Special Relativity

1
PH103
Special Relativity
Dr. James van Howe Lecture 14
April 16, 2008
Albert Einstein when he was a young patent clerk
Some slides courtesy of Prof. Vogel AKA Ms.
Relativity
2
Prelude Define Events

• ?An event is something that occurs at
• One point in space
• One instant in time
• A party is not an event. Your arrival at the
  party is (approx).
• NOTE
• ?Events happen in all frames!
• Events dont move!
• Events dont have a frame!

3
You Can Hide But You Cant Run

• Speed of Light is Measured to be c3X108 m/s by
  all.
• Can you catch up? NO!. No matter how fast you
  go, light still outruns you by c.
• Can you run away? NO! No matter how fast you go,
  light still catches up by c.
• What if the source moves? A lamp coming at you
  (or away from you), light still reaches you at c.

4
Some Consequences

• Can be derived from constancy of speed of light
• Time interval between two events is different
  measured by different observers.
• Length of object or length of a trip is different
  measured by different observers.

5
Recall Classical Relativity
Plane as Reference Frame
Earth as Reference Frame
Inside the plane cabin, tpretzel5.0s
From view of the Earth, the pretzel goes...farther

• At any point, let the velocity of the pretzel
  measured by the plane observer be vp.
• The velocity measured by Earth observer is vplane
  vp. Earth observer measures faster speed
• pretzel goes farther, faster, but same time (5s)

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Einsteins Relativity
Light beam now instead of pretzel
Inside the plane cabin, tligth5.0 ms
From view of the Earth, the beam goes...farther

• At any point, the velocity of the light measured
  by the plane observer is c (the same)
• And the velocity measured by Earth observer is c,
  so Earth observer measures
• Light goes farther, same speed

So longer time!
tgt5ms
7
Time Dilation

• Generalize result

Eq 26-1a

• Dt and Dto are both the time between same events
• measured by different observers
• v is relative speed of the two observers
• Notice that if vltltc, the two times are ?.
• Hard part which time is which?

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Proper time

• Whats the difference between Dt and Dto?
• Dto is the proper time
• It is always less than any other measured time.
• Def proper time is time in frame in which events
  occur at same place
• For example
• If the two events happen to someone or something,
  their frame measures proper time
• your heartbeat

• particles lifetime

• If someone is at both events, (or same distance
  away) their frame measures proper time
• person taking trip

• you and the clock on the wall

9
Problem-solving Tips

• A light-year is distance light travels in a yr
• d vt 1 light-year (c)(1yr) 1c-yr
• Consistent units
• distance in light-years,
• speed as fraction of c,
• time in years

Ex 12c-yr/24yr 0.5c

• If a problem does not say what frame given values
  are relative to ,
• assume they are relative to Earth

10
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?

11
Proper Length

• Whats the difference between L and Lo?
• Lo is the proper 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

12
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?