Michelson-Morley Experiment
Sklar is sometimes unkind to the reader, presumably because he was (when he was young) too smart! Here is a calculation of the time of a round-trip of light in Michelson-Morley Experiment.
Notice that the experimental device is moving with a constant velocity, so that the path of light, perpendicular to the direction of the movement (bc'b), actually goes along the two sides of a triangle; that is, the starting point b and the terminal point b are separated by a certain amount of interval, and the device moves a bit to the left.
Despite the difference between t and T thus predicted (which should have produced interference bands), the experiment gave null-results.
Notice that in the preceding calculation the factor of (v/c)(v/c) appeared. Any effects which depend on this factor are called quantities of "2nd order"; in contrast to this, effects depending on v/c are called "1st order" quantities or effects. The important fact is that many optical experiments for detecting the 1st order effects were already made before Michelson-Morley; and they consistently failed to detect any effects. Lorentz managed to adapt Maxwell's electromagnetic theory to these experimental facts; however, Michelson began new experiments for detecting 2nd order effects, which should be detectable according to Lorentz's theory. This was the situation of the Michelson-Morley experiment. Facing the "null-results" (no 2nd order effect detected), Lorentz and Poincare had to seek a way for explaining this. For more on this, see Hiroshige (1980), as well as Stachel (1995).
Now, if you have felt some interests, it should be a good occasion to pursue the matter a bit further. There are a bunch of related questions:
(1) Why did Michelson and Morley come to the idea of their experiment?
(2) What sort of attempts were made in order to explain their null-results?
(3) What is the relationship between the Michelson-Morley experiment and the genesis of Einstein's special relativity?
You may consult the following books, as a first step.
Ｒ・ハレ『世界を変えた20の科学実験』（小出昭一郎ほか訳）産業図書、1984、11章。For (1) and (2).
『物理学の20世紀』（『科学朝日』編）、1999、第1章。For (2) and (3).
ランダウ+ジューコフ『相対性理論入門』東京図書、1977。For a quick review of relativity (special and general).
広重徹『相対論の形成』みすず書房、1980。
For the history of the relativity theories, an up-to-date and readable exposition by John Stachel is recommended:
Twentieth Century Physics, vol. l, ed. by Laurie M. Brown, Abraham Pais, and Brian Pippard, Institute of Physics, 1995; Japanese translation 『20世紀の物理学』vol. 1、第4章「相対性理論の歴史」、丸善、1999年。
Last modified March 27, 2003. (c) Soshichi Uchii
