Fundamentals of Physics by R. Shankar

Author:R. Shankar [R. Shankar]
Language: eng
Format: epub
Publisher: Yale University Press
Published: 2013-03-03T16:00:00+00:00

At t″ = 0, the whole rod is straight, while at t″ = uL0/c2, even the left end has begun falling.

In your frame, the right edge of the hole moves leftward at speed u, and it is always at z′ = 0. Since it was to the right of the right end of the rod to begin with, it will never overtake the drop-point, which moves leftward at a speed . Since > c, by the time the right edge of the hole crosses any point on the rod, that point will have already fallen below z′ = 0. (That > c does not imply interactions or signals propagating at superluminal velocities. The points that make up the rod fall independently of each other and do not interact with each other in our treatment.)

If this discussion leads you to conclude that the notion of a rigid body does not exist in relativity, you are correct.

In summary, you and I can accuse each other of using shortened rods, and we can both be right. This is because the operational way to find the length of a moving body involves measuring the two ends simultaneously, and simultaneity is relative: you will say you measured the two ends of my rod at the same time and I will disagree, and vice versa.

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