Special Relativity Cont'

1
PH103
Special Relativity Cont.
Dr. James van Howe Lecture 15
April 18, 2008
Albert Einstein when he was a young patent clerk
Some slides courtesy of Prof. Vogel AKA Ms.
Relativity
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Recall our sample problem
Bert
The length between planets measured from the
earth by Bert is 12 c-year as given by the
problem. Bert and Ernie agree that the Ship or
the Earth (depending on your point of view) is
traveling away at 0.6c.
So Bert measures
Ernie
Ernie measures the duration of his trip (start
and stop) in the same place (in the ship), so
Ernie measures the proper time, which is less
than Bert. Recall Einstein thought about the
clock standing still as he sped away from it at
light speed. Berts measurement of Ernies trip
therefore should be longer.
Time Dilation
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Length Contraction

• The problem tells us that from the Earth, Bert
  measures the distance Ernie travels between
  planets as 12 c-years
• Ernie sees the alien planet getting closer at
  0.6c for 16 years.
• d vt (0.6c)(16y) 9.6 c-yr
• Both are measuring the distance between Earth and
  the other planet, yet the distances are different!

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Length Contraction

• Generalize result

Eq 26-3

• L and Lo are both lengths of same thing (or
  trip)
• measured by different observers
• v is relative speed of the two observers
• Notice that if vltltc , the two lengths are ?.
• Hard part which length is which?

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Proper Length

• Whats the difference between L and Lo?
• Lo is the proper length or rest length
• Its always longer than other measured length.
• Def proper length is length in frame in which
  object (or ends of trip) is at rest
• For example
• Object, or anyone at rest relative to it,
  measures objects proper length.
• Your own height

• Length of ship you are riding on

• Someone measures the proper length between two
  objects, if both are at rest relative to them
• person on either planet, for a trip between
  planets

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• Can we find the trip length according to Ernie
  from length contraction?
• Yes.
• Who measures proper length?

• Bert

Wow -- it agrees!
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Just How Proper is it?

• If there is a proper time and proper length,
• is there a proper reference frame?
• NO!!!!!!!
• Proper time of trip in example Ernie
• Proper length of trip in example Bert
• Proper time of astronauts heartbeat Astronaut
• How does astronauts heartbeat look to you?
• Proper time of your heartbeat You
• How does your heartbeat look to astronaut?

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Simultaneity
Eraser Demo
Train animation
http//youtube.com/watch?vwteiuxyqtoMfeaturerel
ated
-Dont confuse the fact that first signal arrives
because the speed shorter, or that the distance
is shorter. The distance from the passenger to
the ends of the train doesnt change in her own
frame, nor the speed of light (in any frame for
that matter).
-Really, to her one lightning strike physically
occurs first, and the other later
-In relativity, if two events are simultaneous in
one frame, they are not in another and visa-versa
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Pole-Barn Paradox
20 m
10 m
For an observer in the barn, the pole just fits
as it passes through. We could close the doors
for a split second without busting them
10 m
10 m
But for the observer on the pole, the bar doesnt
have a chance.
20 m
5 m
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Simultaneity to the Rescue
In the Barn Frame
10 m
10 m
-front of pole enters the front of the barn at
t0 -back of pole enters barn at t10 m/0.86c
38.76 ns -this is the time where it just fits so
we could close both doors quickly at 38.76 ns and
then open them
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In the Pole Frame
20 m
5 m
-front of pole enters the front of the barn at
t0 -front of pole leaves barn at 5 m/0.86c
19.38 ns -back of pole enters barn at t20
m/0.86c 77.52 ns -back of pole leaves barn at
77.52 ns 5 m/0.86c 77.52 ns 19.3896.9 ns
So back door closes at 19.38 ns for one instant
and opens and then front door closes at 77.52 ns
for one instant. In the pole frame the events are
not simultaneous (one door closes first like
train example rather than both at 38.76 ns)!
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Twin Paradox

• Remember that an astronaut ages slowly as viewed
  by you
• But you age slowly as viewed by them
• What if you were twins before the trip,
• who would really age more slowly
• Who will be younger when you meet up again

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Twin Paradox

• Who would really age more slowly
• Both of your observations are real!
• Who will be younger when you meet up again
• You will not meet up again
• if you both continue at constant velocity
• if you both stay in inertial frames

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Twin Paradox

• Who will be younger when you meet up again, if
  one of you turns around and comes back?
• The one who turns back accelerates time
  dilation does not hold in accelerated frame
• The one who accelerated will be younger because
  both agree that the one in the accelerated frame
  ages slowly

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Next time Everything is Energy
Speeding up a mass makes it effectively heavier

• Kinetic energy
• is zero when v0
• K mc2 - moc2

• When v 0
• Energy is not zero
• rest energy moc2