Announcements 4/8/11
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Prayer
Wednesday next week: Project Show & Tell
a. 5 extra credit points for volunteering, 10 points if I pick you
b. Applications due this afternoon, 5 pm
Definitions:
1
v


1  2
c
Lorentz transformations:
x2   x1   (ct1 )
ct2   x1   (ct1 )
x  
  
 ct  2  
  x 
 
  ct 
1
(can also write time on
top on both sides, since
matrix is symmetric)
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).
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
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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 “…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.)
Worked Problems
12   23
13 
1  12  23
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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?
answer: 0.974c
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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
“Linear” transformation: Lines always transform into lines!
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This case: downward sloping line. There will be some
points having ct=2 (Earth), that are at negative time
(Colton)!
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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. Causality!
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45 degree lines always transform into 45 deg lines.
a. Speed of light the same in all reference frames!
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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