"He hopes that further study will remove this obstacle. He meets with the conception of 'simultaneity,' which is defined for him anew, and is disclosed as being 'relative.' He manœuvres further towards the fundamental theorem that every body of reference has its own particular time.
"His popular booklet makes this clear to him by quoting the example of a flying-machine, or, better still, a railway train that is rushing along an embankment at a very great speed, and that carries a passenger. Two strokes of lightning I and II are to take place at two widely distant points on the embankment. The question is then: When are these two flashes of lightning to be considered 'simultaneous'? What conditions must be fulfilled to ensure this? It is found—incontrovertibly—that the light-rays starting out from the two strokes of lightning must meet at the mid-point of the embankment.
"It now follows from a short chain of argument that the observer in the train will see flash II earlier than flash I, if they reach the observer, who is at rest, at the same moment. That is, two events that are simultaneous with respect to the embankment are not simultaneous for a moving system (such as a train or a flying-machine); the converse is, of course, also true.
"Here, again, the eager layman encounters difficulty, for he asks himself: Why should the two events be characterized or defined by lightning-flashes in particular? If acoustic signals were used instead, nothing would be altered in the fundamental determination, for the sound rays (sound-waves) would likewise meet at the mid-point of the line joining the sources of disturbance. What is the reason that the relativity of time arises only when phenomena are regarded optically, and that rays of light play the deciding part in all later developments?
"And this particular query is followed by one which is more general: Why does the popular pamphlet not read this question in my mind? I know that the author of it is more skilled in these matters than I, but just this superiority should help him to divine what is passing in my mind when I make efforts to follow his reasoning."
Einstein had listened to me patiently, and then he explained to me at considerable length why in this case optical signals cannot be replaced by sound signals: light is the only mode of motion that shows itself to be entirely independent of the carrier of the motion, of the transmitting medium. Thus the constancy of velocity is assumed in the above argument, and as this constancy is an exclusive property of light, every other method must be discarded as unallowable for investigating the conception "simultaneity." Furthermore, he showed me how, on the basis of relativity, starting from the embankment-experiment, we may arrive at a perfectly consistent representation of the conception of Time. He certainly did this by applying subtle physical arguments that exceed the scope of the present book.[7] He added, in substance, that it was futile and impossible to discuss in detail all the conceivable objections that might arise in the mind of one reading a popular work of this kind: it was a futile undertaking, because the true purpose was defeated, inasmuch as a clear development of the fundamental thought would be almost impossible under the cross-fire of so many random questions.
[7]In these arguments, arrangements of synchronous clocks occur, which are fixed into the co-ordinate systems, the positions of their hands being compared with one another. The "time" of an event is then defined as the position of the hands of a clock immediately adjacent to the scene of the event.
Thus, in this matter, Einstein takes the same stand as Schopenhauer in the preface of his chief work, in which he says: "To understand this work no better way can be advised than to read it twice (at least), inasmuch as the beginning assumes the end, almost as much as the end assumes the beginning; the smallest part cannot be understood if the whole has not already been understood." Whoever accepts and follows this advice will find that the intermediate objections will gradually balance and cancel one another, and that it is not necessary that they should interrupt the steady and consistent line of development.
The position would be different if a disciple of the new theory should resolve to dispense with strictly scientific reasoning altogether, and should wish to meet the wishes of his readers or hearers by discarding accuracy entirely. Such a programme seems quite feasible.
"This would be merely following the sketchy method of a magazine," Einstein remarked, "but you do not seriously think that it would lead to anything?"