Announcements 12/2/11 Prayer Project Show & Tell winners: a. a.Darren & Lisa - constructing a vowel synthesizer b. b.Linea - creating a virtual "marching band" string quartet c. c.Joshua M and Ryan - measuring the speed of sound in gases d. d.Mike and James - Christmas caroling with PVC pipes Office hours: a. a.Today: Colton none; Chris 2:30-5 pm b. b.Monday: Colton regular; Chris regular c. c.Wed: Colton none; Chris 5-7 pm Lorentz transformations: (can also write time on top, on both sides, since matrix is symmetric)

Frank & Ernest

Quick Writing Lee is standing on a train going past Cathy (on the ground) at +0.5 c. John is also on the train, running past Lee at +0.5 c (relative to Lee). Draw a space-time diagram from Lee’s point of view. Draw a space-time diagram from Cathy’s point of view (roughly). --Lorentz program-- What is slope of John’s worldline, in Cathy’s point of view? What is velocity of John with respect to Cathy?

Velocity transformations General formula, derived using that same approach: Compare to “Galilean”: “1-3” = “of object 1 with respect to object 3” or “…in object 3’s reference frame” 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 Problems Bryan is moving at 0.9c relative to Marcus. Marcus is moving at 0.6c relative to Aaron. What is Bryan’s speed relative to Aaron? Emily is moving at ___ c relative to Joshua. David is moving at ___ c relative to Joshua. What is Emily’s speed in David’s reference frame? answer: 0.974c

Worked problem 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

Some things to notice “Linear” transformation: Lines always transform into lines! 45 degree lines always transform into 45 deg lines. a. a.Speed of light the same in all reference frames! This case: downward sloping line. There will be some points having ct=2 (Earth), that are at negative time (Colton)! As mentioned last time… – – 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. a. a.Causality!

Worked Problem (on handout) Optional problem from HW 40

Worked Problem (on handout) Optional problem from HW 40