Special Relativity 1

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Special Relativity1
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Topics

• Einsteins Early Years
• Special Relativity
• Postulates
• Simultaneity
• Summary

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The Einsteins
Pauline Einstein
Albert
Hermann Einstein
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Aarau Class of 1896
Marcel Grossman
Einstein entered the Eidgenössische Technische
Hochschule, Zurich in 1896. Graduated in 1900.
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Technical Expert, Third Class

• Einstein got a job at the Swiss Patent Office in
  Bern, on the 23 June 1902
• Six months later, he married his Serbian
  girlfriend, Mileva

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1905 Annus Mirabilis

• 17 March
• A new theory of light
• 30 April
• A new method to infer the size of molecules
• 11 May
• A new theory of Brownian motion
• 30 June
• A new theory of space and time

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Special Relativity Postulates

• Principle of Relativity
• The laws of physics are the same in all inertial
  frames
• Principle of Constancy of Speed of Light
• The speed of light in vacuum is independent of
  the motion of its source
• The first principle implies that the speed of
  light is also independent of the motion of the
  observer

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Experiment At Rest
Measure time for a light ray to go from A to B to
A in a frame of reference in which experiment is
at rest relative to the observer
A
t 2d / c
d distance between A and B t time to go from
A to B to A c speed of light in vacuum
B
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Experiment Moving
We now look at the same experiment from an
inertial reference frame in which the experiment
is moving relative to that frame
A
The emission of the light ray at A and its
arrival At B must also occur in the moving
frame Why?
t 2d / c
B
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Because Events are Real !

• An event is a physical occurrence
• The birth of a baby
• The emission of a light pulse
• The explosion of a star, etc
• Therefore, every observer will agree on the
  existence of events.

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Experiment - Moving
A
(cT/2)2 (vT/2)2 d2
vT/2
But,. t 2d / c
d
cT/2
B
T time to go from A to B to A
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Experiment - Conclusion
The only way to avoid a contradiction is if
Time dilation
where
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Moving Clocks Run More Slowly
Therefore, if you move at a constant velocity
relative to me, your clock runs slower relative
to mine. But, from the principle of
relativity, this law must be the same for you
too, therefore, you see my clock run slower that
yours!
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Relativity of Simultaneity
This paradoxical situation is resolved, as are
most paradoxes in relativity, because of
the relativity of simultaneity Two events that
are simultaneous in one inertial frame are not,
in general, simultaneous in another inertial
frame moving relative to the first
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Space-Time Diagrams
Events can be represented as points in
a space-time diagram
Those that have the same time values, such as
events A and B, are said to be simultaneous
Time
A
B
Space
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Relativity of Simultaneity
A
B
C
A flash of light at C, midway between A and
B, will be detected at A and B simultaneously
when viewed by an observer at rest relative C
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Relativity of Simultaneity
A flash of light at C, midway between A and
B, will be detected at A before B when viewed by
an observer moving relative to C
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Summary

• Postulates of Relativity
• Laws of physics are the same in all inertial
  frames
• The speed of light in vacuum is independent of
  motion of source (and observer)
• Time Dilation
• Moving clocks run more slowly
• Relativity of Simultaneity
• Events simultaneous in one frame need not be
  simultaneous in another