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Grade: 11
        
Two observers, one at rest in S and one at rest in S', each carry a meter stick oriented parallel to their relative motion. Each observer finds upon measurement that the other observer's meter stick is the shorter of the two sticks. Does this seem like a paradox to you? Explain. (Hint: Compare with the following situation. Harry waves goodbye to Walter who is in the rear of a station wagon driving away from Harry. Harry says that Walter gets smaller. Walter says that Harry gets smaller. Are they measuring the same thing?)
4 years ago

Answers : (1)

Kevin Nash
askIITians Faculty
332 Points
							No, this does not seem like a paradox. It is just a length contraction.
Each frame of reference has its own particular time. To measure the length of an object means to locate its end points simultaneously. As simultaneity depends upon the frame of reference, the length measurements will also depend on the frame of reference. Thus the length is a relative concept, not an absolute one.
The essence of relativity of relativity is that results of measurements of length and time intervals are subject to the state of motion of the observer relative to the events being measured and refer only to measurements by a particular observer in a particular frame of reference. If different observers were to bring the rod to rest in their individual inertial frames, each would measure the same value for the length of the rod. In this respect, special theory of relativity is a theory of measurement that simply says “motion affects measurements”. Thus due to their relative motion, the two observers (one at rest in S and one at rest in Sʹ) will observe their meter stick is the shorter of the two sticks due to length contraction.
4 years ago
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