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lecture2 - Physics 126 Lecture 2 11 Feb. 2011 Relativity of...

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Unformatted text preview: Physics 126 Lecture 2 11 Feb. 2011 Relativity of Time Relativity of Simultaneity Reading: Ch. 1.2 of Beiser Outline: Michelson-Morley experiment Failure of classical velocity addition formula Special Relativity: Einstein’s Two Postulates Time dilation Loss of universal simultaneity M.Loy 2009 2 Motion in ‘Ether’ and the Velocity of Light p By 1880, the velocity of light has been measured (by A.A. Michelson) to be 2.99 x 10 8 m/sec. p Ether (the medium light waves travel in) is believed to be stationery, and the earth is traveling at about 30,000 m/sec (motion of the earth around the sun) in this ether. p Thus β = v/c is about 10-4 p All attempts to measure this value failed, since only effects due to β 2 can be detected (just as in the two swimmers problem). One needs to measure 1 part in 10 8 ! How can this be seen? p “ ..no experiment can be devised with sufficient sensitivity to measure .. the earth’s motion through the ether.” (Maxwell) p Michelson, using interference between two light beams traveling normal to each other, designed an experiment to measure this effect : Michelson-Morley (MM) Experiment of 1887. M.Loy 2009 3 Michelson and Morley (MM) Experiment p Use two light paths – parallel and normal to the earth motion, as in the two swimmers problem. p Take advantage of light being a wave, and the change in relative propagation lengths of two light beams can be seen in interference: a length change of λ /2 (or time change of λ /2c) will change from constructive to destructive interference – changing from bright to dark. This technique can measure length c h a n g e of λ /2 (about 3x10-7 m for visible light) or equivalently the time difference λ /2c. Constructive (bright) Destructive (dark) M.Loy 2009 4 Michelson-Morley experiment (1887) •The MM experiment is cleverly designed to look for change of interference (equivalent to change in propagating length or time) when the direction of the ether flow – the direction of the earth motion in ether - is changed . •Thus, the experiment was put on a stone slab turntable and set into slow rotation, so the two arms will alternatively be along the direction of the earth’s motion •And to look for a c h a n g e in the interference pattern correlated to this rotation motion of the slab. Flow direction M.Loy 2009 5 The MM experiment : what we expect classically The basic (classical) result: t 1 (along flow) = γ t 2 (across flow) t A-t B = ++ ~ 0-- Classical A B A B A B There should be changes in the interference pattern ( either from dark to bright, or from bright to dark) as the platform is rotated. M.Loy 2009 6 MM Experiment of 1887 Theory Observation M.Loy 2009 7 The MM experiment : what we expect classically and the MM experimental result The basic (classical) result: t 1 (along flow) = γ t 2 (across flow) t A-t B = ++ ~ 0-- t A-t B ~ 0 ~ 0 ~ 0 Classical MM Exp....
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lecture2 - Physics 126 Lecture 2 11 Feb. 2011 Relativity of...

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