Chapter S2: Space and Time
Introduction
Einstein
1905: Special Theory of Relativity -> Space and Time
1915: General Theory of Relativity -> Space, Time, and Gravity
This chapter is about the Special Theory of Relativity
Underlying "assumptions" of Special Relativity
1.) The laws of physics work just as well in any reference frame as in any other
2.) The speed of light seems to be the same, no matter what reference frame
you are in
i.e. If light is produced in a different reference frame (moving at velocity = v1),
you, in your frame, don't see light's velocity as c + v1,
you see light's velocity as c!
1887, Michelson Morley Experiment
Binary stars example
Car example
Colliding cars are equivalent to colliding galaxies
(NGC 5426 & 5427 and
NGC 4038 & 4039
and we don't see crumpled galaxies waiting to be hit!)
Clarifications
To notice the effects of relativity, you need very fast motions
Slow objects act in ways we are familiar with
(Example)
But light doesn't (Example)
We assume that the light is traveling through a vacuum
(not glass, etc.)
Ramifications:
Time Dilation:
Jackie => moving reference frame
Everyday, non-relativistic experience with a ball:
Ball example
Ball's path is longer path in viewer's frame than in
thrower's frame
Same geometry, but using light rather than a ball:
Light Example
You still see a longer path than Jackie does
Light moves at same speed in all inertial reference frames
time = distance / velocity
Therefore, you measure a longer time than Jackie does
Note: test with "pi+" meson traveling at fast speed.
Slowed the decay time in our reference frame
(which, to the pi+ meson, is moving)
Note: in 1975 someone tested this by putting a clock on an airplane.
After 15 hours in flight, the on-board clock was 6 nanoseconds
behind the Earth clocks
Length contraction:
Figure
Mass Dilation:
Figure
Velocity Addition:
Figure
Summary of Important Ramifications:
1.) Time runs slower in a moving object's reference frame
2.) If you look at a moving object, it looks shorter to you
(and you look shorter to it)
3.) If you look at a moving object, it seems more massive to you
(and you look more massive to it)
4.) Two events that are simultaneous in one reference frame
are not simultaneous in other inertial reference frames
5.) Nothing can move faster than the speed of light
