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In page Fringe shift:

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In the 1887 Michelson–Morley experiment, the speed that the two beams traveled down the perpendicular arms was expected to be altered by an apparent aether wind caused by the Earth's motion through the luminiferous aether. This time difference was calculated to result in a phase shift of 0.4 wavelengths. This means that as the interferometer's arms were spun to face into and against the ether wind, the vertical fringe lines should have moved across the viewer 0.4 fringe widths left and right for a total of 0.8 fringes from maximum to minimum. Michelson reported that only between one-sixth and one-quarter of the expected reading was found.[1]