Week 7 Physics 120-01
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This 3 page Class Notes was uploaded by Alexandra Graham on Friday March 6, 2015. The Class Notes belongs to Physics 120-01 at University of Massachusetts taught by Guy Blaylock in Spring2015. Since its upload, it has received 90 views. For similar materials see Big Bang to Black Hole in Physics 2 at University of Massachusetts.
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Date Created: 03/06/15
Class Notes 32 These ideas from the Equivalence Principle led to Einstein39s new understanding of Gravity 1 Light bends in a gravitational eld 2 Gravitational redshift is a thing Two Notes 0 In the absence of gravity or material light goes in a straight line 0 The reason that light sometimes curves is because spacetime in curved so light is always trying to go straight but the straightest path looks curved to us What is a quotstraight linequot in curved space In a small enough region space will appear at To make a straight line you draw a straight line in every local region Euclidean Flat Geometry The stuff you learned in high school 0 Parallel lines never cross Geometry of a Sphere quotstraightquot lines will always cross somewhere all straight lines will always interact with all other lines Pythagorean Theorem always fails even on right triangles on the sphere The rules are all different in curved space Types of Curvature images on slides Positive curvature Sphere Geometry of a sphere the same all lines interact Neoative curvature saddle Many lines never cross in negative But many do Angles of a triangle add up to less than 180 degrees Secret of General Relativity Light beams try and follow local topography as if in straight paths but the topography is curved because space time itself is curved What Causes Spacetime to Curve MASS or any other form of energy quotMass tells spacetime how to curve Spacetime tells mass how to movequot It took Einstein 8 years to gure out how much spacetime curves Embedding Diagrams representative pictures of curved space Questions Curved space Answers 0 Why do all masses have the same acceleration o All masses are subject to the same curved spacetime Why does light bend 0 It39s just following the curve of the path 0 Why do clocks tick slower in a gravity eld 0 Both space and time are stretched so there are longer intervals bn ticks of a clock And once prediction Objects moving through curved spacetime will be delayed they have farther to travel 34 Reasons Why Light Bends Near a Gravitational Mass How to Prove This quotquotquot Prediction Radio waves or a beam of light shot past a heavv star You want to time the waves but how do you make the measurements You have it bounce them off something like a planet behind the sun cough Venus cough and come back to us so we can measure any delay L39ght Retardation light passing close to a large mass will experience a time delay as well as a de ection 1970 Shapiro measured time delay of radar re ection off Venus as it went through superior conjunction was right behind the sun 1 Equivalence principle light bends in each local reference frame 2 Because spacetime is bent adjacent local reference frames are not all lined up in the same direction good image on slides BLACK HOLES What does spacetime look like near a black hole Embedding diagram pothole goes on forever in nitely deep 0 Space to strongly curved near center that nothing can escape Karl Schwarzschild 2 months after general relativity published by Einstein Schwarzschild applied to the vicinity of massive stars invented black holes without even knowing it Why Can39t Light Escape a Black Hole Spacetime is not static A really good image would not be a snapshot but a movie and that movie would show space owing into the pothole Space is moving at the speed of light so the light is trying unsuccessfully to travel upstream Unfortunately I could not attend Friday s lecture
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