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Relativity in Physics

Relativity begins with a failed experiment. Physicists expected the Earth's motion through space to change the measured speed of light, built an interferometer precise enough to see the difference, and found nothing at all. Taking that null result seriously forces a single change to the rules, that the speed of light is the same for everyone, and almost everything else follows. If light will not oblige by going faster when you chase it, then time and length have to give way instead, so moving clocks run slow and moving objects shorten. The blocks give the older Galilean rules first so the contrast is visible, then the Lorentz factor and the two effects it controls, the transformations, and the energy and momentum relations that replace their Newtonian versions once speeds approach that limit.

Galilean coordinate transformation between two frames

Given

  • (m/s)
Galilean velocity transformation

Given

  • (m/s)
  • (m/s)
The Michelson-Morley Experiment
Einstein's Principle of Relativity
Lorentz factor

Given

  • (m/s)
  • (m/s)

Constant used

Time dilation between a moving clock and a stationary one

Given

  • (s)
Length contraction along the direction of motion

Given

  • (m)
Relativistic Doppler effect for an approaching source

Given

  • (Hz)
  • (m/s)

Constant used

Lorentz transformation equations

Given

  • (m/s)
Lorentz velocity transformation

Given

  • (m/s)
  • (m/s)

Constant used

Relativistic linear momentum

Given

  • (kg)
  • (m/s)
Relativistic total energy of a particle

Given

  • (kg)
  • (m/s)

Constant used

Rest energy of a mass

Given

  • (kg)
  • (m/s)

Constant used

Relativistic kinetic energy

Given

  • (kg)
  • (m/s)

Constant used

Energy and momentum of a relativistic particle

Given

  • (J)
  • (kg m/s)
  • (kg)

Constant used

The General Theory of Relativity