AS109_lec14(2) - Everyday Relativity AS 109 Special...

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3/18/14 1 AS 109 3/18/14 Special Relativity: Motion Near the Speed of LightEveryday RelativityIf speeds are much less than the speed of light c: - Velocities add -Time & space are the same for all reference frameswhere phenomena take place & observers make measurements Time and SpaceNewtonassumed that time and space are absolute - Universal system of coordinates for measurements - Measurements of lengths and times should not depend on motion of the observer or presence of massive objects Einstein: this is notthe case Speed of Light: Constant, Nothing FasterMichelson-Morley experiment (1887): the speed of light in a vacuum is constant (c= 3×108m/s) -Does notdepend on motion of either the source of light or the observer -Only wavelength (or frequency) of light is affected by relative motion - Doppler effect - If the speed of light depended on the motion of the source, it would be possible for phenomena to be observed before the event that caused them Einstein: nothing physical, nor any information, can travel faster than light Einstein’s Special Relativity (1905)Special Relativity: compare measurements made from reference frames moving at constant velocityrelative to each other [concept: relative velocity] - Rest frame: platform where velocity is zero Assumptions: 1.Speed of light does not depend on relative motion of source & observer 2.Measurements made of phenomena occurring in observer’s rest frame give usual, “normal” results - Einstein worked out consequences using high-school algebra Special Relativity: Einstein’s ResultsFor measurements of objects & events occurring in a reference frame moving at a constant velocity relative to observer 1. Time passes more slowly in the moving system (as measured by observer) (Time passes normally if measured inside the system) 2. Lengths & distances are shorter along direction of motion than in rest frame (as measured by observer) (Length is normal if measured inside the system)
3/18/14 2 Lorentz Factor: Quantifies Effects of RelativityLorentz factor Γ(v= relative velocity of frames): v = 0: Γ= 1 v = 0.98c: Γ

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