Transcript Announcements 11/26/12

Announcements 11/26/12
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Prayer
Exam 3 ongoing, ends on Saturday
Review session: today 4:30-6 pm, in this room
Next Wednesday: Project “Show & Tell”
a. I’ll pick 4 groups to do 10 min presentations
b. If I select you, you get 5 extra credit pts
c. If I pick you, but you then back out, you get docked pts
d. To volunteer, send me an email by Wed night. Tell me
why I should pick you: what is especially cool about
your project that other students will be interested in?
Foxtrot
From warmup
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Extra time on?
a. “more real life experiments” ;-)
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Other comments?
a. not in particular
From warmup
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Last class period we briefly discussed the famous
"twin paradox". What is the seeming paradox,
and how is it resolved?
a. That if you have a set of twins and one heads
off at a significant speed of light, they both
undergo time dilation in the other's reference
frame, so who would be older when they met
up again? It is solved by the realization that
the one who flies the spaceship changes his
[inertial] reference frame during his flight, so
his observations are incorrect and the twin
who stayed on the ground would have the
proper time.
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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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
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
Simultaneity
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Viewed from the ground; train moving to right.
Events which happen simultaneously in one
“reference frame” do NOT happen
simultaneously in any other reference frame
Which light ray travels farther?
Which light ray hits the wall first?
Video
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Albert, Henry, and simultaneity (expanding
spheres of light) (1:35)
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 aged so little
because…
a. time was slowed down Earth F.O.R.
b. the distance shrank Colton F.O.R.
Video
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Twin paradox (3:40)
From warmup
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What is the "rest length" of an object?
a. the length of an object as measured by
someone who is at rest relative to the object.
From warmup
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What is the "proper time" of a journey?
a. The time measured by an observer who
sees the two events happen at the same
position.
b. The time of the journey as measured by a
clock moving at the same speed as the
vessel.
Proper time & Rest length
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Dr. Colton aged so little because…
a. time was slowed down for him (Earth view)
b. the distance shrank for him (Colton view)
Who measures Dr. Colton’s trip’s “rest length”?
Who measures Dr. Colton’s trip’s “proper time
interval”?
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
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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
cv
f f
c v
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1 
or... f   f
1 
If moving towards each other:
num: +
den: -
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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