Announcements 11/29/10
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Prayer
Exam 3 starts tomorrow!
Exam 3 – “What’s on the exam” handout
Exam 3 review session tonight, 5 – 6:30 pm, room
C261
Lab 10 due tomorrow
Friday’s lecture: syllabus says “reading: website
handout”. However… there is no website handout;
I’ll just discuss things in class. Therefore, no
reading assignment.
Project final reports & “Show & Tell”—see email
Reading Quiz
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Which was not a topic related to relativity in
today’s reading assignment?
a. “length contraction”
b. “rest energy”
c. “simultaneity”
d. “time dilation”
e. “twin paradox”
What we learned last time
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Einstein’s postulates
Light: like sound, speed of wave doesn’t depend on
speed of source
Light: unlike sound, there is no medium… if source is in
an enclosed train car, observer on ground will still see
light waves travel at c.
“Time dilation”
g
1
v
g

c
1  2
ground point of view:  t train  g  t  ground
train point of view:  t  ground  g  t train
v/c
What we learned last time, cont.
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Delayed observation due to time of light travel
a. We’ll ignore, unless specifically stated in problem.
b. I.e., if problem says “Joe measures such-and-such to
occur at t = 5 s,” that means he has already
accounted for that time delay somehow
Twin paradox
a. Resolved because the equations we’ll discuss only
apply to inertial reference frames (no acceleration).
Simultaneous events
a. Things that happen at same time in one reference
frame will NOT be simultaneous in another one.
b. Dr. Colton with flashlights in train
Video
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Albert, Henry, and expanding spheres of light
Considering space travel…
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Dr. Colton takes his rocket (0.9 c, g = 2.29) to
planet Zyzyx, 1 light year away.
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Earth frame: how long does it take?
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Earth frame: how much does Dr. Colton age? 0.485 year
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Colton frame: how much does Dr. Colton age? 0.485 year
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Colton frame: how fast was planet Zyzyx
“approaching”? 0.9 c
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Do you see a problem?
x = vt
x=vt: t=1.11 year
Length contraction
ground point of view:  x train 
train point of view:  x  ground 
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1
g
 x  ground
1
g
 x train
Which is correct?: Dr. Colton experienced such
a short trip because…
a. time was slowed down for him
b. the distance shrank for him
Reading quiz
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The length of an object measured by
someone at rest with respect to the object is
called the object’s:
a. Lorentz length
b. proper length
c. relativistic length
d. zeit-length
The term I prefer: “rest length”
Proper time & Rest length
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It took Dr. Colton so little time because…
a. time was slowed down for him
b. the distance shrank for him
Who measures Dr. Colton’s trip’s “proper time”?
Who measures Dr. Colton’s trip’s “rest length”?
Barn paradox
Thought question: Does Dr. Colton fit inside the
barn?
a. Yes
b. No Dr. Colton
doors
c. It depends
Barn frame:
Colton frame:
Relativistic Doppler effect
A.k.a. “Doppler effect for light”
a. Must be relativistic, because you don’t get
a measurable frequency/wavelength shift
until source/observer speed is close to
speed of light wave
 Equation, used back in HW 19-4
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cv
f f
c v
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1 
or... f   f
1 
What do the symbols all stand for?
Relativistic Doppler effect: Derivation
wavelength l, frequency f
v
source of red
light waves
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c
Dr. Colton
Source frame: after Dr. Colton hits one wave crest, how fast
does the gap between him and next crest “close”?
v+c
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Source frame: what’s the time between wave crests for Dr.
Colton?
t = dist./vel. = ls/(v+c)
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Colton frame: is the time between wave crests faster or slower
than that? (and by how much?)
Faster, by factor of g
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Colton frame: therefore, time between wave crests = …
l
period   source
 vc
 1
 g 
  
Events
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What’s an event?
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When did that happen?
Where did that happen?
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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?