“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

v2

c2d2

c2

dcx

tB2 = d2

c2[1 – ]v2

c2

1 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