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Seating—6-person “ Pod ” arrangement

Seating—6-person “ Pod ” arrangement. Reading Quiz – August 31, 2012. True or False: In SR units, the speed of light is defined as c = 1 ( unitless ). Reading Quiz – August 31, 2012. True or False: In SR units, the speed of light is defined as c = 1 ( unitless ) . TRUE.

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Seating—6-person “ Pod ” arrangement

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  1. Seating—6-person “Pod” arrangement

  2. Reading Quiz – August 31, 2012 • True or False: In SR units, the speed of light is defined as c = 1 (unitless).

  3. Reading Quiz – August 31, 2012 • True or False: In SR units, the speed of light is defined as c = 1 (unitless). TRUE

  4. Reading Quiz – August 31, 2012 • True or False: In SR units, the speed of light is defined as c = 1 (unitless). • Which of the world-lines in the space-time diagram represents the motion of an object sitting at rest?

  5. Reading Quiz – August 31, 2012 • True or False: In SR units, the speed of light is defined as c = 1 (unitless). TRUE • Which of the world-lines in the space-time diagram represents the motion of an object sitting at rest? D—as time increases, the object doesn’t move

  6. Volume R, Chapter 2 Synchronizing Clocks

  7. R1T.8 • Imagine you are in a train traveling at one-half of the speed of light relative to the earth. Assuming that photons emitted by the train’s headlight travel at the speed of light relative to you, they would (according to the Galilean velocity transformation) travel at 1.5 times the speed of light relative to the earth? • True • False

  8. R1T.8 • Imagine you are in a train traveling at one-half of the speed of light relative to the earth. Assuming that photons emitted by the train’s headlight travel at the speed of light relative to you, they would (according to the Galilean velocity transformation) travel at 1.5 times the speed of light relative to the earth? • True • False Earth is Home Frame Other Frame is me on the train We want to know the speed of the photons as seen from HF Galilean velocity transformation v’ = v – β v = ? = v’ + β (using a little algebra) v’ = c Β = 0.5c So v = v’ + β = c + 0.5c = 1.5c

  9. R1T.8 • Imagine you are in a train traveling at one-half of the speed of light relative to the earth. Assuming that photons emitted by the train’s headlight travel at the speed of light relative to you, they would (according to the Galilean velocity transformation) travel at 1.5 times the speed of light relative to the earth? • True • False But you all probably learned that the speed of light cannot be exceeded…so what happened?

  10. Light and Time Video: https://www.youtube.com/watch?v=7qJoRNseyLQ (NieldeGrasse Tyson explains Michelson-Morley)

  11. Experimental Idea: Michelson-Morley “Swimming” with the river “Swimming” across the river

  12. “Out of Tune” speed of light (expected) Video http://video.mit.edu/watch/tuning-forks-resonance-a-beat-frequency-11447/ (MIT video: beats. Start at 1:30)

  13. “Out of Tune” speed of light (expected)

  14. “In Tune” speed of light (actual result!)

  15. R1T.8 • Imagine you are in a train traveling at one-half of the speed of light relative to the earth. Assuming that photons emitted by the train’s headlight travel at the speed of light relative to you, they would (according to the Galilean velocity transformation) travel at 1.5 times the speed of light relative to the earth? • True • False But you all probably learned that the speed of light cannot be exceeded…so what happened? Galilean transformations make sense but are INCORRECT!

  16. Light and Time • Einsteinian Relativity – light is fundamental • Jettison the ether • v’ light,x = vlight,x = c = 2.998x108 m/s • In SR units, c = 1 exactly • There is no absolute universal time! • Has been confirmed experimentally in many ways • A direct demonstration involves measuring the speed of photons emitted by particles traveling near the speed of light. • Confirms the speed of light to five significant figures • We must alter our common-sense notions of space and time.

  17. Distance and Time • Synchronizing Clocks • Use light pulses  Δx = c (tB – tA) • For known distances, check the time passed, use known c • SR Units • Distance  Δt = Δx/c =3.33x10-9 s Simplifies equations to use light-time units • Velocity  unitless, a fraction of the speed of light; c=1

  18. R2T.1 • Imagine that in the distant future there is a space station on Pluto. While you (on earth) are watching a video transmission from Pluto, which at the time is known to be 5.0 light-hours from earth, you notice that a clock on the wall behind the person speaking in the video reads 12:10 p.m. You note that your watch reads exactly the same time. Is the station clock synchronized with your watch? • Yes, it is. • No, it is not. • The problem doesn’t give enough information to tell.

  19. R2T.1 • Imagine that in the distant future there is a space station on Pluto. While you (on earth) are watching a video transmission from Pluto, which at the time is known to be 5.0 light-hours from earth, you notice that a clock on the wall behind the person speaking in the video reads 12:10 p.m. You note that your watch reads exactly the same time. Is the station clock synchronized with your watch? • Yes, it is. • No, it is not. • The problem doesn’t give enough information to tell.

  20. R2T.2 • Imagine that you receive a message from a starbase that is 13 light-years from earth. The message is dated July 15, 2127. What year does your calendar indicate? • 2127 • 2114 • 2140 • Other (specify)

  21. R2T.2 • Imagine that you receive a message from a starbase that is 13 light-years from earth. The message is dated July 15, 2127. What year does your calendar indicate? • 2127 • 2114 • 2140 • Other (specify)

  22. R2T.3 • The speed of a typical car on the freeway expressed in SR units is most nearly • 10-7 • 10-10 • 10-8 • 10-4 • 10-6 • Other (specify) • None of these answers is right: we have to state units.

  23. R2T.3 • The speed of a typical car on the freeway expressed in SR units is most nearly • 10-7 • 10-10 • 10-8 • 10-4 • 10-6 • Other (specify) • None of these answers is right: we have to state units. (Note: in SR units, velocity is unitless!)

  24. Spacetime Diagrams • Graphical representation of relativistic motion • Position on horizontal, time on vertical • Use SR units – both position and time in seconds • Worldline – represents motion, slope = 1/v

  25. R2T.4 • The spacetime diagram in the figure shows the worldlines of various objects. Which object has the largest speed at time t = 1s?

  26. R2T.4 • The spacetime diagram in the figure shows the worldlines of various objects. Which object has the largest speed at time t = 1s?

  27. R2T.5 • The spacetime diagram in the figure shows the worldlines of various objects. Which object has the largest speed at time t = 4s?

  28. R2T.5 • The spacetime diagram in the figure shows the worldlines of various objects. Which object has the largest speed at time t = 4s?

  29. R2T.6 • The spacetime diagram in the figure shows the worldlines of various objects. Which one cannot possibly be correct? Explain why.

  30. R2T.6 • The spacetime diagram in the figure shows the worldlines of various objects. Which one cannot possibly be correct? Explain why.

  31. R2T.7 • The object whose worldline is labeled B is moving along the x axis, true (T) or false (F)?

  32. R2T.7 • The object whose worldline is labeled B is moving along the x axis, true (T) or false (F)?

  33. Example • At time t = 0, two spaceships are moving through the region of space near planet Earth as shown in the diagram below. Assume you are observing from Earth, which is at x = 0s, and assuming that both ships travel at constant velocities, create a space-time diagram showing the earth and both ships.

  34. AS A MOVIE…

  35. AS A MOVIE…

  36. AS A MOVIE…

  37. AS A MOVIE…

  38. AS A MOVIE…

  39. R2T.8 • A light flash leaves a master clock at x = 0, at time t = -12 s. It is reflected from an object at a certain distance in the –x direction from the origin, and then returns to the origin at t = +8s. From this information, we can infer that the spacetime coordinates of the reflection event are [t, x] = • [4s, 20s] • [-4s, -20s] • [10s, -2s] • [2s, -10s] • [-2s, -10s] • Other (specify)

  40. R2T.8 • A light flash leaves a master clock at x = 0, at time t = -12 s. It is reflected from an object at a certain distance in the –x direction from the origin, and then returns to the origin at t = +8s. From this information, we can infer that the spacetime coordinates of the reflection event are [t, x] = • [4s, 20s] • [-4s, -20s] • [10s, -2s] • [2s, -10s] • [-2s, -10s] • Other (specify)

  41. R2T.8 • A light flash leaves a master clock at x = 0, at time t = -12 s. It is reflected from an object at a certain distance in the –x direction from the origin, and then returns to the origin at t = +8s. From this information, we can infer that the spacetime coordinates of the reflection event are [t, x] = • [4s, 20s] • [-4s, -20s] • [10s, -2s] • [2s, -10s] • [-2s, -10s] • Other (specify)

  42. R2T.8 • A light flash leaves a master clock at x = 0, at time t = -12 s. It is reflected from an object at a certain distance in the –x direction from the origin, and then returns to the origin at t = +8s. From this information, we can infer that the spacetime coordinates of the reflection event are [t, x] = • [4s, 20s] • [-4s, -20s] • [10s, -2s] • [2s, -10s] • [-2s, -10s] • Other (specify) (It’s light, so it has a slope of 1 or -1)

  43. R2T.8 • A light flash leaves a master clock at x = 0, at time t = -12 s. It is reflected from an object at a certain distance in the –x direction from the origin, and then returns to the origin at t = +8s. From this information, we can infer that the spacetime coordinates of the reflection event are [t, x] = • [4s, 20s] • [-4s, -20s] • [10s, -2s] • [2s, -10s] • [-2s, -10s] • Other (specify)

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