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Announcements 12/2/11

Announcing the winners of the Project Show & Tell, including presentations on a vowel synthesizer, virtual marching band, measuring the speed of sound in gases, and Christmas caroling with PVC pipes. Also, an update on office hours for today and next week.

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Announcements 12/2/11

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

  2. Frank & Ernest

  3. 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?

  4. 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 39.16 and 39.18. Far simpler; works every time! Caution: terms are sometimes negative. (Don’t need to know transverse velocity formula, eqn 39.17.)

  5. 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

  6. Worked problem • Four “simultaneous” events: viewed by Earth, (x, ct) = … • (0.5, 2) • (0, 2) • (-1, 2) • (-2, 2) • Dr. Colton’s rocket comes by going 0.5 c in the positive x direction. Where/when does he measure these events? g = 1.1547, bg = 0.5774 a = (-0.5774, 2.0207); b = (-1.1547, 2.3094); c = (-2.3094, 2.8868); d = (-3.4642, 3.4642) Lee’s program

  7. Some things to notice • “Linear” transformation: Lines always transform into lines! • 45 degree lines always transform into 45 deg lines. • 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. • Causality!

  8. Worked Problem (on handout) • Optional problem from HW 40

  9. Worked Problem (on handout) • Optional problem from HW 40

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