Handy Dandy Chart 1 2 5 7 100

Is time dilation important in everyday life? Typical jet airplane speed is v =

Alice v Bob A Seinfeld episode normally lasts 30 minutes. Alice watches a tape

Relativity: Time Dilation “Rest clocks run slowest”* = 1 2 v 1 - 2

Alice v people Bob Now consider things in Alice’s frame of reference. According to

Suppose Alice only shows a 3 minute videotape of an ad … and she

Special Relativity If the speed of light is constant, then the clocks and rulers

What about Distance? Add a rocket to the Dinky so it moves at v

Same events observed in the Alice’s reference frame; Here the earth is moving at

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

Rest clocks run the slowest TIME DILATES tmoving = trest Rest Distance between points

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

Length Contraction Alice loads a meter stick on her spaceship, then fires up the

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

Slides: 16

Download presentation

Handy Dandy Chart = 1 = 2. 5 = 7 = 100 v=0 v =. 866 c v =. 92 c v =. 995 c v =. 99995 c

Is time dilation important in everyday life? Typical jet airplane speed is v = 300 m/s. Plug into formula, get = 1. 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. )

Alice v 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

Relativity: Time Dilation “Rest clocks run slowest”* = 1 2 v 1 - 2 c time measured in rest frame of clock t. MOVING = t. REST time measured by observer who sees clock move at speed v *least time elapsed

Alice v people 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 to his watch), how long does it take according to Alice? A. 3 minutes B. 30 minutes C. 300 minutes

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? ?

Special Relativity If the speed of light is constant, then the clocks and rulers used to measure velocities must not be constant!

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: v Princeton Junction LB=5 km

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

Rest clocks run the slowest (that is, register the least amount of time) tmoving = trest 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 1 Lmoving = Lrest

Rest clocks run the slowest TIME DILATES tmoving = trest Rest Distance between points (or rest length of an object) along the direction of motion is longest SPACE CONTRACTS 1 Lmoving = Lrest

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

Length Contraction Alice loads a meter stick on her spaceship, then fires up the rocket until she is moving with =2. Alice 0 0 1 v 1 Bob Whose view does this cartoon represent?

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