Special Relativity

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Special Relativity
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Topics

• Motion is Relative
• Michelson-Morley Experiment
• Postulates of the Special Theory of Relativity
• Simultaneity
• Spacetime
• Time Dilation
• The Twin Trip
• Addition of Velocities
• Space Travel
• Length Contraction
• Relativistic Momentum
• Mass, Energy, and E mc2
• The Correspondence Principle

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Mechanical Universe

• 41. The Michelson-Morley Experiment
• In 1887, an exquisitely designed measurement of
  the earth's motion through the ether results in
  the most brilliant failure in scientific history.
  
• http//www.learner.org/resources/series42.html

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Motion is Relative

• Frame of Reference place from which motion is
  observed and measured
• An object may have different velocities from
  different frames of reference

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Relative Velocity
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Michelson-Morley Experiment
Null Result

• Designed to prove the existence of the ether
  the still reference frame
• Speed of light was the same no matter the
  direction relative to the earths motion

Interferometer
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Lorentz-Fitzgerald Contraction

• Length is contracted in the direction of motion
• Accounts for the null result
• Amount of shrinkage

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Special Theory of RelativityPostulates

• All laws of nature are the same in all uniformly
  moving frames of reference.
• The speed of light in free space has the same
  measured value for all observers, regardless of
  the motion of the source or the motion of the
  observer that is, the speed of light is a
  constant.

The speed of a light flash emitted by the space
station is measured to be c by observers on both
the space station and the rocket ship.
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Simultaneity

• two events are simultaneous if they occur at the
  same time.

From the point of view of the observer who
travels with the compartment, light from the
source travels equal distances to both ends of
the compartment and therefore strikes both ends
simultaneously.
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Simultaneity

• Two events that are simultaneous in one frame of
  reference need not be simultaneous in a frame
  moving relative to the first frame.

Because of the ship's motion, light that strikes
the back of the compartment doesn't have as far
to go and strikes sooner than light strikes the
front of the compartment.
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Check Yourself

• Suppose that the observer standing on a planet
  sees a pair of lightning bolts simultaneously
  strike the front and rear ends of the high-speed
  rocket ship compartment. Will the lightning
  strikes be simultaneous to an observer in the
  middle of the rocket ship compartment?

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Check Yourself

• No an observer in the middle of the compartment
  will see the lightning that hits the front end of
  the compartment before seeing the lightning that
  hits the rear end.
• (a), we see both lightning bolts striking the
  ends of the compartment simultaneously according
  to the outside observer.
• (b), light from the front lighting bolt reaches
  the observer within the rocket ship.
• (c) Slightly later, light from the rear lightning
  bolt reaches this observer.

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Time Dilation
Time can be stretched.

• A light clock. A flash of light will bounce up
  and down between parallel mirrors and tick off
  equal intervals of time.

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Time Dilation

• Light Clock Movie open from browser
• Time Dilation Movie open from browser

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Mechanical Universe

• 42. The Lorentz Transformation If the speed of
  light is to be the same for all observers, then
  the length of a meter stick, or the rate of a
  ticking clock, depends on who measures it.
• 43. Velocity and Time Einstein is motivated to
  perfect the central ideas of physics, resulting
  in a new understanding of the meaning of space
  and time.
• 44. Mass, Momentum, Energy The new meaning of
  space and time make it necessary to formulate a
  new mechanics.