Physics 26: Special Theory of Relativity

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Physics 26 Special Theory of Relativity

• Christopher Chui

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Galilean-Newtonian Relativity

• Inertial reference frames are reference frames in
  which Newtons 1st law, the law of inertia, is
  valid
• Relativity principle the laws of physics are the
  same in all inertial reference frame
• In classical mechanics, space and time are
  absolute
• All inertial reference frames are equally valid
• Michelson-Morley experiment did not detect ether
• Special relativity includes 2 postulates the
  relativity principle and the constancy of the
  speed of light light propagates through empty
  space with a definite speed c independent of the
  speed of the source or observer

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Simultaneity is Relative

• 2 simultaneous events to 1 observer may not be
  simultaneous to a 2nd observer?time is not
  absolute
• Time-dilation clocks moving relative to an
  observer are measured by that observer to run
  more slowly
• Formula t to/1-v2/c2½ where to is at rest
  frame
• Twin paradox the traveling twin will age less
• Length contraction L Lo 1-v2/c2½ where Lo
  is at rest frame
• 4-dimensional space-time time as the extra
  dimension
• Mass increase m mo/1-v2/c2½ where mo is at
  rest
• KE mc2 moc2 ? E mc2 moc2 KE

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Relativistic Momentum

• p mv mov/ 1-v2/c2½
• Energy-momentum relation E2 p2c2 mo2c4
• Units for p is eV/c
• Units for m is eV/c2
• Relativistic addition of velocitiesu(vu)/
  1vu/c2 when v and u in the same direction.
  For opposite directions, u is negative?
  u(v-u)/ 1-vu/c2
• A more general theory gives the same results as a
  more restricted theory is called the
  correspondence principle