Why did the Michelson Morley experiment fail

Sexl Physik 8, textbook

Historical experiment: Michelson-Morley experiment (1887) 7.1 E 1 For their attempt to determine the speed of the earth relative to the ether, Michelson and Morley used an interferometer developed by Michelson (7.1). A light beam coming from a light source L is split into two coherent ones by a semitransparent mirror S, i.e. H. Partial beams capable of interference are split up. The first of these partial beams runs from S to mirror A, is reflected by this and runs back to S, where it is reflected to the screen. The second partial beam runs from S to mirror B, is reflected by this and runs back to S, where it is let through to the screen. The two partial beams overlap between S and the screen. Finally, they fall on the screen on which interference fringes are observed (7.2). Since the light source does not emit completely parallel light, interference rings appear on the screen and not just a bright or dark point. The distances between mirrors A and B and S are the same: äääää SA = äääää SB = D. Does the movement through the ether cause a path difference between the partial rays? (7.3, on the interference of light rays see Physik 7, p. 65, Physik 6, p. 45) We assume that the interferometer arm SA is parallel to the direction of movement of the earth (7.1). The first partial ray then runs towards the aether on the way from S to A. Relative to the earth it has the speed c - v. (v denotes the speed of the earth through the ether.) On the way back from A to S the beam runs towards the earth and thus the interferometer with the speed c + v. The time that the light needs from S to mirror A and back is therefore t SAS = D _ c - v + D _ c + v = 2 Dc _ c 2 - v 2 = 2 D _ c 1 _ 1 - v 2 _ c 2. The speed of the light beam that passes through the interferometer arm SB perpendicular to the earth's movement is 9 ___ c 2 - v 2 (7.3). It therefore needs the time t SBS = 2D __ 9 _ _ c 2 - v 2 = 2 D _ c 1 _ 9 ___ 1 - v 2 _ c 2 from S to B and back The light should therefore move in different directions at different speeds. As we can see, t SBS

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