# AS109_lec15 - Special Relativity Quantitative Results 1...

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3/19/14 1 AS 109 3/20/14 General Relativity: Einstein’s Theory of Gravity Special Relativity: Quantitative Results 1. Time passes more slowly in the moving system t = Γ t rest “time dilation” 2. Lengths & distances are shorter along direction of velocity than in rest frame L = L rest / Γ “length contraction” Γ = 1 1 v c Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ 2 v = 0: Γ = 1 v = 0.98 c : Γ = 5 v = 0.995 c : Γ = 10 v = c : Γ = Before trip After trip Relativistic (near light-speed) Trip: The View Since length contraction only works parallel to direction of motion, view from spaceship would be distorted Most of view is collapsed toward forward direction Video clip: View of Orion at 3 different velocities toward center of belt: Special & General Relativity Special Relativity : Phenomena in - & viewed from - reference frames at rest or with constant velocities General Relativity : Phenomena in accelerating reference frames & in presence of gravity (mass) Space-time : The 4-dimensional structure of the universe Einstein’s General Relativity (1915) Assumptions : 1. All observers in freely falling reference frames obtain same results for all experiments performed in those frames Freely falling : either no gravity or dropping in a gravitational field Einstein’s General Relativity (1915) Assumptions : 2. Equivalence Principle: a. Gravitational mass = inertial mass b. Einstein’s version: no experiment can discern the difference between acceleration by gravity or by another force If you were in a spaceship accelerating at 9.8 m/s 2 ,y ou would feel the same downward acceleration as if you were on Earth
3/19/14 2 Einstein’s Results (10 years of work) Mass bends space-time 1. Shortest distance between 2 points - geodesic - is not necessarily a straight line -