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“Physics for FUTURE LEADERS”Prof. Paul Steinhardt
Physics 115
Princeton in the Nation’s ServiceWoodrow Wilson, 1896
Take out your A, B, C, D cardHW11 due a week from Friday
Relativity Revolution
•Alice is in the Dinky. Bob is by the side of the tracks.
•The Dinky has velocity vAB = 5 m/s to the right.
•Alice, travelling in the Dinky, throws the ball withvelocity vA = 5 m/s relative to herself.
A
B
A) 0 m/s B) 5 m/s C) 10 m/s D) more information needed
A 0 5
0 5 10B
12:00:00TIMEX
A 0 5
0 5 10B
12:00:01TIMEX
•Alice, standing on the train, sees the ball move 5 m in one sec
•Bob, standing on the ground next to the tracks, sees the Alice move 5 m and the ball move 5 m ahead of her
•So Bob see balls move 10 m in one second, or 10 m/s
A 0 5
0 5 10B
12:00:00TIMEX
A 0 5
0 5 10B
12:00:01TIMEX
•Alice, standing on the train, sees the ball move 5 m in one sec
•Bob, standing on the ground next to the tracks, sees the Alice move 5 m and the ball move 5 m ahead of her
•So Bob see balls move 10 m in one second, or 10 m/s VELOCITIES ARE RELATIVE
VELOCITIES ADD
0 500:00:00
ACM
E
Imaginary speed-of-light measurement device.
lightdetectors
rulerstopwatch
incoming pulseof light
A
B
5 m/sflashlight
Bob (standing still) measures the same pulse of light.What does he get? 300,000,000 m/s + 5 m/s = 300,000,005 m/s
A flashlight in the train makes a pulse of light.Alice (in the train) measures light’s speed to be 300,000,000 m/s
relative to her.
Maxwell’s equations say: No! speed should be the same.
So say Newton and Galileo…
Maxwell’s Equations (1873)
1831-1879
If the speed of light is the same, then the clocks and rulers used to measure velocities must
measure different times and distances!
Special Relativity
mirror
mirror
d
Alice is now in a spaceship.
Two mirrors are separated by distance d.
Time for a pulse of light to go from floor to ceiling is ?
cdtA =
Worksheet
•Bob is outside the spaceship, which moves by with speed v.
•He sees the light pulse take the path shown above, which islonger than the path seen by Alice.
v
Bob
L d
tA
v
d
v tB
L = d2 + (v tB)2
tB = L/c
tB2
tB2 [1 – ] =
tB = 1
1 –(v/c)2
L
1c= d2 + (v tB)2
= [d2 + (v tB)2]1c2
v2c2
d2c2
dcx
tB2 = d2
c2[1 – ]v2c21 x
Relativity: Time Dilation
22
cv1
1g-
=tMOVING = g tREST
time measured in restframe of clock
time measured by observer whosees clock move at speed v
“Rest clocks run slowest”*
*least time elapsed
Typical jet airplane speed is v = 300 m/s.
Plug into formula, get g = 1.000 000 000 000 5.
Time between takeoff and landing measured by a passenger would be about one-trillionth less than that measured by
someone on the ground. (0.000 02 sec difference in 1 year.)
==> Not significant.
(...but it has been measured, using atomic clocks.)
Is time dilation important in everyday life?
war & peace
• Spacecraft moving at 99% the speed of light.(v = 0.99c = 297,000,000 m/s)
• g = 7
• 7 years of rocket travel measured by someone on Earthwould only be 1 year for the astronaut.
• This is REAL. In 7 years of space travel (according to Bob) at 0.99 c,---Alice’s watch would show only 1 year of elapsed time
---Alice would age only 1 year
Is time dilation important to interstellar space travelers?
Handy Dandy Chart
g = 1 v = 0g= 2 v = .866 cg= 2.5 v = .92 cg= 7 v = .99 cg= 10 v = .995 cg = 100 v = .99995 c
vAlice
Bob
A Seinfeld episode normally lasts 30 minutes. Alice watches a tape of a Seinfeld show on her VCR as her spacecraft passes
Bob with speed v = 0.995 c. The Lorentz factor is g = 10.How long does the show last, according to Alice?
A. 3 minutesB. 30 minutesC. 300 minutes
vAlice
Bob
A Seinfeld episode normally lasts 30 minutes. Alice watches a tape of a Seinfeld show on her VCR as her spacecraft passes
Bob with speed v = 0.995 c. The Lorentz factor is g = 10.How long does the show last, according to Bob?
A. 3 minutesB. 30 minutesC. 300 minutes
v
Alice
Bob
Now consider things in Alice’s frame of reference. According to Alice, her rocket is standing still, while Bob is flying off at
speed v = 0.995 c. (g = 10).If Bob takes 30 minutes to read a magazine article (according to
his watch), how long does it take according to Alice?A. 3 minutesB. 30 minutesC. 300 minutes
people
Puzzler :
Suppose Alice only shows a 3 minute videotape.
According to Bob, this take 30 minutes –Precisely the same time it takes for him to read his
magazine!So, according to him, he can start and stop reading
his magazine simultaneous with the start and stop of the tape.
Yet Alice, who sees the tape last 3 minutes, measures that Bob takes 300 minutes to read his magazine.
How can that be? If they start and end simultaneously according to Bob, doesn’t it have to be simultaneous according to Alice??
If the speed of light is constant, then the clocks and rulers used to measure velocities must not
be constant!
Special Relativity
LB=5 km
v
Princeton Princeton Junction
What about Distance?
Add a rocket to the Dinky so it moves at
v = 260 000 km/s = 0.866 c g=2
The Dinky trip viewed by Bob:
Princeton Princeton Junctionv
Princeton Princeton Junction
LA
Same events observed in the Alice’s reference frame; Here the earth is moving at speed v.
Bt = vBL 𝑡" =
𝐿"v