Early measurements Michelson was fascinated by light all his life. Once asked why he studied light, he reputedly said, "because it's so much fun". As early as 1869, while serving as an officer in the
United States Navy, Michelson started planning a repeat of the rotating-mirror method of
Léon Foucault for measuring the speed of light, using improved optics and a longer baseline. He conducted some preliminary measurements using largely improvised equipment in 1878, about the same time that his work came to the attention of
Simon Newcomb, director of the Nautical Almanac Office who was already advanced in planning his own study. Michelson's formal experiments took place in June and July 1879. He constructed a frame building along the north sea wall of the Naval Academy to house the machinery. Michelson published his result of 299,910 ± 50 km/s in 1879 before joining
Newcomb in Washington DC to assist with his measurements there. Thus began a long professional collaboration and friendship between the two.
Simon Newcomb, with his more adequately funded project, obtained a value of 299,860 ± 30 km/s, just at the extreme edge of consistency with Michelson's. Michelson continued to "refine" his method and in 1883 published a measurement of 299,853 ± 60 km/s, rather closer to that of his mentor. Albert A. Michelson while serving in the
U.S. Navy. He rejoined the U.S. Navy in World War I, when this portrait was taken.
Mount Wilson and Lookout Mountain In 1906, a novel electrical method was used by
E. B. Rosa and the
National Bureau of Standards to obtain a value for the
speed of light of 299,781 ± 10 km/s. Though this result has subsequently been shown to be severely biased by the poor electrical standards in use at the time, it seems to have set a fashion for rather lower measured values. From 1920, Michelson started planning a definitive measurement from the
Mount Wilson Observatory, using a baseline to
Lookout Mountain, a prominent bump on the south ridge of
Mount San Antonio ("Old Baldy"), some 22 miles distant. In 1922, the
United States Coast and Geodetic Survey began two years of painstaking measurement of the baseline using the recently available
invar tapes. With the baseline length established in 1924, measurements were carried out over the next two years to obtain the published value of 299,796 ± 4 km/s. Famous as the measurement is, it was beset by problems, not least of which was the haze created by the smoke from forest fires which blurred the mirror image. It is also probable that the intensively detailed work of the
geodetic survey, with an estimated error of less than one part in 1 million, was compromised by a shift in the baseline arising from the
Santa Barbara earthquake of June 29, 1925, which was an estimated magnitude of 6.3 on the
Richter scale. The now-famous
Michelson–Morley experiment also influenced the affirmation attempts of peer
Albert Einstein's theory of
general relativity and
special relativity, using similar optical instrumentation. These instruments and related collaborations included the participation of fellow physicists
Dayton Miller,
Hendrik Lorentz, and
Robert Shankland. portrait by
Auguste Léon, 1921
Michelson, Pease, and Pearson The period after 1927 marked the advent of new measurements of the speed of light using novel
electro-optic devices, all substantially lower than Michelson's 1926 value. Michelson sought another measurement, but this time in an evacuated tube to avoid difficulties in interpreting the image owing to atmospheric effects. In 1929, he began a collaboration with
Francis G. Pease and Fred Pearson to perform a measurement in a 1.6 km tube 3 feet in diameter at the Irvine Ranch near Santa Ana, California.
Application of basic statistical principles in Michelson's study of speed of light During June and early July 1879, Michelson refined experimental arrangements from those developed by
Hippolyte Fizeau and
Léon Foucault. The experimental setup was as follows: Light generated from a source is directed towards a rotating mirror through a slit on a fixed plate; the rotating mirror reflects the incoming light and at a certain angle, towards the direction where another fixed flat mirror is placed whose surface is perpendicular to the incoming ray of light; the rotating mirror should have rotated by an angle
α by the time the ray of light travels back and is reflected again towards the fixed plate (the distance between the fixed mirror and the rotating one is recorded as
D); a displacement from the slit is detected on the plate which measures
d; the distance from the rotating mirror to the fixed plate is designated as the radius
r while the number of revolutions per second of the mirror is recorded as
ω. In this way, ; ; speed of light can be derived as . While at plain sight, four measured quantities are involved: distance
D, radius
r, displacement
d and rotating mirror revolution per second
ω, which seems simple; yet based on the limitation of the measurement technology at that time, great efforts were made by Michelson to reduce
systematic errors and apply subsequent corrections. For instance, he adopted a steel measuring tape with a said length of 100 feet and he intended to measure tens of times across the distance; still, he measured its length against a copy of the official standard yard to find out it as 100.006 feet, thus eliminating a systematic error, albeit small. Aside from the efforts to reduce as much as possible the systematic errors, repeated measurements were performed at multiple levels to obtain more accurate results. As R.J. MacKay and R.W. Oldford remarked in their article, 'It is clear that Michelson appreciated the power of averaging to reduce variability in measurement', it is clear that Michelson had in mind the property that averages vary less which should be formally described as: the standard deviation of the average of
n independent random variables is less than that of a single random variable by a factor of the square root of
n. To realize that, he also strived to have each measurement not influencing each other, thus being mutually
independent random variables. A
statistical model for repeated measurements with the assumption of independence or identical distributions is unrealistic. In the case of light speed study, each measurement is approached as the sum of quantity of interest and measurement error. In the absence of systematic error, the measurement error of speed of light can be modeled by a random sample from a distribution with unknown expectation and finite variance; thus, the speed of light is represented by the expectation of the model distribution and the ultimate goal is to estimate the expectation of the model distribution on the acquired dataset. The law of large numbers suggests to estimate the expectation by the sample mean.
Michelson–Morley experiment In 1887, he collaborated with colleague
Edward Williams Morley of Western Reserve University, now part of
Case Western Reserve University, in the
Michelson–Morley experiment. Their experiment for the expected motion of the
Earth relative to the
aether, the hypothetical medium in which light was supposed to travel, resulted in a
null result. Surprised, Michelson repeated the experiment with greater and greater precision over the next years, but continued to find no ability to measure the aether. The Michelson–Morley results were immensely influential in the physics community, leading
Hendrik Lorentz to devise his now-famous
Lorentz contraction equations as a means of explaining the null result. There has been some historical controversy over whether
Albert Einstein was aware of the Michelson–Morley results when he developed his theory of
special relativity, which pronounced the aether to be "superfluous". In a later interview, Einstein said of the Michelson–Morley experiment, "I was not conscious it had influenced me directly ... I guess I just took it for granted that it was true." Regardless of Einstein's specific knowledge, the experiment is today considered the canonical experiment in regards to showing the lack of a detectable aether. The precision of their equipment allowed Michelson and Morley to be the first to get precise values for the
fine structure in the atomic spectral lines for which in 1916
Arnold Sommerfeld gave a theoretical explanation, introducing the
fine-structure constant. == Astronomical interferometry ==