Announcements 11/28/12
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Prayer
Exam 3 going on through tomorrow (T.C. closes at 4 pm)
Project Show & Tell winners:
a.
b.
c.
d.
e.
Cade & Seth – musical cadences
Tess & Brigham - pvc instrument
Tyler - sonoluminescence
Ryan Peterson - particle collision simulator
Konrie, Dallin, Hsin Ping – hot air balloon
Review: Lorentz transformation equations
x2   x1   (ct1 )
ct2   x1   (ct1 )
x  
  
 ct  2  
  x  (can also write time on
 
  ct  top, on both sides, since
1
matrix is symmetric)
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Rate the Tutorial Lab TAs (with photos)
http://gardner.byu.edu/tas/tutorrating.php
Frank &
Ernest
From warmup
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Extra time on?
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Other comments?
Lee’s Lorentz program, again
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Demonstrating space contraction
Quick Writing
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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).
a.Draw a space-time diagram from Lee’s point of
view.
b.Draw a space-time diagram from Cathy’s point
of view (roughly).
a.What is slope of John’s worldline, in Cathy’s
point of view?
b.What is velocity of John with respect to Cathy?
Velocity transformations
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General formula, derived using that same
approach:
12   23
13 
1  12  23
Compare to “Galilean”:
v13  v12  v23
“1-3” = “of object 1 with respect to object 3”
or “of object 1 as measured by 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.)
From warmup
12   23
13 
1  12  23
[Dr. Colton on a train, class on ground.] Suppose I throw
the ball at 0.5 c. What speed does the class observe the
ball to travel at when the train is moving at 0.01c?
0.50c? 0.99c? (Give 4 sig figs.) What do these answers
teach you?
a. 0.01c  0.5075c (compare to 0.51c)
b. 0.50c  0.8000c (compare to 1.00c)
c. 0.99c  0.9967c (compare to 1.49c)
For situations with small velocities, the answers are close to
what Newton would predict. For situations with large
velocities, the answer is always limited by the speed of
light.
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Class-designed problem
12   23
13 
1  12  23
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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?
Worked problem
Four “simultaneous” events: viewed by Earth, (x, ct) = …
a. (0.5, 2)
b. (0, 2)
c. (-1, 2)
d. (-2, 2)
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Dr. Colton’s rocket comes by, going 0.5 c in the positive x
direction. Where/when does he measure these events?
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 = 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
Some things to notice
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“Linear” transformation: Lines always transform into lines!
45 degree lines always transform into 45 deg lines.
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 inside the light cone for one observer
(“timelike”), then it’s inside the cone for all observers.
I.e. no observer can see it happen at negative time.
– If a point is outside the light cone (“spacelike”), you can
always find some observer that sees it happen at a
negative time.
a. Causality & God
Worked Problem (on handout)
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Optional problem from HW 40
Worked Problem (on handout)
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Optional problem from HW 40