Having established the relative nature of physical simultaneity, we find it an easy matter to rediscover that other consequence of the theory, namely, the contraction of length. Consider, for example, an observer at rest on a track observing a train also at rest. What is the length of the train as referred to the observer’s frame, namely, to the earth? Obviously it is the difference in his distance from the engine and from the rear car. But if now we consider the more general case where the train or the observer with his reference frame is in relative motion (either choice comes to the same thing, so long as the motions are Galilean), it becomes imperative to state that the measurements must be performed at the same instant of time. It would be absurd to measure our distance from the rear car at one o’clock, then our distance from the engine at two o’clock; for we might find that the train had a length of over sixty miles owing to its displacement during the interval. But whereas in classical science the significance of the same time in two different places was absolute, the same for all observers, in relativity it becomes indeterminate. According to the relative motion of the observer, different simultaneity determinations will be obtained, and as a result the length of the same train will vary in value. This is what is meant by the relativity of length. Calculation proves that the greater relative velocity, the shorter will the train measure out.
In short, classical science recognised that apart from our intuitional understanding of the succession or simultaneity of the awareness of two sense impressions, such as two impressions of pain for instance (i.e., the here-now type of simultaneity), the succession or simultaneity of events could be determined only indirectly by physical means. And even so, there always remained a certain indeterminateness owing to our ignorance of the velocity of the ether drift. Assuming, however, a spread of simultaneous events to have been determined by any given observer, it was thought that these same events would remain simultaneous for any other observer. In other words, time and simultaneity were absolute.
Einstein’s theory compels us to revise the classical views. It still permits us to retain our belief in the absolute nature of a coincidence of events, that is, of events which are copunctual and which occur at the same time in any given frame. But it denies the absoluteness of the simultaneity of spatially separated events. Thus, if two observers pass each other, the events which are simultaneous with one another and with this passage according to one of the observers would be recognised as unfolding themselves in succession for the other observer. It follows that a simultaneity of events, or a sameness of time throughout space, becomes an indeterminate concept until an observer or a frame of reference has been specified; in much the same way, the weight of a given brick situated anywhere in space will be indeterminate until such time as the distribution of the surrounding masses has been decided upon. So far as the special theory is concerned, this is the sole difference between classical science and relativity.
We may say that in the general theory, where large masses of matter are in relative motion, the entire concept of the simultaneity of external events becomes obscured, for space and time determinations over extended areas become impossible. In the general theory, therefore, relativity breaks away completely from classical science. And here we may mention a number of criticisms directed against Einstein’s selection of optical signals for the purpose of defining simultaneity.
Thus, Dr. Whitehead writes: “The very meaning of simultaneity is made to depend on light signals. There are blind people and dark cloudy nights and neither blind people nor people in the dark are deficient in a sense of simultaneity. They know quite well what it means to bark both their shins at the same instant.”[56]
In this illustration, Dr. Whitehead, by referring somewhat loosely to a sense of simultaneity, is confusing the two species of simultaneity which physicists have found it imperative to treat separately. We may recall that these two types were exemplified by a simultaneity in our awareness of two impressions (psychological simultaneity) and by a simultaneity in the occurrence of two external events (physical simultaneity). Of course, in the illustration selected by Whitehead, all the events considered, namely, our awareness of the two pains and the actual coming into contact of our shins with the rail, are so close together both in space and in time that for all practical purposes the confusion would be legitimate. Nevertheless, inasmuch as a confused and obscure illustration is liable to generate confused conclusions, it is necessary to clear up the matter from the start and specify the type of simultaneity we propose to discuss.
First let us assume, for argument’s sake, that it is the psychological type of simultaneity which is at stake. The criticism would then amount to this: Einstein has sought to render our immediate awareness of the simultaneity of two sense impressions contingent on the results of optical measurements executed a posteriori. In other words, if we should ask our friend whether he had sensed two sounds simultaneously or in sequence, he would answer: “I cannot tell you before I have looked up Einstein’s rules for simultaneity determinations and performed certain optical measurements.” It would follow that were no light rays obtainable or were our friend blind, he would never be able to give us an answer. Einstein would thus have made our immediate recognition of a simultaneity or of a sequence of sensations contingent on the accidental circumstance that we were gifted with eyesight. This seems to be Dr. Whitehead’s contention, as would appear from his reference to “blind people” in his criticism.
It seems scarcely necessary to state that neither Einstein nor any other scientist has ever attempted to defend so paradoxical an assertion. Quite the reverse. Both classical and relativistic science are fully agreed that our ability to recognise the simultaneity of two impressions (be they visual, tactual or auditory) is in the nature of a fundamental recognition which cannot be analysed further. We know that we feel two pains at the same instant, or that two thoughts flash through our mind simultaneously, and that is all there is to be said about it. Any discussion as to why we know or how we know does not concern the physicist. It is a problem which must be left to the brain specialist or psychologist. So far as the physicist is concerned, it constitutes a form of a priori knowledge over which it is useless to argue. On no account, then, can it be claimed that the theory of relativity professes to interpret this psychological species of simultaneity in terms of optical measurements or, for that matter, of physical measurements of any kind.
But there is another way to view the problem. We might claim that though Einstein has never sought to render psychological simultaneity contingent on the performance of optical measurements, yet, on the other hand, his theory fails to take this fundamental type of simultaneity into account.
But any one at all conversant with physical science would perceive the fallacy of this contention at first blush. He would realise that physical science would be quite impossible were we to disregard the data furnished us by our fundamental recognitions. Consider, for instance, the manner in which Einstein defines the simultaneity of external events, e.g., of two flashes occurring on the embankment. He tells us that this simultaneity will be realised if the observer standing at a midpoint between the two flashes becomes aware of the two luminous impressions simultaneously. Obviously, for this definition to convey any meaning, it is essential that we credit the observer with the ability to recognise the simultaneity of these two luminous impressions. Had this fact been ignored or denied by the theory, Einstein would never have suggested his definition.