This is my very first post on this website, which I find fascinating. Thanks to all the active members and team !
Two questions, related to special relativity in flat space time :
1) I have read that length contraction is occurring only in the direction parallel to the velocity. Can you prove this to me in a system where the velocity and the acceleration are not parallel ? I would accept a mathematical proof ("thought experiment") or also possible observations (for example, if you tell me that people studying accelerated particles in the LHC see a contraction only in the direction of the particles velocity but no contraction in the direction of their acceleration.)
Yes, this question arises from the Ehrenfest paradox.
2) I know that if two referential R and R' are inertial, then we have cdt^2 - dx^2 - dy^2 - dz^2 = cdt'^2 - dx'^2 - dy'^2 - dz'^2. My question is simple : is the reciprocity true ? ("if we have ds^2 = ds'^2, then R and R' are inertial"). Proofs are welcome !
Thank you so much,