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Announcements 11/26/12

Announcements 11/26/12. Prayer Exam 3 ongoing, ends on Saturday Review session: today 4:30-6 pm, in this room Next Wednesday: Project “Show & Tell” I’ll pick 4 groups to do 10 min presentations If I select you, you get 5 extra credit pts

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Announcements 11/26/12

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  1. Announcements 11/26/12 • Prayer • Exam 3 ongoing, ends on Saturday • Review session: today 4:30-6 pm, in this room • Next Wednesday: Project “Show & Tell” • I’ll pick 4 groups to do 10 min presentations • If I select you, you get 5 extra credit pts • If I pick you, but you then back out, you get docked pts • To volunteer, send me an email by Wed night. Tell me why I should pick you: what is especially cool about your project that other students will be interested in? Foxtrot

  2. From warmup Extra time on? “more real life experiments” ;-) Other comments? not in particular

  3. From warmup Last class period we briefly discussed the famous "twin paradox". What is the seeming paradox, and how is it resolved? That if you have a set of twins and one heads off at a significant speed of light, they both undergo time dilation in the other's reference frame, so who would be older when they met up again? It is solved by the realization that the one who flies the spaceship changes his [inertial] reference frame during his flight, so his observations are incorrect and the twin who stayed on the ground would have the proper time.

  4. g v/c What we learned last time • Einstein’s postulates • Light: like sound, speed of wave doesn’t depend on speed of source • Light: unlike sound, there is no medium… if source is in an enclosed train car, observer on ground will still see light waves travel at c. • “Time dilation”

  5. What we learned last time, cont. • Twin paradox • Resolved because the equations we’ll discuss only apply to inertial reference frames (no acceleration). • Simultaneous events • Things that happen at same time in one reference frame will NOT be simultaneous in another one. • Dr. Colton with flashlights in train • Delayed observation due to time of light travel • We’ll ignore, unless specifically stated in problem. • I.e., if problem says “Joe measures such-and-such to occur at t = 5 s,” that means he has already accounted for that time delay somehow

  6. Simultaneity • Viewed from the ground; train moving to right. Events which happen simultaneously in one “reference frame” do NOT happen simultaneously in any other reference frame Which light ray travels farther? Which light ray hits the wall first?

  7. Video • Albert, Henry, and simultaneity (expanding spheres of light) (1:35)

  8. Considering space travel… • Dr. Colton takes his rocket (0.9 c, g = 2.29) to planet Zyzyx, 1 light year away. • Earth frame: how long does it take? • Earth frame: how much does Dr. Colton age? • Colton frame: how much does Dr. Colton age? • Colton frame: how fast was planet Zyzyx “approaching”? • Do you see a problem? x=vt: t=1.11 year 0.485 year 0.485 year 0.9 c x = vt

  9. Length contraction • Which is correct?: Dr. Colton aged so little because… • time was slowed down • the distance shrank Earth F.O.R. Colton F.O.R.

  10. Video • Twin paradox (3:40)

  11. From warmup What is the "rest length" of an object? the length of an object as measured by someone who is at rest relative to the object.

  12. From warmup What is the "proper time" of a journey? The time measured by an observer who sees the two events happen at the same position. The time of the journey as measured by a clock moving at the same speed as the vessel.

  13. Proper time & Rest length • Dr. Colton aged so little because… • time was slowed down for him (Earth view) • the distance shrank for him (Colton view) • Who measures Dr. Colton’s trip’s “rest length”? • Who measures Dr. Colton’s trip’s “proper time interval”?

  14. Barn paradox • Thought question: Does Dr. Colton fit inside the barn? • Yes • No • It depends Dr. Colton doors Barn frame: Colton frame:

  15. Relativistic Doppler effect • A.k.a. “Doppler effect for light” • Must be relativistic, because you don’t get a measurable frequency/wavelength shift until source/observer speed is close to speed of light wave • Equation, used back in HW 19-4 • If moving towards each other: num: + den: -

  16. Relativistic Doppler effect: Derivation wavelength l, frequency f • Source frame: after Dr. Colton hits one wave crest, how fast does the gap between him and next crest “close”? • Source frame: what’s the time between wave crests for Dr. Colton? • Colton frame: is the time between wave crests faster or slower than that? (and by how much?) • Colton frame: therefore, time between wave crests = … v source of red light waves Dr. Colton c v+c t = dist./vel. = ls/(v+c) Faster, by factor of g

  17. Events • What’s an event? • When did that happen? • Where did that happen?

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