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PH 301

PH 301. Dr. Cecilia Vogel Lecture 4. Lorentz transformation simultaneity twin paradox. Review. Consequences of Einstein’s postulates length contraction Relativistic Doppler Effect. Outline. John saw Nick’s trip to take 20 years, so John aged 20 yrs.

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PH 301

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  1. PH 301 Dr. Cecilia Vogel Lecture 4

  2. Lorentz transformation simultaneity twin paradox Review • Consequences of Einstein’s postulates • length contraction • Relativistic Doppler Effect Outline

  3. John saw Nick’s trip to take 20 years, so John aged 20 yrs. Nick saw the trip to take 16 years, so Nick aged 16 yrs. Moving clocks run slowly, moving bodies age slowly, … Nick ages slowly from John’s point of view. Recall Trip Example

  4. Symmetry • From Nick’s reference frame. • Nick is at rest • John is moving • If moving bodies age slowly, then John should age slowly, as seen by Nick.

  5. John’s Timeline • x=0 is Earth 0 0 takeoff (both are 20) 20 12 landing (I am 40, Nick is 36) landing celebration (I am 40, Nick is 36) 0 20

  6. Nick’s Timeline • x=0 is ship 0 0 takeoff (both are 20) landing (I am 36, John is 32.8) 16 0 landing celebration (I am 45, John is 40) -x 25

  7. Twin Paradox • If John sees Nick aging slowly, and Nick sees John aging slowly, • what happens if Nick comes back to Earth and they see each other face-to-face? • Who has actually aged less?

  8. Not Actually Symmetric • On way there, each sees the other age slowly, • On way back, each sees the other age slowly. • both are inertial reference frames • so time dilation holds • While Nick is turning around • Nick is not in inertial reference frame • He knows it – acceleration can be felt/detected • He sees John age quickly, catch up, and get ahead • Enough so that he agrees, John has aged more in the end.

  9. Can we at least agree on what things happen at the same time (simultaneous)? No. Example – John said he celebrated Nick’s arrival at the same time as Nick’s arrival happened In Nick’s frame the celebration happened 9 years later! If events happen at different places, one observer might see them as simultaneous, another not. If they happen at same place & same time all agree often physical consequences Simultaneity

  10. If events 1 & 2 happen at different places and some reference frames measure them to be simultaneous others measure event 1 to happen first still others measure event 2 to happen first However…. If the earlier event causes later event all agree on order often physical consequences Simultaneity

  11. Pretend the last part of the demo was done with light flashes rather than erasers. If any answer is no, say which is larger. In your frame: Did the light flashes travel the same distance? Did the light flashes travel at the same speed? Did the light flashes travel for the same amount of time, ttravel=d/v? Did the light flashes arrive at the same time? (tarrive) Did the light flashes actually occur at the same time? Simultaneous?

  12. Pretend the last part of the demo was done with light flashes rather than erasers. If any answer is no, say which is larger. In my frame: Did the light flashes travel the same distance? Did the light flashes travel at the same speed? Did the light flashes travel for the same amount of time, ttravel=d/v? Did the light flashes arrive at the same time? (tarrive) Did the light flashes actually occur at the same time? Simultaneous?

  13. Pretend the last part of the demo was done with light flashes rather than erasers. If any answer is no, say which is larger. In my frame: Did the light flashes travel the same distance? Did the light flashes travel at the same speed? Did the light flashes travel for the same amount of time, ttravel=d/v? Did the light flashes arrive at the same time? (tarrive) Did the light flashes actually occur at the same time? Simultaneous?

  14. Hitler born 20 April 1889 in Germany. Call that x1=0, t1=0, x1'=0, t1'=0 Suppose history book published in New York on 20 April 2010, t2 = 121 yr= 3.8 × 109, x2=6800 km. How fast would observer need to go to observe events in opposite order, t2'<0? Answer should describe all velocities that work, and should be in units of c. PAL – part 1

  15. PAL – part 2 • Vera’s Frame. x=0 is Earth 0 0 departure (both are 20) 20 12 arrival (I am 40, Ryan is 36) landing celebration (I am 40, Ryan is 36) 0 20

  16. Fill in Table • Ryan’s frame. x=0 is ship 0 0 departure (both are 20) arrival (I am 36, Vera is ___) __ __ landing celebration (I am ___, Vera is __) __ __

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