Experimental evidence
- Michelson-Morely: speed of light is constant
- Hafele-Keating: atomic clocks on planes
- Eastward clock slower
- Westward clock faster
- 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
- 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