thumb|300px|Michelson and Morley's [[interferometer|interferometric setup, mounted on a stone slab that floats in an annular trough of mercury]]
The Michelson–Morley experiment was an attempt to measure the motion of the Earth relative to the luminiferous aether,
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. More recently, in 2009, optical resonator experiments confirmed the absence of any aether wind at the 10<sup>−17</sup> level.]]
Michelson had a solution to the problem of how to construct a device sufficiently accurate to detect aether flow. In 1877, while teaching at his alma mater, the United States Naval Academy in Annapolis, Michelson conducted his first known light speed experiments as a part of a classroom demonstration. In 1881, he left active U.S. Naval service while in Germany concluding his studies. In that year, Michelson used a prototype experimental device to make several more measurements.
The device he designed, later known as a Michelson interferometer, sent yellow light from a sodium flame (for alignment), or white light (for the actual observations), 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 by small mirrors. They then recombined on the far side of the splitter in an eyepiece, producing a pattern of constructive and destructive interference whose transverse displacement would depend on the relative time it takes light to transit the longitudinal vs. the transverse arms. If the Earth is traveling through an aether medium, a light beam traveling parallel to the flow of that aether will take longer to reflect back and forth than would a beam traveling perpendicular to the aether, because the increase in elapsed time from traveling against the aether wind is more than the time saved by traveling with the aether wind. Michelson expected that the Earth's motion would produce a fringe shift equal to 0.04 fringes—that is, of the separation between areas of the same intensity. He did not observe the expected shift; the greatest average deviation that he measured (in the northwest direction) was only 0.018 fringes; most of his measurements were much less. His conclusion was that Fresnel's hypothesis of a stationary aether with partial aether dragging would have to be rejected, and thus he confirmed Stokes' hypothesis of complete aether dragging.). d, d' and e are mirrors. e' is a fine adjustment mirror. f is a telescope.]]
In 1885, Michelson began a collaboration with Edward Morley, spending considerable time and money to confirm with higher accuracy Fizeau's 1851 experiment on Fresnel's drag coefficient, Use of partially monochromatic light (yellow sodium light) during initial alignment enabled the researchers to locate the position of equal path length, more or less easily, before switching to white light.
The mercury trough allowed the device to turn with close to zero friction, so that once having given the sandstone block a single 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. The hypothesis of aether drift implies that because one of the arms would inevitably turn into the direction of the wind at the same time that another arm was turning perpendicularly to the wind, an effect should be noticeable even over a period of minutes.
The expectation was that the effect would be graphable as a sine wave with two peaks and two troughs per rotation of the device. This result could have been expected because during each full rotation, each arm would be parallel to the wind twice (facing into and away from the wind giving identical readings) and perpendicular to the wind twice. Additionally, due to the Earth's rotation, the wind would be expected to show periodic changes 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 annual variations.
Most famous "failed" experiment
thumb|300px|Michelson and Morley's results. The upper solid line is the curve for their observations at noon, and the lower solid line is that for their evening observations. Note that the theoretical curves and the observed curves are not plotted at the same scale: the dotted curves, in fact, represent only one-eighth of the theoretical displacements.
After all this thought and preparation, the experiment became what has been called the most famous failed experiment in history.
:<math>T_\ell-T_t=\frac{2L}{c}\left(\frac{1}{1-\frac{v^2}{c^2-\frac{1}{\sqrt{1-\frac{v^2}{c^2}\right)</math>
To find the path difference, simply multiply by <math>c</math>;
<math>\Delta{\lambda}_1=2L\left(\frac{1}{1-\frac{v^2}{c^2-\frac{1}{\sqrt{1-\frac{v^2}{c^2}\right)</math>
The path difference is denoted by <math>\Delta \lambda</math> because the beams are out of phase by a some number of wavelengths (<math>\lambda</math>). To visualise this, consider taking the two beam paths along the longitudinal and transverse plane, and lying them straight (an animation of this is shown at minute 11:00, The Mechanical Universe, episode 41). One path will be longer than the other, this distance is <math>\Delta \lambda</math>. Alternatively, consider the rearrangement of the speed of light formula <math>c{\Delta}T = \Delta\lambda</math> .
If the relation <math>{v^2}/{c^2} << 1</math> is true (if the velocity of the aether is small relative to the speed of light), then the expression can be simplified using a first order binomial expansion;
<math>(1-x)^n \approx {1-nx}</math>
So, rewriting the above in terms of powers;
<math>\Delta{\lambda}_1 = 2L\left(\left({1-\frac{v^2}{c^2\right)^{-1}-\left(1-\frac{v^2}{c^2}\right)^{-1/2}\right)</math>
Applying binomial simplification;
<math>\Delta{\lambda}_1 = 2L\left( (1+\frac{v^2}{c^2}) - (1+\frac{v^2}{2c^2})\right)={2L}\frac{v^2}{2c^2}</math>
Therefore;
<math>\Delta{\lambda}_1={L}\frac{v^2}{c^2}</math>
The derivation above shows that the presence of an aether wind would produce a difference in optical path lengths between the two arms of the interferometer. This path difference depends on the orientation of the interferometer relative to the aether wind. Specifically, the derivation assumes that the longitudinal arm is aligned parallel to the presumed direction of the aether wind. If instead the longitudinal arm is oriented perpendicular to the aether wind, the resulting path difference would have the opposite sign.
The magnitude of the path difference can vary continuously and may represent any fraction of the wavelength, depending on both the angle between the apparatus and the aether wind and the wind's speed.
To detect the existence of the aether, Michelson and Morley aimed to observe a "fringe shift" in the interference pattern. The underlying principle is straightforward: when the interferometer is rotated by 90°, the roles of the two arms are exchanged, altering the path difference due to the aether wind. The fringe shift is determined by calculating the difference in path differences between the two orientations, and then dividing that value by the wavelength. but in 1977 Brecher observed X-rays from binary star systems with similar null results. Furthermore, Filippas and Fox (1964) conducted terrestrial particle accelerator tests specifically designed to address Fox's earlier "extinction" objection, the results being inconsistent with source dependence of the speed of light.
Subsequent experiments
thumb|250px|Simulation of the Kennedy/Illingworth refinement of the Michelson–Morley experiment. (a) Michelson–Morley interference pattern in monochromatic [[mercury-vapor lamp|mercury light, with a dark fringe precisely centered on the screen. (b) The fringes have been shifted to the left by 1/100 of the fringe spacing. It is extremely difficult to see any difference between this figure and the one above. (c) A small step in one mirror causes two views of the same fringes to be spaced 1/20 of the fringe spacing to the left and to the right of the step. (d) A telescope has been set to view only the central dark band around the mirror step. Note the symmetrical brightening about the center line. (e) The two sets of fringes have been shifted to the left by 1/100 of the fringe spacing. An abrupt discontinuity in luminosity is visible across the step.]]
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. Miller's findings were considered important at the time, and were discussed by Michelson, Lorentz and others at a meeting reported in 1928.
Using a special optical arrangement involving a 1/20 wave step in one mirror, Roy J. Kennedy (1926) and K.K. Illingworth (1927) (Fig. 8) converted the task of detecting fringe shifts from the relatively insensitive one of estimating their lateral displacements to the considerably more sensitive task of adjusting the light intensity on both sides of a sharp boundary for equal luminance. New technologies, including the use of lasers and masers, have significantly improved measurement precision. (In the following table, only Essen (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.)
{| class=wikitable
|-
! Author !! Year !! Description !! Upper bounds
|-
| Louis Essen
<!--ref name=desit></ref-->