Alice is driving a car around a circular track. Brian, who is sitting at a fixed

Question

Alice is driving a car around a circular 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 (first sketch below), and Dave happens to pass Brian just as Alice passes Brian the second time (second sketch below). Assume that the clocks used by Alice, Brian, and Cara are close enough together so that we can consider them all to be "present" at event F. Assume that the ground frame is an inertial reference frame. Who measures a proper time between events E and F? Who measures a coordinate time between events E and F? Who (if anyone) measures the "spacetime" time interval between events E and F? Carefully explain your reasoning in each case.

Explanation / Answer

a) alice measures a proper time between events E and F because she is present when she leaves the position at the edge of the track and she is also present when she arrives

b) The coordinate time in event E is measured by Cara and, in event F, is measured by Dave. This is because the coordinate time is measured in a different reference frame

c)The spacetime interval could be measured by Brian because spacetime interval is the length between two events in space and time. brain is at constant distance with respect to moving earth.

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