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PeterDonis is offline
Nov28-10, 12:21 AM
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Quote Quote by sylas View Post
Not really. In the plunger frame, the plunger is significantly longer than the cylinder, because of length contraction of the cylinder. This means that the plunger reaches the end of the cylinder and presses the button well before the T-bar hits.

As soon as you say they have the same proper length and that the relative velocity is relativistic, all the leeway is gone completely.
Ok, I see now. Even if the proper length of the plunger is slightly shorter, as soon as the relative velocity is such that the cylinder, in the plunger frame, is length contracted by an amount larger than the difference in proper lengths, there's no leeway any more. So even if, say, the plunger was 10 cm shorter than the cylinder (to give a significant gap when both are at rest), as soon as the length contraction factor is less than 9/10, which corresponds to a relative velocity greater than 1/sqrt(10) or about 0.3c, the plunger will hit the button before the cylinder hits the bar, in the plunger frame.