1 – Langevin's twin paradox and the forwards and backwards movement of a rotating cylinder experiment: Logical incompatibility of special relativity with mechanics of elastic bodies

This paper is a didactic version, slightly long but very detailed, of one shorter but more difficult to read. The contradiction shown forces a modification of the theory in a way which does not involve its pragmatic part, which conforms to experiment. A later paper (already written in French, not yet in English) will demonstrate it.Langevin's twin experiment does not lead to a contradiction within the frame of special relativity. Though, such is not the case of one of is variants, the forwards and backwards movement, relative to a Galilean space, of a thin elastic spinning cylinder. The crucial difference is that the space between the 'motionless' part and the one making the journey is always bridged by some continuous portion of the cylinder. Within the frame of special relativity, the study of the cylinder's behaviour and of its changes of shape shows that the experiment can be run with zero intrinsic twist and with intrinsic angular speeds of sections remaining constantly equal to the same value ω. Then, if we calculate the numbers m and n of turns around the axis that two particular points M and N make, we prove n-m is both a zero and a non-zero integer. David Wands, world-renowned expert in general relativity wrote the following about this demonstration " I cannot point the author to where the mistake lies"..