The train / embankment thought experiment , Einstein ’ s second postulate of special relativity and relativity of simultaneity

The relativistic time dilatation effect and Einstein's second postulate of special relativity are used to analyse train/embankment thought expriments, both Einstein's original one, and an extension where observers on two trains moving at different speeds, as well as on the embankment, are considered. Whereas the relativistic analysis of Einstein's experiment shows, in contradiction to Einstein's interpretation, no 'relativity of simultaneity' effect, the latter is apparent for certain events in the two-train experiment. The importance of relativistic kinematics –embodied for photons in Einstein's second postulate– for the correct interpretation of the experiments is pointed out and demonstrated by detailed calculation of a related example. PACS 03.30.+p