1. Special Relativity: Time Dilation and Length Contraction
SPH4U

2. Einstein’s Postulates
All laws of physics are valid in all inertial (non-accelerated) reference frames.

3. Einstein’s Postulates
Light travels at c = 3.0 x 108 m/s relative to all reference frames.

4. Simultaneity
This implies that events that are simultaneous (occurring at the same time) for one observer are not simultaneous for an observer in a different reference frame.
C will see the lightning flashes at A and B at the same time.
D will see the flash at B happen before the flash at A.

5. Measurement
And that observers in different reference frames measure time and length differently.
One observer bounces a laser off a mirror on the ceiling.
The other sees the light travelling a longer path in a longer time.

6. Time Dilation
By the Pythagorean Theorem:
vt’ ct
ct’

7. Time Dilation
By the Pythagorean Theorem:
vt’ ct
ct’

8. Time Dilation
(for an event that occurs in the non-prime reference frame)
vt’ ct
ct’

9. Time Dilation
dilation = expansion
(for an event that occurs in the non-prime reference frame)
vt’ ct
ct’

10. Minutephysics

11. Gamma The factor is often written as g:
Note that g is dimensionless (it has no units).

12. Length Contraction
Similarly, it can be shown that lengths parallel to the direction of motion are contracted:

13. Muons
Muons created in the upper atmosphere have a lifetime of 2.2 ms in their reference frame but reach the Earth’s surface because they see the distance to the surface as contracted and/or we see the lifetime as dilated.

14. Example
What is the apparent lifetime of a muon travelling at 0.99c?

15. Example
What is the apparent lifetime of a muon travelling at 0.99c?

16. Example
What is the apparent lifetime of a muon travelling at 0.99c?

17. More Practice
Textbook Questions
p. 573 #2, 3
p. 576 #6, 7, 8

18. Recommended: “Old School” Relativity