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Volume 15: Pages 422-438, 2002
First Order Effects in the Michelson‐Morley Experiment
R. C. de Miranda Filho 1,2, N. P. Andion 3,4, N. C. Ada Costa 5
1Instituto de Física, Universidade Federal da Bahia, Salvador, Brazil
2Departamento de Filosofia, Universidade de São Paulo, São Paulo, Brazil
3Instituto de Física, Universidade Federal da Bahia, Salvador, Brazil
4Departamento de Filosofia, Universidade de São Paulo, São Paulo, Brazil
5Departamento de Filosofia, Universidade de São Paulo, São Paulo, Brazil
It is well known that the Lorentz‐Fitzgerald hypothesis of contraction, when applied to the apparatus in the Michelson‐Morley experiment, compensates for the delay between the two interfering rays, explaining the absence of fringe shift. A detailed analysis of the theory of the experiment, however, reveals that this explanation is valid only for the case in which the telescope is focused on one of the mirrors. In the general case, that is, if the interference pattern is formed on a vertical screen, besides the second order term considered hitherto, a first order term will appear and the referred contraction cannot explain the negative result of the experiment. On the other hand, special relativity explains the absence of fringe shift in both cases. Other aspects of the original calculation held by Michelson and Morley that remain obscure after more than a century are also clarified: for example, the identification between the fringe shift and the variation of the optical path difference; the relevant segment of the trajectories for obtaining the optical path difference; the necessity of tilting at least one of the mirrors to obtain an interference pattern even when the ether wind is considered. An algorithm for making the calculations for any configuration of the apparatus is developed.
Keywords: Michelson‐Morley experiment, Lorentz‐Fitzgerald contraction, reflection law for moving mirrors, ether theories, special relativity experimental basis
Received: July 9, 2002; Published online: December 15, 2008