Handy Dandy Chart

= 1 v = 0= 2 v = .866 c= 2.5 v = .92 c= 7 v = .99 c= 10 v = .995 c = 100 v = .99995 c

http://www.physi.uni-heidelberg.de/~fp/anleitg/F13/jpg/RHIC_Complex.jpg

Typical jet airplane speed is v = 300 m/s.

Plug into formula, get = 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?

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 = 10.How long does the show last, according to Alice? A. 3 minutes B. 30 minutes C. 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 = 10.How long does the show last, according to Bob? A. 3 minutes B. 30 minutes C. 300 minutes

Relativity: Time Dilation

2

2

cv1

1

tMOVING = tREST

time measured in rest frame of clock

time measured by observer whosees clock move at speed v

“Rest clocks run slowest”*

*least time elapsed

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. ( = 10).If Bob takes 30 minutes to read a magazine article (according tohis watch), how long does it take according to Alice? A. 3 minutes B. 30 minutes C. 300 minutes

people

Suppose Alice only shows a 3 minute videotape of an ad …and she starts the tape simultaneous with Bob’s opening his magazine....

According to Bob, the commercial take 30 minutes –

he completes the magazine simultaneous with the ending of the commercial!!

But what does Alice see??If it simultaneous according to Bob, doesn’t it have to be simultaneous 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 =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.

vB

B

Lt

AB LL

AtvAL

RULERat REST

MOVING

LrestLmoving

tmoving = trest

1

Rest clocks run the slowest (that is, register the least amount of time)

Rest Distance between points (or rest length of an object) along the direction of motion is longestObserver moving with respect to a ruler measures the shorter distance

LrestLmoving

tmoving = trest

1

Rest clocks run the slowest

TIME DILATES

Rest Distance between points (or rest length of an object) along the direction of motion is longestSPACE CONTRACTS

v

Spacecraftat Rest

Spacecraft in Motion

v = 0

Length Contraction

0 1

Bob

Alice

0 1v

Alice loads a meter stick on her spaceship, then fires up the rocket until she is moving with =2.

Length Contraction

Whose view does this cartoon represent?

0 1

Bob

Alice

0 1v

Length Contraction

Alice’s view

But who is right ??