
Concept explainers
You are standing on a train platform watching a high-speed train pass by. A light inside one of the train cars is turned on and then a little later it is turned off. (a) Who can measure the proper time interval for the duration of the light: you or a passenger on the train? (b) Who can measure the proper length of the train car: you or a passenger on the train? (c) Who can measure the proper length of a sign attached to a post on the train platform: you or a passenger on the train? In each case explain your answer.
(a)

Whether passenger on train or observer in platform measures Proper time
Explanation of Solution
The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time.
Conclusion: The time measured from frame where the relative velocity between two events is zero is called the proper time. Proper time is measured from frame where there is no relative motion between events.
(b)

Passenger on train or observer in platform measures the proper length.
Explanation of Solution
The Proper length is the length measured by observer at rest in his own frame. The relative velocity between passenger and train is zero, time measured by passenger in train is the proper time Since the passenger in train is at rest in his own frame, he can measure proper length of train Since the sign is attached to ground ,relative velocity between observer in platform and ground is zero, he measures the proper length of sign.
Conclusion: Proper length is measured from frame where there is no relativity between events.
(c)

Whether observer on platform or passenger on train measures proper length of sign post attached to ground.
Explanation of Solution
The time measured from frame where the relative velocity between two events is zero is called the proper time. The relative velocity between observer on platform and sign post is zero, time measured by observer on platform is the proper time.
Conclusion: Proper length is measured from frame where there is no relative motion between events.
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University Physics with Modern Physics (14th Edition)
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