PH 103

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PH 103

• Dr. Cecilia Vogel
• Lecture 14

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Review

• Einsteins relativity
• 1st and 2nd postulates of special relativity
• equivalence principle of general relativity

Outline

• Consequences of Einsteins postulates
• time dilation
• simultaneity

3
Some Consequences

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

4
Recall Classical Relativity

• Suppose two observers time the pretzel you throw
  and catch. One observer on plane, one on Earth.
  Same pretzel.

Go-stop. t5 s
Go------------------------------stop. t ?
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Recall Classical Relativity
Compared to this frame,
in this frame, 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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Now Einsteins Relativity

• That worked for pretzels, what about light?
• Person on super-plane shines light at mirror.
• Suppose two observers time the light that shines
  and reflects. One observer on plane, one on
  Earth. Same light.

Go-------------stop. t?
Go-stop. to5 ms
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Now Einsteins Relativity
in this frame, light goes...
Compared to this frame,
farther

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

tgt5ms
longer time!
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Time Dilation

• Generalize result

• 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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Time Dilation

• Units comment
• If velocities are given as a fraction of c,
• then the cunits cancel.
• Example
• If v 0.8 c,
• then (v/c) (0.8c/c) 0.8 (no units)

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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.
• Definition proper time is time in frame in which
  the two events occur at same place
• Events are
• single instant in time, single point in space,
• Events dont move.
• They dont have reference frame. Occur in all
  frames
• Time interval is time between two events
• One event makes you start your timer
• other even makes you stop you timer.

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Proper time

• Whats the difference between Dt and Dto?
• Dto is the proper time
• Definition 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 Dx away)
  their frame measures proper time
• person taking trip

• you and the clock on the wall

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Time Trip

• Nikos travels to a planet 12 light-years away at
  a speed of 0.6 c. Juan stays on Earth. Each
  measures the trip to take a different amount of
  time. Note
• A light-year is distance light travels in a yr
• 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

• The values in example are relative to Earth
• In that frame (in any one frame), the laws of
  physics hold, including d vt

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More Example

• If Nikos makes a 12 light-year trip at 0.6c, Juan
  sees him moving at 0.6c for 20 years.
• d vt (0.6c)(20 y) 12c-yr.
• Nikos sees himself moving at
• Nikos sees the 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
  planet, yet the distances are different!

14
Proper Length

• Whats the difference between the two lengths?
• One is the proper length
• Its always longer than any 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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Just How Proper is it?

• If there is a proper time and a proper length,
• is there a proper reference frame?
• NO!!!!!!!
• Proper time of trip in example Nikos
• Proper length of trip in example Juan
• Proper time of astronauts heartbeat Astronaut
• Astronauts heartbeat looks SLOW to you.
• Proper time of your heartbeat You
• Your heartbeat looks SLOW to astronaut.

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Simultaneity

• How do we know whether 2 events are simultaneous?
  
• If signals coming from events arrive at the same
  time, the events might not have been simultaneous
• how long did it take the signal to get here?

demo
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If tarrive, d, and v the same, conclude tevent
same
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Veraser-vthrower
veraservthrower
If tarrive, is smaller and d/v also smaller,
can conclude tevent same
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SIMULTANEITY IS NOT ABSOLUTE
If tarrive is earlier and d/v is same, must
conclude tevent is earlier!
one observer says two events are
simultaneous, other says they are not!!