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Published on November 6, 2007

Author: Wen12

Source: authorstream.com

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Special Relativity:  Special Relativity Physics 102: Lecture 28 Make sure your grade book entries are correct Bring ID to Final EXAM!!!! Today’s Lecture will cover chapter 26.1 – 26.7 Take a look at Special Relativity in 14 Easy (Hyper)lessons: http://web.hep.uiuc.edu/home/g-gollin/relativity/ Inertial Reference Frame:  Inertial Reference Frame Frame in which Newton’s Laws Work Moving is OK but…. No Accelerating No Rotating Technically Earth is not inertial, but it’s close enough. Postulates of Relativity:  Postulates of Relativity Laws of physics are the same in every inertial frame Perform experiment on train going east gives same results as on train going west. Speed of light in vacuum is c for everyone Measure c=3x108 m/s if you are on train going east or on train going west, even if light source isn’t on the train. Postulates of Relativity:  Postulates of Relativity Laws of physics are the same in every inertial frame Perform experiment on train going east gives same results as on train going west. Speed of light in vacuum is c for everyone Measure c=3x108 m/s if you are on train going east or on train going west, even if light source isn’t on the train. Relative Velocity (Ball):  Relative Velocity (Ball) ______ throws ball 30 mph. How fast do I think it goes when I am: Standing still? Running 15 mph towards? Running 15 mph away? (Review Lecture 14 for help with Relative Velocities) Relative Velocity (Light):  Relative Velocity (Light) _____ throws photon (3x108 m/s). How fast do I think it goes when I am: Standing still Running 1.5x108 m/s towards Running 1.5x108 m/s away Relative Velocity (Light):  Relative Velocity (Light) _____ throws photon (3x108 m/s). How fast do I think it goes when I am: Standing still Running 1.5x108 m/s towards Running 1.5x108 m/s away Strange but True! 3x108 m/s 3x108 m/s 3x108 m/s Simultaneous?:  Simultaneous? At Rest Moving A flash of light is emitted from the exact center of a box. Does the light reach all the sides at the same time? Simultaneous?:  Simultaneous? At Rest Moving YES NO Simultaneous depends on frame! A flash of light is emitted from the exact center of a box. Does the light reach all the sides at the same time? Simultaneous?:  Simultaneous? http://web.hep.uiuc.edu/home/g-gollin/relativity/p112_relativity_8.html Time Dilation:  Time Dilation t0 is proper time Because it is rest frame of event Time Dilation:  Time Dilation t0 is proper time Because it is rest frame of event Time Dilation:  Time Dilation You and a friend are having a drinking contest. Your friend is on a train traveling at speed v=0.9 c. By her watch, she finishes her drink in 5 seconds. Determine the time you measure, if you are standing still at the train station. Time Dilation:  Time Dilation You and a friend are having a drinking contest. Your friend is on a train traveling at speed v=0.9 c. By her watch, she finishes her drink in 5 seconds. Determine the time you measure, if you are standing still at the train station. Since drinking is happening on the train, that is the “proper” time. Time Dilation 2:  Time Dilation 2 Now it is your turn to drink. According to your watch you finish your drink in 5 seconds. How long does your friend think it took you to finish the drink? Time Dilation 2:  Time Dilation 2 Now it is your turn to drink. According to your watch you finish your drink in 5 seconds. How long does your friend think it took you to finish the drink? Now drinking is happening at the station, so that is the “proper” time. Both people think they won! Space Travel:  Space Travel Alpha Centauri is 4.3 light-years from earth. (It takes light 4.3 years to travel from earth to Alpha Centauri). How long would people on earth think it takes for a spaceship traveling v=0.95c to reach A.C.? How long do people on the ship think it takes? Space Travel:  Space Travel Alpha Centauri is 4.3 light-years from earth. (It takes light 4.3 years to travel from earth to Alpha Centauri). How long would people on earth think it takes for a spaceship traveling v=0.95c to reach A.C.? How long do people on the ship think it takes? People on ship have ‘proper’ time they see earth leave, and Alpha Centauri arrive. Dt0 Dt0 = 1.4 years Twin Paradox Preflight 28.2:  Twin Paradox Preflight 28.2 Twins decide that one will travel to Alpha Centauri and back at 0.95c, while the other stays on earth. Compare their ages when they meet on earth. Twin Paradox Preflight 28.2:  Twin Paradox Preflight 28.2 Twins decide that one will travel to Alpha Centauri and back at 0.95c, while the other stays on earth. Compare their ages when they meet on earth. Earth twin thinks it takes 2 x 4.5 = 9 years Traveling twin thinks it takes 2 x 1.4 = 2.8 years Traveling twin will be younger! Note: Traveling twin is NOT in inertial frame! Length Contraction:  Length Contraction People on ship and on earth agree on relative velocity v = 0.95 c. But they disagree on the time (4.5 vs 1.4 years). What about the distance between the planets? Earth/Alpha d0 = v t Ship d = v t Length Contraction:  Length Contraction Sue is carrying a pole 10 meters long. Paul is on a barn which is 8 meters long. If Sue runs quickly v=.8 c, can she ever have the entire pole in the barn? Paul: Sue: Length Contraction:  Length Contraction People on ship and on earth agree on relative velocity v = 0.95 c. But they disagree on the time (4.5 vs 1.4 years). What about the distance between the planets? Earth/Alpha d0 = v t = .95 (3x108 m/s) (4.5 years) = 4x1016m (4.3 light years) Ship d = v t = .95 (3x108 m/s) (1.4 years) = 1.25x1016m (1.3 light years) Length Contraction Gifs :  Length Contraction Gifs Preflight 28.3:  Preflight 28.3 You’re eating a burger at the interstellar café in outer space - your spaceship is parked outside. A speeder zooms by in an identical ship at half the speed of light. From your perspective, their ship looks: (1) longer than your ship (2) shorter than your ship (3) exactly the same as your ship Preflight 28.3:  Preflight 28.3 You’re eating a burger at the interstellar café in outer space - your spaceship is parked outside. A speeder zooms by in an identical ship at half the speed of light. From your perspective, their ship looks: (1) longer than your ship (2) shorter than your ship (3) exactly the same as your ship Comparison: Time Dilation vs. Length Contraction:  Comparison: Time Dilation vs. Length Contraction Dto = time in same reference frame as event i.e. if event is clock ticking, then Dto is in the reference frame of the clock (even if the clock is in a moving spaceship). Lo = length in same reference frame as object length of the object when you don’t think it’s moving. Relativistic Momentum:  Relativistic Momentum Relativistic Momentum Note: for v<<c p=mv Note: for v=c p=infinity Relativistic Energy Note: for v=0 E = mc2 Objects with mass can’t go faster than c! Note: for v<<c E = mc2 + ½ mv2 Note: for v=c E = infinity (if m<> 0) Summary:  Summary Physics works in any inertial frame Simultaneous depends on frame Proper frame is where event is at same place, or object is not moving. Time dilates Length contracts Energy/Momentum conserved For v<<c reduce to Newton’s Laws Gook Luck on the Exam!:  Gook Luck on the Exam!

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