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Special Relativity

Special Relativity. 1900 +/- 5 The End of physics: Black Body Radiation -> Quantum mechanics Velocity of light With Respect to ether Maxwell ’ s Equations… But what does light move through? Ether. Michelson-Morley. Path parallel to ether should take a bit longer, Tried it in June/January

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Special Relativity

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  1. Special Relativity • 1900 +/- 5 • The End of physics: • Black Body Radiation -> Quantum mechanics • Velocity of light With Respect to ether • Maxwell’s Equations… • But what does light move through? • Ether

  2. Michelson-Morley Path parallel to ether should take a bit longer, Tried it in June/January The Earth is at rest in ether, ether drag, Lorentz contraction, or...

  3. Einstein’s Gedanken If we caught up to an EM wave what would we see: B and E fields with nothing to create them This is impossible Therefore we cannot catch up to light waves…

  4. Postulates of Special Relativity • First Postulate: • The laws of physics are the same in all inertial frames of reference • There is no experiment you can do to ascertain whether you are moving. • (i.e. all motion is relative) • Second Postulate: • The speed of light is the same no matter what speed the source or observer is going • (i.e the speed of light is a law of physics) • (examples of this with cars/observers/galilean vs relativistic transforms)

  5. The speed of the photons was independent of the speed of the pion

  6. Time Dilation How the clock works What proper time is

  7. Moving Clock slower, Derive, examples with elapsed time,

  8. Lorentz factor: You can safely ignore relativistic effects to about .2 c

  9. Length Contraction l lo Moving objects shrink in the direction of motion

  10. Length Contraction l lo Moving objects shrink in the direction of motion This reconciles the frames of reference

  11. Mass Dilation Electron with 1.0 MeV Ke: m = 1.00 MeV + 0.511 MeV =1.511 MeV Electron at rest mo = 0.511 MeV e e Moving objects gain mass (The gained mass is energy mass as in E = mc2)

  12. Example: What is the length of a 1.00 m stick if it is moving parallel to its length at .90 c? 43.6 cm

  13. Example 2: What is the speed of an electron if it has a mass of 0.634 MeV. (Its rest mass is 0.511 MeV) 0.592 c

  14. Whiteboards: Time Dilation, Length Contraction, Mass Dilation 1 | 2 | 3 | 4

  15. Moe and Joe have clocks that tick every 10.00 seconds. Joe is flying by at .85 c. What time does Moe see Joe’s clock take to tick? (trick with c) 19 s

  16. Two stopwatches, one sitting still, one moving in a very large circle. The clock at rest ticks every .800 s, the moving one ticks every 1.200 s. What speed is the moving watch going? .75 c or 2.24 x 108 m/s

  17. Moe and Joe both have identical watches. Joe is moving with respect to Moe at .85c. If 15 s elapse on Moe’s clock, how much time has elapsed on Joe’s clock? 7.9 s

  18. Muons have a mean life of 2.2 x 10-6 s at rest. What speed are they traveling if they they have an average lifetime of 2.6 x 10-6 s? How far would they travel before decaying on the average? .53c, 1.6 x 108 m/s, 415 m

  19. An electron has a rest mass of 0.511 MeV, and a moving mass of 1.511 MeV. What is its speed ? 0.941 c

  20. What speed does a 45 foot long bus need to go to fit exactly into a tunnel that is 40. feet long? 0.46 c

  21. The Twin “Paradox” Planet X Joe stays on earth Moe goes to planet X that is 30 Ly away at .99 c, Comes back How old Moe is/Joe is Does this violate Special relativity?,Inertial means no acceleration, What they see

  22. Paradoxes Planet X Planet X It’s all relative Moe sees our clocks slow down too Postulates only apply to inertial frames of reference

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