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Special Relativity

Learn about the laws and postulates of special relativity, including the concept of time dilation. Explore examples and understand the effects of relative velocity on time perception.

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Special Relativity

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  1. Physics 102: Lecture 28 Special Relativity • 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/ • Make sure your grade book entries are correct • Bring ID to Final EXAM!!!! Physics 102: Lecture 28, Slide 1

  2. 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. Physics 102: Lecture 28, Slide 2

  3. 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. Physics 102: Lecture 28, Slide 3

  4. Weird! 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. Physics 102: Lecture 28, Slide 4

  5. Example 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) Physics 102: Lecture 28, Slide 5

  6. Preflight 28.1 Example 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 Physics 102: Lecture 28, Slide 6

  7. Preflight 28.1 Example 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 3x108 m/s 3x108 m/s 3x108 m/s Strange but True! Physics 102: Lecture 28, Slide 7

  8. Simultaneous? A flash of light is emitted from the exact center of a box. Does the light reach all the sides at the same time? At Rest Moving Physics 102: Lecture 28, Slide 8

  9. Simultaneous? A flash of light is emitted from the exact center of a box. Does the light reach all the sides at the same time? At Rest YES Moving NO Simultaneous depends on frame! Physics 102: Lecture 28, Slide 9

  10. Simultaneous? http://web.hep.uiuc.edu/home/g-gollin/relativity/p112_relativity_8.html Physics 102: Lecture 28, Slide 10

  11. D Time Dilation t0 is proper time Because it is rest frame of event Physics 102: Lecture 28, Slide 11

  12. L=v Dt D D ½ vDt Time Dilation t0 is proper time Because it is rest frame of event Physics 102: Lecture 28, Slide 12

  13. Example 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. Physics 102: Lecture 28, Slide 13

  14. Example 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. Physics 102: Lecture 28, Slide 14

  15. Example 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? Physics 102: Lecture 28, Slide 15

  16. Example 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! Physics 102: Lecture 28, Slide 16

  17. Example 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? Physics 102: Lecture 28, Slide 17

  18. Example 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 Physics 102: Lecture 28, Slide 18

  19. Twin ParadoxPreflight 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. Physics 102: Lecture 28, Slide 19

  20. Twin ParadoxPreflight 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! Physics 102: Lecture 28, Slide 20

  21. Length in moving frame Length in object’s rest frame Example 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 Physics 102: Lecture 28, Slide 21

  22. Example 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: Physics 102: Lecture 28, Slide 22

  23. Length in moving frame Length in object’s rest frame Example 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) Physics 102: Lecture 28, Slide 23

  24. v=0.1 c v=0.8 c v=0.95 c Length Contraction Gifs Physics 102: Lecture 28, Slide 24

  25. 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 Physics 102: Lecture 28, Slide 25

  26. In the speeder’s reference frame Lo > L In your reference frame Always <1 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 Physics 102: Lecture 28, Slide 26

  27. Time seems longer from “outside” Dt > Dto Length seems shorter from “outside” Lo > L 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. Physics 102: Lecture 28, Slide 27

  28. Relativistic Momentum Relativistic Momentum Note: for v<<c p=mv Note: for v=c p=infinity Relativistic Energy Note: for v=0 E = mc2 Note: for v<<c E = mc2 + ½ mv2 Note: for v=c E = infinity (if m<> 0) Objects with mass can’t go faster than c! Physics 102: Lecture 28, Slide 28

  29. 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 Physics 102: Lecture 28, Slide 29

  30. Gook Luck on the Exam! Physics 102: Lecture 28, Slide 30

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