Announcements 11/28/11 Prayer Exam 3 ongoing, ends on Saturday Next Wednesday: Project “Show & Tell” a. a.I’ll pick 4 groups to do 10 min presentations b. b.If you volunteer, you get 3 extra credit pts c. c.If I select you, you get 6 more extra credit pts d. d.If I pick you, but you then back out, you get docked pts e. e.To volunteer, send me an 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

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” v/cv/c 

What we learned last time, cont. Twin paradox a. a.Resolved because the equations we’ll discuss only apply to inertial reference frames (no acceleration). Simultaneous events a. a.Things that happen at same time in one reference frame will NOT be simultaneous in another one. b. b.Dr. Colton with flashlights in train Delayed observation due to time of light travel a. a.We’ll ignore, unless specifically stated in problem. b. b.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

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

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

Considering space travel… Dr. Colton takes his rocket (0.9 c,  = 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 year 0.9 c x = vt

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

Video Twin paradox (3:40)

Reading quiz The length of an object measured by someone at rest with respect to the object is called the object’s: a. a.Lorentz length b. b.proper length c. c.relativistic length d. d.zeit-length The term I prefer: “rest length”

Proper time & Rest length Dr. Colton aged so little because… a. a.time was slowed down for him (Earth view) b. b.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”?

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

Relativistic Doppler effect A.k.a. “Doppler effect for light” a. a.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: -

Relativistic Doppler effect: Derivation 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 Dr. Colton source of red light waves c wavelength, frequency f v+c t = dist./vel. = s /(v+c) Faster, by factor of 

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