1. Special Relativity II
Two-minute movie
Quiz
Breakdown of simultaneity
Length Contraction
Time Dilation
(Some clicker examples here
after derivation)

2. Simultaneity Movie

3. Breakdown of Simultaneity Example
Lightening bolts appear to be simultaneous to Stanley.
Lightning at same time
At different times
On the train no-one can hear you scream
What does Mavis see ? 3

4. Breakdown of Simultaneity Example
Lightening bolts appear to be simultaneous to Stanley.
Lightning at same time
At different times
On the train no-one can hear you scream
What does Mavis see ? 4

5. A. reaches point A before it reaches point B.
Q9.1
As a high-speed spaceship flies past you at half the speed of light, a strobe light fires at the center of a room aboard the spaceship. As measured by you, the light from the strobe
A. reaches point A before it reaches point B.
B. reaches point B before it reaches point A.
C. reaches points A and B simultaneously.
D. not enough information given to decide
Answer: B (the wavefronts arrive from the bulb arrive at B first with respect to the earth observer).

6. A. reaches point A before it reaches point B.
Q9.1
As a high-speed spaceship flies past you at half the speed of light, a strobe light fires at the center of a room aboard the spaceship. As measured by you, the light from the strobe
A. reaches point A before it reaches point B.
B. reaches point B before it reaches point A.
C. reaches points A and B simultaneously.
D. not enough information given to decide
Answer: B (the wavefronts arrive from the bulb arrive at B first with respect to the earth observer).
The wavefronts arrive from the bulb arrive at B first with respect to the earth observer

7. A. reaches point A before it reaches point B.
Q9.2
An astronaut on the spaceship is also viewing this event. What does she see?
A. reaches point A before it reaches point B.
B. reaches point B before it reaches point A.
C. reaches points A and B simultaneously.
D. not enough information given to decide
Answer: B (the wavefronts arrive from the bulb arrive at B first with respect to the earth observer).

8. A. reaches point A before it reaches point B.
Q9.2
An astronaut on the spaceship is also viewing this event. What does she see?
A. reaches point A before it reaches point B.
B. reaches point B before it reaches point A.
C. reaches points A and B simultaneously.
D. not enough information given to decide
Answer: B (the wavefronts arrive from the bulb arrive at B first with respect to the earth observer).
This must be true for the speed of light to be the same in all inertial reference frames

9. Breakdown of Simultaneity
Going back to Mavis and Stanley (again)
Note that both sets of wavefronts from A’ and B’ (as well as from A and B) are moving at c 9

10. Breakdown of Simultaneity Example
N.B. that both sets of wavefronts from A’ and B’ are moving at c in Mavis’ frame of reference. The first wavefront reaches Mavis early
Mavis says that the lightening hit the front of the train first and the back of the train later. The two events are not simultaneous. 10

11. Breakdown of Simultaneity Example
Stanley says that the lightening hit the front of the train and the back of the train at the same time (simultaneously).
Stanley and Mavis do not agreesimultaneity has broken down (depends on frame of reference) 11

12. Pole Vaulter “classic” problem
1.6m barn, 2m pole
Run “really fast” through barn
Back door initially closed
Pole (and vaulter) entirely inside and Front door closed 12

13. Pole Vaulter (ladder and garage) Paradox
What we see observing the barn (garage)
Ladder shorter when
However our pole vaulter (ladder bearer) sees pole/ladder as same length!
How can this be?
Think about “events” !! 13

14. Pole Vaulter Resolution
Pole longer than barn, what a fly on pole sees 14

15. Some places where Special Relativity is needed
Supernova in a distant galaxy. Remember the universe is expanding !
Particle accelerator: electrons and positrons moving at 99.99% c
GPS satellite in orbit (v~3.9 km/sec, 7μs/day SR correction) 15

16. Review from Friday: Einstein’s postulates
Einstein’s first postulate: The laws of physics are the same in all inertial reference frames
Einstein’s second postulate is that the speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source.
We must modify determination of space and time intervals when a frame of reference is moving relative to us at high velocity. (Today’s class: tough deep material, please slow me down if I start going too fast. Reread the textbook when you go home).
Another consequence: it is impossible for an inertial observer to travel at c, the speed of light in the vacuum.
We will do two derivations (time dilation and length contraction). These are quite deep (not just algebra).
We will do two derivations (time dilations and length contraction) These are quite deep (not just algebra). 16

17. Relativity of time intervals and Time Dilation
The two observers (Mavis and Stanley) measure different time intervals due to their relative motion. Let’s work out this important example in full detail. 17

18. Relativity of time intervals and Time Dilation
The two observers (Mavis and Stanley) measure different time intervals due to their relative motion. Let’s work out this example.
Mavis in reference frame S’ fires a light source at a mirror and measures the time interval. What does she find ?
This is a “proper time interval” – a time interval between events at the same space point. 18

19. Relativity of time intervals and Time Dilation
Stanley in reference S measures this time interval. What does he find ?
What length does Stanley measure ? 19

20. Relativity of time intervals and Time Dilation
The time intervals measured by Mavis (frame S’) and Stanley (frame S) are different !
Let’s compare the two results 20

21. Relativity of time intervals and Time Dilation
The time intervals measured by Mavis (frame S’) and Stanley (frame S) are different ! Let’s work out how they are related.
Now square this and collect Δt terms
Insert d into the delta t expression. 21

22. Relativity of time intervals and Time Dilation
Question: does Stanley measure a longer or shorter time interval ?
Stanley measures a longer round trip time than Mavis !
This is called relativistic time dilation 22

23. Time dilation vs velocity (let’s plot the “gamma factor”)
Introduce the γ factor. 23

24. Time dilation vs velocity (let’s plot the “gamma factor”)
At what speed is γ = 2 ?
(in other words, twice the time)
0.5c
0.75c
0.866c
0.913c 24

25. Time dilation vs velocity (let’s plot the “gamma factor”)
At what speed is γ = 2 ?
(in other words, twice the time)
0.5c
0.75c
0.866c
0.913c 25

26. Do muons produced in cosmic rays make it to ground level ?
Flux of muons at ground level ~1/cm2/min
Apparent Paradox ?
The lifetime of the muon is 2.2 microseconds. It is moving close to the speed of light (3 x 108m/s). Therefore it will travel about 6.6 x 102 m before decaying. But the earth’s atmosphere is over 20 km high. So no muons will be found at ground level. 26

27. Time dilation example
A muon decays into other particles with a mean lifetime of 2.20 μs = 2.20 x 10-6 sec as measured in a reference frame in which it is at rest.
If a muon is moving at 0.990c relative to the earth, what will an observer on earth measure its mean lifetime to be ?
Reference frame S’ of the muon, proper lifetime Δt0= 2.20 μs
Reference frame S of the earth; relative speed of S’ and S is u=0.990c
7.1
8.2
9.3
10.4
11.5
What is the gamma factor here ? 27

28. Time dilation example
A muon decays into other particles with a mean lifetime of 2.20 μs = 2.20 x 10-6 sec as measured in a reference frame in which it is at rest.
If a muon is moving at 0.990c relative to the earth, what will an observer on earth measure its mean lifetime to be ?
Reference frame S’ of the muon, proper lifetime Δt0= 2.20 μs
Reference frame S of the earth; relative speed of S’ and S is u=0.990c
Question: What is the gamma factor here ?
7.1 ! 28

29. For next time Relativity continues
Read and study in advance ( )
Concepts require wrestling with material