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Rasalhague
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In Tipler & Mosca: Physics for Scientists and Engineers, e5, extended edition (page R-14 of the supplementary section on special relativity), there is a question:
“You are standing on a corner and a friend is driving past in an automobile. Each of you is wearing a wrist watch. Both of you note the times when the car passes two different intersections and determine from your watch readings the time that elapses between the two events. Which of you has determined the proper time interval.”
My answer: the friend. The two events (the car passing each intersection) happen in the same place (at the same spatial coordinates) in a reference frame in which the car is at rest, namely the location of the car. And the friend's watch is at rest with respect to the friend’s car in this frame.
Book’s answer: “Neither of you has determined the proper time interval. By definition the proper time interval is measured by a clock in the rest frame of the car, that is by a clock in the car.”
But assuming that an automobile is a car, and a wrist watch is a clock, and the friend’s wrist is attached to the friend, why would that not count as a clock in the car? Also, could a clock still be said to measure the proper time interval between the two events even if it wasn’t in the car, so long as it was in the same inertial reference frame, and that the delay in information from the events reaching the clock was taken into account? Earlier (p. R-6), Tipler & Mosca define the proper time interval between two events as “the time between events 1 and 2 in a frame of reference in which the two events occur at the same location”.
“You are standing on a corner and a friend is driving past in an automobile. Each of you is wearing a wrist watch. Both of you note the times when the car passes two different intersections and determine from your watch readings the time that elapses between the two events. Which of you has determined the proper time interval.”
My answer: the friend. The two events (the car passing each intersection) happen in the same place (at the same spatial coordinates) in a reference frame in which the car is at rest, namely the location of the car. And the friend's watch is at rest with respect to the friend’s car in this frame.
Book’s answer: “Neither of you has determined the proper time interval. By definition the proper time interval is measured by a clock in the rest frame of the car, that is by a clock in the car.”
But assuming that an automobile is a car, and a wrist watch is a clock, and the friend’s wrist is attached to the friend, why would that not count as a clock in the car? Also, could a clock still be said to measure the proper time interval between the two events even if it wasn’t in the car, so long as it was in the same inertial reference frame, and that the delay in information from the events reaching the clock was taken into account? Earlier (p. R-6), Tipler & Mosca define the proper time interval between two events as “the time between events 1 and 2 in a frame of reference in which the two events occur at the same location”.