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Published byDylan Angevine Modified about 1 year ago

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v v c + v c - v Expected if speed of light depends on emitter Observed speed of light independent of emitter Binary Stars Apparent motion as seen from Earth

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Stellar Aberration v c v c v v v c

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Michelson-Morley Experiment Light source (LS) Beam splitter (BS) Mirror 1 (M1) Mirror 2 (M2) Telescope (T) L L Time difference: t = t 2 – t 1 = 2L/c (1 + V e ²/c² – (1 + V e ²/c²/2)) = LV e ²/c³ Corresponding path length: d = c t Turn setup by 90° changes role of P1 and P2, doubling the effective difference in path length Experimental parameters: L =11 m,V= 3× 10 4 m/s, = 500 nm = 5×10 -7 m, c = 3×10 8 m/s 2 d = 0.4 Sensitivity of M&M (1887): 2 d = 0.01 S Ether frame V S'S' Earth frame P1 (BS – M1 – BS): Approximation: (perpendicular motion) (paralle motion) P2 (BS – M2 – BS): c 1 ' = c² – V e ² c 2 ' = c – V e ; c 2,r ' = c + V e t 1 = 2L / (c² – V e ²) 1/2 = 2L/c /(1 – V e ²/c²) 1/2 t 2 = L/(c + V e ) + L/(c – V e ) = 2Lc / (c² – V e ²) = 2L/c / (1 – V e ²/c²) 1/(1 – x²) = (1 – x²)/(1 – x²) + x²/(1 – x²) = 1 + x² + x 4 + … 1 + x²(for x << 1) 1/(1 – x²) 1/2 = (1/(1 – x²)) 1/2 = (1 + x² + x 4 /4 + 3x 4 /4 + …) 1/2 1 + x²/2(for x << 1)

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v c + v c - v Speed of light independent of emitter Binary Stars Stellar Aberration Earth not at rest with respect to ether Michelson/Morley No relative motion between Earth and ether

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