(The question is below)

I first quote this paper by Einstein :

Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.

IX.The Relativity of Simultaneity

Up to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity vand in the direction indicated in Fig. 1. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises:1Are two events ( e.g.the two strokes of lightningAandB) which are simultaneouswith reference to the railway embankmentalso simultaneousrelatively to the train?We shall show directly that the answer must be in the negative.

FIG. 1.2When we say that the lightning strokes AandBare simultaneous with respect to the embankment, we mean: the rays of light emitted at the placesAandB,where the lightning occurs, meet each other at the mid-pointMof the lengthA —> Bof the embankment. But the eventsAandBalso correspond to positionsAandBon the train. LetM'be the mid-point of the distanceA —> Bon the travelling train. Just when the flashes 1 of lightning occur, this pointM'naturally coincides with the pointM,but it moves towards the right in the diagram with the velocityvof the train. If an observer sitting in the positionM’in the train did not possess this velocity, then he would remain permanently atM,and the light rays emitted by the flashes of lightningAandBwould reach him simultaneously,i.e.they would meet just where he is situated. Now in reality (considered with reference to the railway embankment)he is hastening towards the beam of light coming fromB,whilst he is riding on ahead of the beam of light coming fromA.Hence the observer will see the beam of light emitted fromBearlier than he will see that emitted fromObservers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flashA.Btook place earlier than the lightning flashA.We thus arrive at the important result:3Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa(relativity of simultaneity).Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.4Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e.that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of lightin vacuoand the principle of relativity (developed in Section VII) disappears.5We were led to that conflict by the considerations of Section VI, which are now no longer tenable. In that section we concluded that the man in the carriage, who traverses the distance w per secondrelative to the carriage, traverses the same distance also with respect to the embankmentin each secondof time. But, according to the foregoing considerations, the time required by a particular occurrence with respect to the carriage must not be considered equal to the duration of the same occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the man in walking travels the distancewrelative to the railway line in a time which is equal to one second as judged from the embankment.6Moreover, the considerations of Section VI are based on yet a second assumption, which, in the light of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the introduction of the theory of relativity. 7

*Reading the first text in bold :

(I understand the Lorenz contraction, time dilatation , the formula,

what it means, the correlations between v and c etc.)

He moved a short distance towards B , so he caught the light going from B to M earlier on his mirror, his mirror being at a slightly more advanced point M'.

So he looks in that instant at his clock and notes an earlier time, that is as obvious as it can get.

(And the observer on the embankment will see the beem from B just an instant later because he did not move towards B in that same amount of time travelled by the train, he stayed at rest, thus the beam took longer for him to get to his mirror than it did for the observer on the moving train.)

*Then looking at the second text in bold :

Why do we say that this observer on the train (in a different reference-body, coördinate system) has his own particular time ?

He simply looked at his clock earlier,because of the above reasons.

> What am i missing here ?

The strange thing is that i do not ask this because i would not believe in the whole case of time dilatation (Hafele-Keating) - i do -

but reading the above puzzles me.