This document discusses the key principles of special relativity, including: 1) The postulates of relativity state that the laws of physics are the same in all inertial reference frames, and that the speed of light has the same value in all reference frames. 2) Consequences of relativity include that there is no absolute length, time, or simultaneity between reference frames. Mass increases and mass and energy are equivalent based on the formula E=mc^2. 3) Time dilation describes how moving clocks run slower than stationary clocks by a factor of gamma, as demonstrated through experiments with muons.

1. Special Relativity
AP Physics

2. Relative Velocity of Light
Either
1. Addition of Velocities are WRONG
2. Laws of E and M are not the same in
all inertial frames of reference

3. Principle of Relativity
The Postulates
1) Laws of Physics are same in all inertial
frames of reference (at rest or constant v)
2) Speed of light in a vacuum has the same
value (3 x 108
m/s) regardless of the motion of
the observer or source.
Note: There is no preferred frame of reference

4. Consequences of Relativity
• No Absolute Length
• No Absolute Time
• Simultaneous or NOT
• Mass Increase
• Equivalence of Mass and Energy
• New Math - for velocity addition

5. Simultaneity
2 events simultaneous in one reference frame
are in general NOT simultaneous in a 2nd frame
moving relative to the first.
There is no preferred inertial frame of reference!

6. Time Dilation - The Light Clock
Light bounces off
the mirrors. Each
up and down
“bounce” is a tick
on the clock.
∆tproper =
2d
c

7. Time Dilation
c∆t
2




2
=
v∆t
2




2
+ d
2 ∆t =
2d
c2
− v2

8. Time Dilation
∆tproper =
2d
c
∆t =
2d
c2
− v2
=
2d
c 1 − v2
c2
∆t =
∆tp
1 − v2
c2
= γ∆tp

9. Time Dilation
Moving clocks run slower than those at
rest by a factor of γ-1

10. Experimental Proof - Muon Decay
What will the lifetime of a muon
measured if it is moving at 0.60 c?
The mean lifetime at rest is
2.2 x10-6
s.
Answer: 2.8 x 10-6
s

11. Another Problem
Mr. Smith travels at 0.99 c for 1 year (to
him). How much time goes by for his
physics class at relative rest?

12. Twin Paradox