Handy Dandy Chart  = 1v = 0  = 2v =.866 c  = 2.5v =.92 c  = 7v =.99 c  = 10v =.995 c  = 100v = c

Typical jet airplane speed is v = 300 m/s. Plug into formula, get  = Time between takeoff and landing measured by a passenger would be about one-trillionth less than that measured by someone on the ground. ( sec difference in 1 year.) ==> Not significant. (...but it has been measured, using atomic clocks.) Is time dilation important in everyday life?

v Alice 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 = c. The Lorentz factor is  = 10. How long does the show last, according to Alice? A. 3 minutes B. 30 minutes C. 300 minutes

v Alice 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 = 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 c v 1 1    t MOVING =  t REST time measured in rest frame of clock time measured by observer who sees 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 = c. (  = 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 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

L B =5 km v PrincetonPrinceton Junction What about Distance? Add a rocket to the Dinky so it moves at v = km/s = c  =2 The Dinky trip viewed by Bob:

PrincetonPrinceton Junction v PrincetonPrinceton Junction LALA Same events observed in the Alice’s reference frame; Here the earth is moving at speed v. RULER at REST MOVING

L rest  L moving  t moving =  t rest 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 longest Observer moving with respect to a ruler measures the shorter distance

L rest  L moving  t moving =  t rest 1 Rest clocks run the slowest TIME DILATES Rest Distance between points (or rest length of an object) along the direction of motion is longest SPACE CONTRACTS

v Spacecraft at Rest Spacecraft in Motion v = 0 Length Contraction

0 1 Bob Alice 0 1 v 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 1 v Length Contraction Alice’s view But who is right ??