Announcements 12/3/10 Prayer Wednesday next week: Project Show & Tell

a. 5 extra credit points for volunteering, 10 points if I pick youb. Applications due tomorrow night; 5 volunteers so far

Lee’s program: see email TA ratings: see email Survey about Optics HW problems: extended until tomorrow Definitions:

v

c 2

1

1

Lorentz transformations:

2 1

x x

ct ct

2 1

ct ct

x x

or also

2 1 1

2 1 1

( )

( )

x x ct

ct x ct

Worked problem #1

Four “simultaneous” events: viewed by Earth, (x, ct) = …

a. (0.5, 2)b. (0, 2)c. (-1, 2)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? = 1.1547, = 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

Worked problem, cont Some things to notice:

a. “Linear” transformation: Notice that lines transform into lines

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. 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. Causality!

point “e” = (5.773, -1.155)

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. In Cathy’s frame: draw the world lines of Cathy, Lee, and the right end of the meterstick.

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. Find slope of new line (which is inverse of ) Result: vJohn-Cathy = 0.8 c General formula:

1 2 2 31 3

1 2 2 31

1 3 1 2 2 3v v v Compare to “Galilean”:

“1-3” = “of object 1 with respect to object 3”

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.)

Worked Problem #3

HW 39-2 (the one that got canceled)

0.99687

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