Announcements 12/3/10 Prayer Wednesday next week: Project Show & Tell a. a.5 extra credit points for volunteering, 10 points if I pick you b. b.Applications due tomorrow night; 5 volunteers so far Lee’s program: see TA ratings: see Survey about Optics HW problems: extended until tomorrow Definitions: Lorentz transformations: or also

Worked problem #1 Four “simultaneous” events: viewed by Earth, (x, ct) = … a. a.(0.5, 2) b. b.(0, 2) c. c.(-1, 2) d. d.(-2, 2) Dr. Colton’s rocket comes by going 0.5 c in the positive x direction. Where/when does he measure these events?  = ,  = a = ( , ); b = ( , ); c = ( , ); d = ( , ) Lee’s program

Worked problem, cont Some things to notice: a. a.“Linear” transformation: Notice that lines transform into lines b. b.This case: downward sloping line. There will be some point having ct=2, that (in B’s frame) is at negative time! – – Let’s try transforming point “e” = (6, 2) c. c.Turns out… – – If a point is outside the light cone (“spacelike”), you can always find some observer that sees it happen at a negative time. – – If a point is inside the light cone (“timelike”), then no observer can see it happen at negative time. d. d.Causality! point “e” = (5.773, )

Worked problem #2 Lee is running past Cathy at  = +0.5 (  = 1.155). He passes her at t = 0. Cathy is holding the left end of a meterstick, length = 1 m. a. a.In Cathy’s frame: draw the world lines of Cathy, Lee, and the right end of the meterstick. b. b.In Lee’s frame: draw the same worldlines. Lee’s program

Velocity transformations Lee is standing on a train going past Cathy at +0.5 c. John is also on the train, running past Lee at +0.5 c. What is John’s speed relative to Cathy? (NOT 1.0 c!) First: draw diagram from Lee’s frame Then: transform to Cathy’s frame a. a.Find slope of new line (which is inverse of  ) Result: v John-Cathy = 0.8 c General formula: Compare to “Galilean”: “1-3” = “of object 1 with respect to object 3” Use this instead of book eqns and Far simpler; works every time! Caution: terms are sometimes negative. (Don’t need to know transverse velocity formula, eqn )

Worked Problem #3 HW 39-2 (the one that got canceled) Answers: (a) 53.0; (b) 0.083; (c) 53.0

Worked Problem #4 Optional problem from HW 40

Worked Problem #5 Optional problem from HW 40