32] 2007
Eisele et al.[33] 2009
$\lesssim10^{-17}$
Herrmann et al.[34] 2009

## Fallout

### Einstein and special relativity

The constancy of the speed of light was postulated by Albert Einstein in 1905,[35] motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous ether but not, contrary to widespread belief, by the null result of the Michelson–Morley experiment.[36] However the null result of the Michelson–Morley experiment helped the notion of the constancy of the speed of light gain widespread and rapid acceptance.

### Aether dragging

Initially, the experiment of 1881 was meant to distinguish between the theory of Augustin-Jean Fresnel (1818), who proposed an almost stationary aether, and in which the aether is only partially dragged with a certain coefficient by matter; and the theory of George Gabriel Stokes (1845), who stated that the aether was fully dragged in the vicinity of the earth. Michelson initially believed the negative outcome confirmed the theory of Stokes. However, Hendrik Lorentz showed in 1886, that Stokes's explanation of aberration is contradictory.[37][38]

Also the assumption that the aether is not carried in the vicinity, but only within matter, was very problematic as shown by the Hammar experiment (1935). Hammar placed one arm of the interferometer between two huge lead blocks. If aether were dragged by mass, the blocks would, it was theorized, have been enough to cause a visible effect. Once again, no effect was seen, so any such theory is considered as disproved.

### Emission theory

Walter Ritz's emitter theory (or ballistic theory), was also consistent with the results of the experiment, not requiring aether. The theory postulates that light has always the same velocity in respect to the source.[39] However it also led to several "obvious" optical effects that were not seen in astronomical photographs, notably in observations of binary stars in which the light from the two stars could be measured in an interferometer. If this was correct, the light from the stars should cause fringe shifting due to the velocity of the stars being added to the speed of the light, but again, no such effect could be seen.

The Sagnac experiment placed a modified apparatus on a constantly rotating turntable; the main modification was that the light trajectory encloses an area. In doing so any ballistic theories such as Ritz's could be tested directly, as the light going one way around the device would have a different length to travel than light going the other way (the eyepiece and mirrors would be moving toward/away from the light). In Ritz's theory there would be no shift, because the net velocity between the light source and detector was zero (they were both mounted on the turntable). However in this case an effect was seen, thereby eliminating any simple ballistic theory. This fringe-shift effect is used today in laser gyroscopes.

### Length contraction

The explanation was found in the FitzGerald–Lorentz contraction, also simply called length contraction. According to this physical law all objects physically contract along the line of motion (originally thought to be relative to the aether), so while the light may indeed transit slower on that arm, it also ends up travelling a shorter distance that exactly cancels out the drift. In 1932 the Kennedy–Thorndike experiment modified the Michelson–Morley experiment by making the path lengths of the split beam unequal, with one arm being very short. In this version a change of the velocity of the earth would still result in a fringe shift except if also the predicted time dilation is correct. Once again, no effect was seen, which they presented as evidence for both length contraction and time dilation, both key effects of relativity.

Einstein derived the FitzGerald–Lorentz contraction from the relativity postulate; thus his description of special relativity was also consistent with the apparently null results of most experiments (though not, as was recognized at the 1928 meeting, with Miller's observed seasonal effects). Today special relativity is generally considered the "solution" to the Michelson–Morley null result. However, this was not universally recognized at the time. As late as 1920, Einstein himself still spoke of a different concept of ether that was not a "ponderable medium" but something of significance nonetheless.[40]

The Trouton–Noble experiment is regarded as the electrostatic equivalent of the Michelson–Morley optical experiment, though whether or not it can ever be done with the necessary sensitivity is debatable. On the other hand, the 1908 Trouton–Rankine experiment, which can be regarded as the electrical equivalent to the Kennedy–Thorndike experiment, achieved very high sensitivity.

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## Bibliography

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• Michelson Morley — Wenn elektromagnetische Wellen an einen ruhenden Äther gebunden wären, müsste man die Eigenbewegung von Erde und Sonne als Ätherwind messen können. Das Michelson Morley Experiment war ein physikalisches Experiment, das von dem deutsch… …   Deutsch Wikipedia

• Michelson-Morley-Interferometer — Das Michelson Interferometer ist ein Interferometer, das nach dem Physiker Albert Abraham Michelson benannt wurde. Bekanntheit erlangte dieses Messinstrument vor allem durch das Michelson Morley Experiment, durch welches der sogenannte Lichtäther …   Deutsch Wikipedia

• Michelson-Morley-Versuch — Maikelsono ir Morlio eksperimentas statusas T sritis fizika atitikmenys: angl. Michelson Morley experiment vok. Michelson Morley Versuch, m rus. опыт Майкельсона Морлея, m pranc. expérience de Michelson et Morley, f; expérience de Michelson… …   Fizikos terminų žodynas