Recently a question asked by sparsh stimulated my gray matter regarding the invariance of lengths in galilean relativistic classical mechanics. First I state the question.(adsbygoogle = window.adsbygoogle || []).push({});

A man X is sitting at the rear end of a long compartment of a train running at constant horizontal velocity with respect to a ground observer Z. X tosses a coin to a person Y sitting at the front end of the compartment. The trajectory of the ball, as seen by Y and Z, will have : 1) Equal vertical and horizontal ranges OR 2) equal vertical ranges but different horizontal ranges OR 3) Different vertical and horizontal ranges.

Obviously the problem can be solved with a simple galilean transformation. However, consider that the length travelled by the coin as seen by Y is simply the distance between X and Y in the train's reference frame, that is the compartment's length. But when seen Z the point where X released the coin is much further from the point where Y catches it than the length of the compartment.

This seems to indicate that the two inertial observers will not be able to agree on a length measurement. But I was under the impression that in classical mechanics length was strictly invariant and stayed so unless you replaced galilean transformations with relativistic Lorentz ones, when the ability to rotate lengths in an extra dimension meant that spacetime intervals rather than spatial lengths were invariant.

What am I missing here. Can you help me out of this dilemma? Thank you.

Molu

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# Homework Help: Invariance of length in classical mechanics?

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