The evolution of scientific thought from Newton to Einstein

by A. D'Abro

. But situations may arise where a procedure of this sort would be impossible. Suppose, for instance, that we wish to ascertain whether two events occurring one on the sun and the other on the earth by our sides are simultaneous or not. How shall we proceed?

We will note on our watch the precise instants at which we perceive both events. Then we will take into consideration the time required for the light message from the solar event to reach us; we will deduct this duration from the instant at which the solar event was perceived, and we thus obtain the instant at which the event actually occurred on the sun. If this instant of time is identical with the psychological instant at which the earth event at our sides was perceived, we will assert that the two events occurred simultaneously. And now let us notice that by subtracting the time that light has taken to reach us from the solar event and by noting the instant thus defined, we are in effect re-establishing matters as they would have presented themselves had the news of the solar event been propagated to us through our frame instantaneously with infinite speed, so that we may present our definition of simultaneity in the following conceptual way:

We will say that if a perturbation (say, a telepathic one) is propagated with infinite speed from the surface of the sun, coincidently with the occurrence of the solar event and carrying the news of the solar event, and if this perturbation reaches us on earth at the precise psychological instant at which the earth event is perceived at our sides, then the two events will be simultaneous. Likewise, always considering the hypothetical case of instantaneous transmission, if the solar perturbation reaches us prior or subsequent to our perception of the earth event occurring at our sides, we will conclude that the solar event has preceded or followed the earth event. Of course this definition by means of a propagation moving through our frame with infinite speed is purely conceptual, since no such type of propagation is known to physicists; but as it would lead to exactly the same determination of simultaneity, we may retain it provisionally, as it will facilitate our understanding of the nature of Einstein’s discoveries.

Now, according to classical science, simultaneity having been defined in this conceptual way, any other observer, regardless of his motion, would have agreed that the perturbation had travelled from sun to earth with infinite speed, i.e., in zero time; so that in all cases the two events could be regarded as simultaneous in an absolute sense. By this we mean that they would be simultaneous not merely from the local point of view of the observer on earth, but also for all observers. In other words, physical simultaneity would be absolute; likewise, the stretch of physical time separating two successive pairs of simultaneous events occurring in different regions of space would be absolute; in other words, physical time itself would be absolute. This indeed was the belief of classical science.

But if now we view the same problem in the light of Einstein’s theory, and if we remember that an infinite speed is a relative depending on the frame of reference or relative motion of the observer, we find that these opinions are no longer tenable. As before, the observer on the earth will be perfectly justified in believing that the two events (the solar one and the one occurring at his side) are simultaneous; but, on the other hand, another observer in relative motion would discover that the earth observer was wrong, for as referred to his own frame, the perturbation would not have spanned the sun-earth distance in zero time with infinite speed. According to him, therefore, the two events would not be physically simultaneous.

In short, physical simultaneity and duration, which were considered absolutes by classical science, must now be considered relatives having no absolute, universal significance, since they vary when computed in frames moving at various relative speeds.

But it is most important to realise that this relativity of simultaneity holds only for events occurring in different places and does not apply to events occurring in the same place. The reason for this distinction is easily understood. Suppose that two instantaneous events occur at the same point and at the same time in our frame of reference. The events, being simultaneous and copunctual in our frame, are said to constitute a coincidence of events. If now we change our frame of reference, will the two events as referred to this new frame also be simultaneous and copunctual? Obviously yes. The principle of sufficient reason itself should satisfy us on this score, since whatever disruption in copunctuality or simultaneity a change of frame might bring about, as there is nothing to distinguish one event from the other, either in position or in time, there is no reason why one event should precede rather than follow the other, either in position or in time, when the frame is changed. A concrete illustration would be given by a collision between two automobiles. Here we have two bodies situated at the same point of the road (or thereabouts) at the same instant of time; hence the observer on the road is witnessing a coincidence of events in the road-frame. Obviously, were he to view these happenings from some passing train, the collision would occur just the same; hence, so far as the train-reference-system was concerned, the two events would continue to constitute a coincidence. From this we see that, in contradistinction to the simultaneity of events occurring in different places, which is essentially a relative depending on the choice of our frame of reference, a coincidence of events is an absolute, that is, remains a coincidence or a simultaneity in all frames of reference.

We may note that in a world in which coincidences were relative, that is, in a world in which two cars would appear to collide and all the passengers killed when viewed from the road whereas no such collision would take place when viewed from the train, science would be quite impossible; for the opinions of the various observers would be relative to the point of being inconsistent. In the squirming world of relativity something at least must be absolute, and one of these absolutes is found to reside in the coincidences of events.

We may contrast the teachings of classical science and of relativity in the following way: Just as classical science recognised that there was no physical significance in speaking of the same point of space at different times until, by selecting a frame of reference, we had objectivised, as it were, the space we were discussing, so now relativity compels us to add: “There is no meaning in speaking of the same instant of time in different places until we have objectivised time, as it were, by specifying our frame of reference.” In both sciences, however, the classical and the relativistic, the coincidence of events remains an absolute, transcending the choice of a frame of reference. From a philosophical point of view, this discovery of the relativity of simultaneity marks a date of the same momentous importance as did the discovery of the Copernican system in astronomy.[55]