Michelson–Morley experiment

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The Michelson–Morley experiment, one of the most important and famous experiments in the history of physics, was performed in 1887 by Albert Michelson and Edward Morley at what is now Western Reserve Academy. It is generally considered to be the first strong evidence against the theory of a luminiferous aether. Primarily for this work, Albert Michelson was awarded the Nobel Prize in 1907.

[edit] Measuring aether

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 (air), so also light waves require a medium, the "luminiferous aether," or the "ethereal aether." Because light can travel through a vacuum, it was assumed that the vacuum must contain the medium of light. The speed of light being so great, designing an experiment to detect the presence and properties of this aether took considerable ingenuity.

A depiction of the concept of the "aether wind."

Each year, the Earth travels a tremendous distance in its orbit around the sun, at a speed of around 30 km/second or over 100,000 km per hour. The sun itself is traveling 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 analyzing 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-1800s, 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.

[edit] The 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 traveling at right angles to one another. After leaving the splitter, the beams traveled 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 length of the arms. Any slight change in the amount of time the beams spent in transit 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 one twenty-fifth the size of a single fringe.

Michelson had made several measurements with an experimental device in 1881, in which he noticed that the expected shift of 0.04 was not seen, and a smaller shift of about 0.02 was. 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.

He then combined efforts with Edward Morley and spent a considerable amount of time and money creating an improved version with more than enough accuracy to detect the drift. In their experiment, the light was repeatedly reflected back and forth along the arms, 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 located in a closed room in the basement of a stone building, eliminating most thermal and vibrational effects. Vibrations were further reduced by building the apparatus on top of a huge block of marble, which was then floated in a pool of mercury. They calculated that effects of about 1/100th of a fringe would be detectable.

The mercury pool allowed the device to be turned, so that it could be rotated through the entire range of possible angles to the “aether wind.” Even over a short period of time some sort of effect would be noticed simply by rotating the device, such that one arm rotated 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 ether wind to decrease and increase on a yearly basis.

[edit] The most famous failed experiment

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. Instead of providing insight into the properties of the aether, Michelson and Morley’s 1887 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 approximately 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 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. Kennedy and 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 only ~10 kps instead of the ~30 kps 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 experiments have accuracies that rule them out.

In recent times versions of 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.

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. In 1979 the Brillet-Hall experiment put an upper limit of 30 m/s for any one direction, but reduced this to only 0.000001 m/s for a two-direction case (i.e., still or partially entrained aether). A year long repeat known as Hils and Hall, published in 1990, reduced the limit of anisotropy to 2x10^-13.

[edit] Fallout

This result was rather astounding and not explainable by the then-current theory of wave propagation in a static aether. Several explanations were attempted, among them that the experiment had a hidden flaw (apparently Michelson’s initial belief), or that the Earth’s gravitational field somehow “dragged” the aether around with it in such a way as would locally eliminate its effect. Miller would have argued that, in most if not all experiments other than his own, there was little possibility of detecting an aether wind since it was almost completely blocked out by the laboratory walls or by the apparatus itself. Be this as it may, the idea of a simple aether, what became known as the First Postulate, had been dealt a serious blow.

A number of experiments were carried out to investigate the concept of aether dragging, or entrainment. The most convincing was carried out by Hamar, who placed one arm of the interferometer between two huge lead blocks. If aether were dragged by mass, the blocks would, it was theorised, have been enough to cause a visible effect. Once again, no effect was seen.

Walter Ritz’s emitter theory (or ballistic theory), was also consistent with the results of the experiment, not requiring aether, more intuitive and paradox-free. This became known as the Second Postulate. 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 the Second Postulate 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 the Michelson–Morley apparatus on a constantly rotating turntable. 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 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.

Another possible solution was found in the Fitzgerald–Lorentz contraction. According to this hypothesis all objects physically contract along the line of motion 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. For some time it was assumed that the contraction hypothesis could not be experimentally determined to be different from relativity, but 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 the two ends of the experiment were at different velocities due to the rotation of the earth, so the contraction would be different for the two arms and not “work out” to exactly cancel the result. Once again, no effect was seen, which they presented as evidence for time dilation, a key effect of relativity.

Ernst Mach was among the first physicists to suggest that the experiment actually amounted to a disproof of the aether theory. 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 recognised 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 type of ether that was not a “ponderable medium” but something of significance nonetheless:

“...More careful reflection teaches us, however, that the special theory of relativity does not compel us to deny ether. We may assume the existence of an ether... Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether... According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.”

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 an incredible sensitivity.

[edit] Application to Gravitational Wave Detection

Amongst the predictions of Einstein’s later general theory of relativity is that there exist gravitational waves, but as of 2006, these waves have only been indirectly observed. Enormously sensitive, kilometer-scale Michelson interferometers (coupled with Fabry-Perot interferometers) are used in current projects attempting to directly detect gravitational waves, such as LIGO and VIRGO. LISA is a planned joint NASA-ESA mission to put three 5 million kilometer Michelson interferometers in space, with the intent of observing significantly lower-frequency gravitational waves than terrestrial predecessors.

[edit] References

• A. A. Michelson and E.W. Morley, Philos. Mag. S.5, 24 (151), 449-463 (1887), [1]
• A. A. Michelson et al., Conference on the Michelson-Morley Experiment, Astrophysical Journal 68, 341 (1928)
• Robert S. Shankland et al., New Analysis of the Interferometer Observations of Dayton C. Miller, Reviews of Modern Physics, 27(2):167-178, (1955)
• James DeMeo, Dayton Miller's Ether-Drift Experiments: A Fresh Look, (2002)
• For gravitational waves: PostScript file of the newsletter of the Topical Group on Gravitation of the American Physical Society Number 21 Spring 2003; Google.com can be used to extract the text of the document.
• Holger Müller, Sven Herrmann, Claus Braxmaier, Stephan Schiller, and Achim Peters, Phys. Rev. Lett. 91, 020401 (2003) “Modern Michelson-Morley Experiment Using Cryogenic Optical Resonators”
• Renaud Parentani, International Journal of Modern Physics A, Vol. 17, No.20, pg. 2721-2726 “What Did We Learn from Studying Acoustic Black Holes?”
• N. Rashevsky, Light Emission from a Moving Source in Connection with the Relativity Theory,

[edit] External links

• Interferometers Used in Aether Drift Experiments From 1881-1931
• Early Experiments
• Modern Michelson-Morley Experiment improves the best previous result by two orders of magnitude, from 2003

[edit] See also

• Counter-intuitive
• Special relativity
• Aether drag hypothesis
• Hamar experiment
• Ives–Stilwell experiment
• Trouton–Rankine experiment
• Moving magnet and conductor problem