U plug in v for v in the lt to get the inverse

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Unformatted text preview: ry of relaCvity. First American scienCst to win Nobel Prize. Edward Williams Morley (1838- 1923) was an American chemist whose reputaCon as a skilled experimenter aoracted the aoenCon of Michelson. In 1887 the pair performed what has come to be known as the Michelson- Morley experiment to measure the moCon of the earth through the ether. 19 Michelson- Morley Experiment u༇  Michelson interferometer on a block of granite. u༇  Granite block floats in mercury to greatly reduce vibraCon. u༇  Slowly rotate apparatus and measure interference paoern shi^. 20 MM calculaCon with Ether u༇  Ether with just the earth’s velocity would show interference. u༇  As apparatus is rotated, interference changes. u༇  MM found no shi^ in the interference paoern. t1 = L' L' + cc 2 L ' = L + ( vt1 ) t2 = in direction perpendicular to ether motion 2 L L + c+v c−v v2 ≈ L 1+ 2 c in direction parallel to ether motion v2 2L 1+ 2 2 2 2 L (c − v) L (c + v) 2 L ' 2 Lc 2 L ' 2L c ≈ 2 L #1 + v − 1 − v & = L v t 2 − t1 = 2 2 + 2 2 = 2 2= % ( # v2 & c −v c −v c c −v c c c $ c2 2c 2 ' c c 2 c %1 − 2 ( $ c' 2 # 3 × 10 4 & c(t 2 − t1 ) = (11m ) % = 11 × 10 −8 m = 110 nm 8( $ 3 × 10 ' a large fraction of the wavelength of light 21 Extend InerCal Coordinate System Symmetry of Galileo and Newton u༇  THE EINSTEIN PRINCIPLE OF RELATIVITY o  "ALL OF THE LAWS OF PHYSICS are the same for every inerCal observer." u༇  In parCcular, o  "The speed of light is the SAME for all inerCal observers, regardless of the moCon of the source.” u༇  But this required some big changes in our basic understanding of Cme. 22 “On the Electrodynamics of Moving Bodies” u༇  Einstein had read Lorentz’s book and worked for a few years on the problem. u༇  He did not believe there should be one fixed frame. u༇  He had a breakthrough, “the step” in 1905. 23 Velocity AddiCon u༇  Einstein wanted the speed of light to be the same in every frame. o  This would work for EM equaCons. o  It would agree with experiment. •  Einstein did consider experiment but maybe not Michelson Morley. u༇  But velocity addiCon didn’t make sense to anyone. o  How could an observer in an inerCal frame moving at 0.9c measure light to move at the same speed as we do in our frame at rest? x ' = x + 0.9 ct dx ' dx v' = = + 0.9 c = v + 0.9 c dt dt 24 “The Step” u༇  Einstein realized that by discarding x ' = γ ( x − vt ) the concept of a universal Cme, the speed of light...
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This note was uploaded on 02/24/2014 for the course PHYS 2D taught by Professor Hirsch during the Winter '08 term at UCSD.

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