Announcements 12/1/10
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Prayer
Exam 3 ongoing
Friday’s lecture: no reading assignment
Project Show & Tell – only 3 volunteers so far. Up to 15
extra credit points available! (for each group member)
Email me by Saturday night.
All late homework & extra credit papers due Sat, Dec 11
Very Important Definitions
v
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c
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1
1  2
“gamma” is sometimes called “the Lorentz factor” or “the
time dilation factor”
Space-time diagrams
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Example: me slamming the book on the table
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Example: me slamming the book on the table again
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Example: measuring the time between book slams
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Example: measuring the length of the book
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“World lines” for Dr. Colton, book, & for space traveler
passing by earth
a. When/where do these events occur?
t vs. ct
Quick Writing
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Back to Dr. Colton’s trip to Zyzyx (Dr. Colton
traveling at 0.9 c). Draw, as accurately as you can,
these four world-lines:
a. The planet Earth
b. The planet Zyzyx
c. Dr Colton, as he travels to Zyzyx
d. Leaving from the Earth at the same time/place, a
light beam that travels to Zyzyx
Draw, as accurately as possible, the same four
world-lines, from Dr. Colton’s point of view.
Light cones
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Present
Possible futures
Possible pasts
“Elsewhere”
Terminology: “timelike” vs “spacelike”
Example
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Dr. Colton, on a fast train, turns on a
flashlight at ct=1. People on the ground
watch. Draw worldlines for Dr. Colton and
the people on the ground. Draw the light
from the flashlight. Mark the “flashlight
turned on” event.
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Do this for both frames of reference.
Reading Quiz
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The Lorentz transformation equations in the
book assume objects only have relative
motion in the +x or –x directions
a. True
b. False
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The Lorentz transformation equations for y
and z are more complicated than the
equations for x and t.
a. True
b. False
Lorentz Transformations, derived
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Not in this class! ;-)
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Can be done by using properties we’ve
discussed: length contraction, time dilation,
gamma, basic worldline transformations
The Lorentz Transformations
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As regular equations:
xframe2   xframe1   (ct )frame1
(ct )frame2   xframe1   (ct )frame1
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In matrix form:
x
 

 
 ct  frame 2  
  x 
 
  ct 
frame1
Differences between my equations & book’s equations
Disclaimer: I often reverse order of x and ct. That’s OK.
Lorentz transformations, graphically
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Lee’s program
Similarity with rotations
How to choose + vs –
Note: for HW problems, you
can use Lee’s program to
check your answers—but not to
DO your problems.