Alice is driving a race car around an essentially cicular track. Brian, who is s

Question

Alice is driving a race car around an essentially cicular track. Brian, who is sitting at a fixed position at the edge of the track, measures the time that Alice takes to complete a lap by starting his watch when Alice passes by his position (call this event E) and stopping it when Alice passes his position again (call this event F). This situation is also observed by Cara and Dave, who are passengers in a train that passes very close to Brian. Cara happens to be passing Brian just as Alice passes Brian the first time, and Dave happens to pass Brian just as Alice passes Brian the second time. Assume that the clocks used by Alice, Brian, and Cara are close enough together so that we consider them all to be "present" at event E, and similarly that those used by Alice, Brian and Dave are "present" at event F. Assume that the ground frame is an inertial reference frame.

a.) Who measures a proper time between events E and F?

b.) Who measures a coordinate time between events E and F?

c.) Who (if anyone) measures the spacetime interval between events E and F? Carefully explain your reasoning in each sense.

Explanation / Answer

Lets represent by following notation

: A- Alice, B- Brian, CD- Cara and Dave

(a) The Shortest time- A and B measures r Because B measures s also, and A is moving (therefore time moves slower for her) – Alice measures the shortest time.

The longest time- B and CD measures t B measures s which is the shortest possible t. Since CD don’t measure s they measure the longest time interval.

(b) Converting the speed the SR units: 60m/s=20108(SR) tABBrian=100s

Manipulating the equation by subtracting t in order to get the answer:

rABAlicetAB=(10.5v2)tABtAB=(10.5v21)tAB=

=21012s
Time is 2 picosec

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