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
2
Name the Artist/Composer

• Irving Berlin
• Maurice Ravel
• Jeff Buckley
• Rufus Wainwright

3

• You are traveling from Earth to a distant planet
  at near-light speed. I am left on the Earth.
  
• Who measures the proper time of my clock? Of my
  heartbeat? Of your trip to the planet?
  
• Me, me, me
• You, me, me
• Me, me, you
• You, you, you

4
If I am inside a supped-up Lamborghini traveling
near the speed of light and you are clocking my
speed on a track, who measures the proper length
(longer length) of the car?

• me
• you
• C. no one, its relative

5

• You and two friends play a game in space. You
  fly your spaceship from Sarahs planet to
  Jeffrey's. When you are exactly halfway between
  the planets, both friends shine a flash of light
  toward you (simultaneously according to you).
  Which flash eventually gets to you first ,
  according to you?
• The one from Sarah
• The one from Jeffrey
• They both arrive at the same time

6
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
7
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!

8
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 v
• Hard part which length is which?

9
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

10

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

• Bert

Wow -- it agrees!
11
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?

12
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
13
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
14
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 3
8.76 ns -this is the time where it just fits so w
e could close both doors quickly at 38.76 ns and
then open them
15
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)!
16
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

17
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

18
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

19
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

20

• You are traveling from Earth to a distant planet
  at near-light speed. I am left on the Earth.
  
• Who measures the proper time of my clock? Of my
  heartbeat? Of your trip to the planet?
  
• Me, me, me
• You, me, me
• Me, me, you
• You, you, you

21
If I am inside a supped-up Lamborghini traveling
near the speed of light and you are clocking my
speed on a track, who measures the proper length
(longer length) of the car?

• me
• you
• C. no one, its relative

22

• You and two friends play a game in space. You
  fly your spaceship from Sarahs planet to
  Jeffrey's. When you are exactly halfway between
  the planets, both friends shine a flash of light
  toward you (simultaneously according to you).
  Which flash eventually gets to you first ,
  according to you?
• The one from Sarah
• The one from Jeffrey
• They both arrive at the same time