Are time and space, then, merely hallucinations? And, if so, what is real?
No. Once the Relativist has thrown down the tottering ruins, he begins to reconstruct. Behind the veils, now torn down and trodden under foot, a new and more subtle reality is about to appear.
If we describe the universe in the usual way, in separate categories of space and time, we see that its aspect depends upon the observer. Happily, it is not the same when we describe it in the unique category of the four-dimensional continuum in which Einstein locates phenomena, and in which space and time are inseparably united.
If I may venture to use this illustration, time and space are like two mirrors, one convex, the other concave, the curvature of which is accentuated in proportion to the velocity of the observer. Each of these mirrors gives us, separately, a distorted picture of the succession of things. But this is fortunately compensated for by the fact that, when we combine the two mirrors so that one reflects the rays received by the other, the picture of the succession of things is restored in its unaltered reality.
The distance in time and the distance in space of two given events which are close to each other both increase or decrease when the velocity of the observer decreases or increases. We have shown that. But an easy calculation—easy on account of the formula given previously to express the Lorentz-Fitzgerald contraction—shows that there is a constant relation between these concomitant variations of time and space. To be precise, the distance in time and the distance in space between two contiguous events are numerically to each other as the hypotenuse and another side of a rectangular triangle are to the third side, which remains invariable.[6]
Taking this third side for base, the other two will describe, above it, a triangle more or less elevated according as the velocity of the observer is more or less reduced. This fixed base of the triangle, of which the other two sides—the spatial distance and the chronological distance—vary simultaneously with the velocity of the observer, is, therefore, a quantity independent of the velocity.
It is this quantity which Einstein has called the Interval of events. This “Interval” of things in four-dimensional space-time is a sort of conglomerate of space and time, an amalgam of the two. Its components may vary, but it remains itself invariable. It is the constant resultant of two changing vectors. The “Interval” of events, thus defined, gives us for the first time, according to Relativist physics, an impersonal representation of the universe. In the striking words of Minkowski, “space and time are mere phantoms. All that exists in reality is a sort of intimate union of these entities.”
The sole reality accessible to man in the external world, the one really objective and impersonal thing which is comprehensible, is the Einsteinian Interval as we have defined it. The Interval of events is to Relativists the sole perceptible part of the real. Apart from that there is something, perhaps, but nothing that we can know.
Strange destiny of human thought! The principle of relativity has, in virtue of the discoveries of modern physics, spread its wings much farther than it did before, and has reached summits which were thought beyond the range of its soaring flight. Yet it is to this we owe, perhaps, our first real perception of our weakness in regard to the world of sense, in regard to reality.
Einstein’s system, of which we have now to see the constructive part, will disappear some day like the others, for in science there are merely theories with “provisional titles,” never theories with “definitive titles.” Possibly that is the reason of its many victories. The idea of the Interval of things will, no doubt, survive all these changes. The science of the future must be built upon it. The bold structure of the science of our time rises upon it daily.