The Special Theory of Relativity

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The Special Theory of Relativity

• An Introduction to One the Greatest Discoveries

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The Relativity Principle
The Ptolemaic Model
The Copernican Model
Galileo Galilei 1564 - 1642
Problem If the earth were moving wouldnt we
feel it?
No
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The Relativity Principle
v
A coordinate system moving at a constant velocity
is called an inertial reference frame.
Galileo Galilei 1564 - 1642
The Galilean Relativity Principle All
physical laws are the same in all inertial
reference frames.
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The Relativity Principle
Other Examples
Galileo Galilei 1564 - 1642
As long as you move at constant velocity you are
in an inertial reference frame.
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Electromagnetism
A wave solution traveling at the speed of light c
3.00 x 108 m/s
Maxwell Light is an EM wave!
James Clerk Maxwell 1831 - 1879
Problem The equations dont tell what light is
traveling with respect to
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Einsteins Approach to Physics
1. Gedanken (Thought) Experiments E.g., if we
could travel next to a light wave, what would we
see?
2. The Einstein Principle If two phenomena
are indistinguishable by experiments then they
are the same thing.
Albert Einstein 1879 - 1955
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Einsteins Approach to Physics
2. The Einstein Principle If two phenomena
are indistinguishable by experiments then they
are the same thing.
current
current
Albert Einstein 1879 - 1955
A magnet moving
A coil moving towards a magnet
towards a coil
Both produce the same current
?Implies that they are the same phenomenon
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Einsteins Approach to Physics
1. Gedanken (Thought) Experiments E.g., if we
could travel next to a light wave, what would we
see?
c
c
Albert Einstein 1879 - 1955
We would see an EM wave frozen in space next to us
Problem EM equations dont predict stationary
waves
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Electromagnetism
Another Problem Every experiment measured the
speed of light to be c regardless of motion
The observer on the ground should measure the
speed of this wave as c 15 m/s
Conundrum Both observers actually measure the
speed of this wave as c!
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Special Relativity Postulates
Einstein Start with 2 assumptions deduce all
else

• The Relativity Postulate The laws of physics are
  the same in every inertial reference frame.
• The Speed of Light Postulate The speed of light
  in vacuum, measured in any inertial reference
  frame, always has the same value of c.

This is a literal interpretation of the EM
equations
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Special Relativity Postulates
Looking through Einsteins eyes
Both observers (by the postulates) should measure
the speed of this wave as c

• Consequences
• Time behaves very differently than expected
• Space behaves very differently than expected

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Time Dilation
One consequence Time Changes
Equipment needed a light clock and a fast space
ship.
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Time Dilation
In Bobs reference frame the time between A B
is ?t0
?t0
Bob
Ending Event B
Beginning Event A
Sally
on earth
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Time Dilation
In Sallys reference frame the time between A B
is ?t
Bob
Bob
?t
Sally
A
B
on earth
Length of path for the light ray
and
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Time Dilation
Length of path for the light ray
and
Solve for ?t
Time measured by Bob
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Time Dilation
?t0 the time between A B measured by Bob
?t the time between A B measured by Sally
v the speed of one observer relative to the
other
If ?t0 1s, v .999 c then
Time Dilation Moving clocks slow down
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Time Dilation
How do we define time?
The flow of time each observer experiences is
measured by their watch we call this the proper
time

• Sallys watch always displays her proper time

• Bobs watch always displays his proper time

• If they are moving relative to each other they
  will not agree

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Time Dilation
A Real Life Example Lifetime of muons Muons
rest lifetime 2.2x10-6 seconds Many muons in
the upper atmosphere (or in the laboratory)
travel at high speed. If v 0.999 c. What
will be its average lifetime as seen by an
observer at rest?
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Length Contraction
The distance measured by the spacecraft is shorter
Bobs reference frame
Sallys reference frame
Sally
Bob
The relative speed v is the same for both
observers