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Experimental evidence

  • Michelson-Morely: speed of light is constant
  • Hafele-Keating: atomic clocks on planes
  • Eastward clock slower
  • Westward clock faster
  • GPS satellite clocks
  • Muon decay
  • Short half-life
  • Move close to speed of light
  • Measured more muons than predicted at low altitude

The difference is in the lengths of the trips!

The relativistic Doppler effect

  • Light as a wave
  • Stella: each leg takes the same amount of time
  • Moving away: redshift
  • Lower frequency
  • Terri: the outbound trip is long; the trip back is short
  • Sees her age slowly for a long time and quickly for a short time
  • Overall sees Stella age fewer years
  • Moving toward: blueshift
  • Higher frequency

Terri --> Stella

Stella --> Terri

Time

Distance From Earth

Discussion

  • Consequences for travel through space?
  • Factors preventing travel near the speed of light?
  • Could they be overcome in the future?

Special Relativity

A numerical example

  • Developed by Einstein in 1905
  • Postulates:
  • From an inertial frame of reference, all motion is relative
  • Speed of light is constant

http://paulocoelhoblog.com/wp-content/uploads/2012/03/einstein.jpg

  • Implication: time dilation
  • Moving clock runs slowly relative to a stationary clock

Not a true paradox!

  • Special relativity applies only to inertial frames of reference

  • Stella's reference frame is not inertial

Calculating time dilation

  • The Lorentz factor
  • Relative velocity
  • Proper time

Do we need general relativity?

  • Doesn't require an inertial frame of reference, but...

  • Irrelevant to the twin paradox

http://cnx.org/content/m32527/latest/sr6.gif

The Twin Paradox

By Jennifer Lee & Joshua Reinders

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