The Theory of Relativity

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The Theory of Relativity

• To appreciate and understand modern astronomy
  well need some ideas from modern physics
• Weve met quantum mechanics now its time for
  relativity
• Focus on ideas, use equations when they help
• Today Special Relativity. Can be done.

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The Principle of Relativity

• The laws of Physics are the same for two
  observers moving at constant velocity relative to
  each other
• Newtons second law
• F ma
• a is the same for the two observers
• Physical observations cant determine absolute
  motion it is meaningless. Motion is relative.

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Light and Relativity

• Light is an electromagnetic wave and its speed is
  determined from properties of electric and
  magnetic fields
• Since these can be measured they are laws of
  physics
• Speed of light is a law of physics so must be the
  same for all observers
• Does this make sense?

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Gedankenexperiments

• You can look at same situation from two inertial
  reference frames. Details differ but physics is
  the same
• You see Jackie move at 90 mph. Jackie sees you
  move at 90 mph
• You see ball move at 100 mph catch up to Jackie.
  Jackie sees ball move 10 mph while you move 90
  mph away
• V v1 v2

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Same, with light

• You see Jackie move 0.9c. Jackie sees you move
  0.9c
• You see light move at c catch up to Jackie.
  Jackie sees light move at c
• Nothing can move faster than light! No matter
  how fast you move, light will catch up at c.
• V (v1 v2)/(1 v1 v2/c2)

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Space and Time

• Ball on moving train goes farther, moves faster
  as seen from outside than from inside
• Same with light but speed the same so time
  dilates
• Time in a frame moving relative to you moves
  slower.
• NB Your time seems slower to them!
• t t/v(1-v2/c2)

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Simultaneity

• Jackies ship lights flash simultaneously as she
  passes you (ie you see simultaneous flashes).
  But green flash reaches Jackie first because she
  is moving. In Jackies reference frame, green
  light flashed first
• Simultaneity at a distance is relative

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Length

• 8. Jackie measures length of your ship by
  measuring time she takes to pass it. Since her
  time is slow shell pass it in shorter time so
  think it is Lorentz contracted
• Objects moving relative to you are contracted in
  direction of motion
• L Lv(1-v2/c2)

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Mass and Energy

• As Jackie passes you, you push her. You give her
  twin, at rest near you, an identical push. But
  Jackie feels it for a shorter time so accelerates
  less. You think her mass is greater
• Moving objects appear to have greater mass than
  when at rest
• M M0/v(1-v2/c2)

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Spacetime

• We live in a three-dimensional space. A point
  can be represented by three numbers
• Looking at a 3D object from different directions
  gives different 2D images
• Different coordinate frames split East, North
  differently but agree on distance v(x2 y2)

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Combining Space and Time
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• The point Moving observers reference frames in
  spacetime are like coordinate frames.
• They split space and time differently
• Agree on invariant interval v (x2 t2)

• Disagree on simultaneity like coordinate frames
  disagree on equal latitude
• Length contraction is like perspective
  foreshortening

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• Natural scale of axes is seconds and
  light-seconds
• Worldlines of stationary objects are vertical
• Worldlines of light beams are inclined 45o
• Worldline of inertial observer is a straight line
  inclined less
• Future and past lightcones contain events that
  you can influence or can influence you
• Curved worldline means acceleration.
• Newton 1 In absence of external forces
  worldline is straight

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