Now it is the problem of locating external events in a common space and time, or a common space-time according to the modern view, that is the one of paramount importance for the student of nature. Direct intuition failing him, if duration and simultaneity as between external events in the outside world were to have any meaning at all, they could be defined only as a result of some convention similar to that selected for the measurement of space with rigid material bodies. The aim of physics was therefore to decide on some conventional means of determining the simultaneity and succession of external events in a manner compatible with the existence of a common objective universe.
The most obvious method of arriving at some consistent determination of the simultaneity of two external events was to appeal to physical propagations, such as those of light or sound waves, by taking into consideration the times these propagations required to reach us.
Of course, in everyday life, the distinctions the scientist is compelled to consider are very often of scant importance. When, for instance, we bark both our shins and are conscious of a psychological simultaneity of painful impressions, we are perfectly justified in practice in assuming that we have barked our shins simultaneously. It is only when we subject an example of this sort to the rigorous logic of scientific thought that the crude view becomes untenable in theory though of course still permissible as an approximation.
The fact is that the barking of each of our two shins constitutes an external event,[54] and our awareness of each of the two pains that ensue constitutes in turn a psychological event. Thus we have to take into consideration two external events and two psychological events. We have no more right to muddle up these two species of events than we have to confuse the firing of a shot with the hitting of the target. In any case, a certain period of time, however short, must elapse between the instant we bark one of our shins and the instant we become aware of the pain. Physiologists who have measured the speed of nerve transmissions could tell us exactly what the lapse of time would be, as measured by a clock. Unless we have reason to assert that the nerve transmissions proceed at the same speed along both legs, and unless the bruised spots on our two shins are situated at the same distance from the seat of our consciousness, our intuitional sense of the psychological simultaneity of the two sensations of pain does not permit us to decide on the simultaneity of the two external events (the barkings of our shins against some object). In practice, however, as we have mentioned, we may neglect all these subtleties; for as our psychological awareness of simultaneity is after all extremely crude, there would be no advantage in submitting our results to corrections of comparatively insignificant importance.
Nevertheless, although the differentiation we have established is of no practical interest in the case we have discussed, it possesses a vast theoretical importance, as will be seen from the following illustration: If we were to confuse the external events with our awareness of them, we might argue that a human giant with legs extending to the stars and touching, for an instant, the sun with his left knee and Sirius with his right foot, would be aware by direct intuition of the simultaneity of these events; since all he would have to do would be to register the simultaneity of his two conscious impressions—the two burns. But the argument would be faulty; for in a case of this sort, where the external events occurred at such vast distances from the seat of his consciousness, the giant could no longer afford to neglect possible variations in speed of the two nerve propagations and the difference in distance of the two points on his legs at which the external events had occurred. The only reason the popular mind retains a lingering belief in some vague intuitional understanding of the simultaneity of external events, however distant, is because when the events are near us their simultaneous perception justifies our belief in their simultaneous occurrence. We then extrapolate these results unconsciously from place to place, and fall into the erroneous belief that we possess this same intuitional understanding of the simultaneity of external events throughout space.
The significance of the preceding discoveries can be summarised as follows: When considering the simultaneity or order of succession of events, we must differentiate sharply between events which reduce to our awareness of sense impressions, and those which refer to external occurrences. Our recognition of the simultaneity or order of succession of sense impressions or of thoughts flashing through our mind is fundamental in that it cannot be analysed further. For this reason a physical theory cannot be called upon to give a physical definition of judgments which it recognises as a priori. In contradistinction to the temporal position of sense impressions, we have to consider the simultaneity or order of succession of external events. In this case direct recognition fails us. All we can do is to note the instants at which we became conscious of these external events, and then by appealing to physical propagations deduce therefrom the instants at which the events occurred in the outside world. In order to avoid any confusion we shall therefore refer to the simultaneity of external events throughout space as physical simultaneity, reserving the name psychological simultaneity for our awareness of the simultaneity of two sense impressions.
Now all the conclusions we have reached up to this point are quite irrelevant to Einstein’s theory proper. They embody the discoveries of classical science and, while they still hold in the relativity theory, we shall see that Einstein’s contributions to the problem of simultaneity lie in another direction entirely. If these points are understood we may pass to a definite example and investigate how the physicist will proceed when he wishes to determine whether or not two external events occurring in different places are simultaneous in the physical sense.
Suppose that two instantaneous flashes of light occur at two points,
and