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
we cant tell if were moving!
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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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
All physical laws (like electromagnetic
equations) depend only on the relative motion of
objects.
Ex)
same
current
current
current
A magnet moving
A coil moving towards a magnet
towards a coil
?Implies that we can only measure relative
motions, i.e., motions of objects relative to
other objects. By the Einstein Principle this
means all that matters are relative motions!
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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 A
Beginning Event B
Sally
on earth
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Time Dilation
In Bobs reference frame the time between A B
is ?t0
?t0
Bob
Ending Event A
Beginning Event B
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
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Time Dilation
In Sallys reference frame the time between A B
is ?t
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
and solve for ?t
Time measured by Bob
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Time Dilation
?t0 the time between the two events measured by
Bob
?t the time between the two events measured by
Sally
v the speed of one observer relative to the
other
If ?t0 1s, v .9999 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 speeds. If v 0.9999 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
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Length Contraction
L0 the length measured by Sally
L the length measured by Bob
Sally
Bob
If L0 4.2x1022 km, v .9999 c then
Length Contraction
To a moving observer all lengths are shorter!
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Summary

• Einstein, used Gedanken experiments and the
  Einstein Principle to formulate the postulates
  of special relativity
• 1. All physical laws are the same in all
  inertial reference frames
• 2. The constancy of the speed of light
• The consequences were that
• 1. Moving clocks slow down
• 2. To a moving observer all lengths are shorter.

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Special Relativity Beyond

• The special theory of relativity dramatically
  changed our notions of space and time.
• Because of this, mechanics (like notions of
  energy, momentum, etc.) change drastically, e.g.,
  Emc2.
• Special relativity only covers inertial
  (non-accelerated) motion. To include acceleration
  properly we must incorporate gravity. This theory
  is known as the general theory of relativity
  which is Einsteins greatest contribution to
  physics.

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Real Life Application of Relativity

• In Global Positioning Satellite (GPS) general
  relativistic corrections are needed to accurately
  predict the satellites clock which ticks slower
  in orbit. Without it you GPS would be off by at
  least 10 kilometers. With the corrections you can
  predict positions within 5-10 meters

http//www.astronomy.ohio-state.edu/pogge/Ast162/
Unit5/gps.html