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Chapter 27

Chapter 27. 0. Relativity. This presentation makes relativity look independent of electrodynamics, it is not independent historically or concepturally.

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Chapter 27

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  1. Chapter 27 0 Relativity

  2. This presentation makes relativity look independent of electrodynamics, it is not independent historically or concepturally. • On the Electrodynamics of Moving Bodies (actual title "Zur Elektrodynamik bewegter Körper")by Albert Einstein, submitted June 30, 1905 and published September 26, 1905. • The Annus Mirabilis is often called the "Miracle Year" in English or Wunderjahr in German; Albert Einstein’s 1905 year.

  3. 27Relativity Slide 27-2

  4. Slide 27-3

  5. Slide 27-4

  6. Slide 27-5

  7. Two Standard Reference Frames Slide 27-14

  8. Inertial Reference Frames Slide 27-15

  9. The Galilean Velocity Transformations Slide 27-16

  10. Example Problem You are running at 10 m/s relative to the ground. A person standing still behind you throws ball A toward you at 30 m/s. A person standing still in front of you throws ball B toward you at 30 m/s. And another person standing still in front of you throws ball C straight up into the air at 30 m/s. What are the speeds of balls A, B, and C relative to you? Slide 27-17

  11. Einstein’s Principle of Relativity Slide 27-18

  12. The Constancy of the Speed of Light Slide 27-19

  13. Measuring the Velocity of an Object Slide 27-20

  14. Events and Measurements Slide 27-21

  15. Clock Synchronization Slide 27-22

  16. Example Problem • Ann and Bill are standing 1200 m apart. A firecracker explodes 900 m from Ann, and she sees the light flash at t = 5.0 µs. • At what time did the explosion occur? (Use c = 300 m/µs). • Are “sees flash” and “firecracker explodes” the same event? If not, which is more significant? • At what time does Bill see the flash? Slide 27-23

  17. Example Problem • Ann and Bill are still standing 1200 m apart. Firecrackers explode 300 m on either side of Bill, and Bill (using the eyes in the back of his head) sees the two flashes at the same time. • According to Bill, were the two explosions simultaneous? • According to Ann, were the two explosions simultaneous? Slide 27-24

  18. Example Problem • Ann and Bill are still standing 1200 m apart, and again firecrackers explode 300 m on either side of Bill. Ann sees the two flashes at the same time. • According to Ann, were the two explosions simultaneous? • According to Bill, were the two explosions simultaneous? Slide 27-25

  19. The Relativity of Simultaneity Slide 27-26

  20. The Events in Ryan’s Frame Slide 27-27

  21. The Events in Peggy’s Frame (??) Slide 27-28

  22. The Actual Sequence of Events in Peggy’s Frame Slide 27-29

  23. Relativity of Simultaneity discussion in the Wikipedia • http://en.wikipedia.org/wiki/Relativity_of_simultaneity

  24. Time Dilation: a Light Clock Slide 27-30

  25. Analysis of a Moving Clock Time interval in frame in which clock moves at velocity v Time interval in frame moving with clock Slide 27-31

  26. Time Dilation and Proper Time Slide 27-32

  27. The Twin Paradox Slide 27-33

  28. This twin paradox an all of special relativity is handled better in my Introductory Astronomy, AS101 course PowerPoint. • Titled chapterS2SpaceTime.pptx . • General Relativity, a theory of Gravity, and how gravity effects time-space, is also covered in a PowerPoint called chapterS3TimeSpaceGravity.pptx .

  29. Length Contraction Length of object in a frame in which it’s moving at β = v/c. Length of object in frame in which it’s at rest Slide 27-34

  30. Lorentz Velocity Transformations Slide 27-35

  31. Relativistic Momentum where Slide 27-36

  32. Relativistic Energy The total energy is made up of two contributions: Slide 27-37

  33. Conservation of Energy in Relativity Slide 27-38

  34. Summary Slide 27-39

  35. Additional Example Problems Two volcanoes, Mt. Newton and Mt. Einstein, are 600 km apart. You are at rest exactly halfway between the volcanoes and your friend is at rest at the base of Mt. Newton. Both volcanoes erupt. Your friend, based on measurements he or she makes, determines that the two eruptions are simultaneous. Do you see Mt. Newton erupt first, Mt. Einstein erupt first, or both erupt at the same instant of time? Explain. Slide 27-40

  36. Additional Example Problems • A pole vaulter with a 10-m-long pole parallel to the ground races past you at v 0.8c. He is at the center of the pole. Firecrackers at the ends of the pole explode, and a short time later flashes of light arrive at the pole vaulter at the same instant of time. • Are the explosions simultaneous in the pole vaulter’s reference frame? If not, which firecracker (the right one or the left one) explodes first? • Are the explosions simultaneous in your reference frame? If not, which firecracker (the right one or the left one) explodes first? • If you answered No in either part A or part B, what is the time interval between the first explosion and the second explosion? Slide 27-41

  37. Additional Example Problems The earth is 1.5  1011 m from the sun. An alien spaceship crosses the distance in 4.0 minutes, as measured by the crew on the spaceship. How long does the passage take according to the earthly astronomers who are tracking the spaceship? Through what potential difference must an electron be accelerated to reach a speed of 99% of the speed of light. The mass of an electron is 9.11  1031 kg. Slide 27-42

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