The evolution of scientific thought from Newton to Einstein

by A. D'Abro

and distance

. Classical science assumed that this test of objectivity would hold in all cases, regardless of whether our observers were stationary or in motion. The theory of relativity tells us that this is not so. The observer in relative motion would always perceive the pole under a smaller visual angle, so that the mathematical expression purporting to give the length of the pole would no longer be an invariant.[71] Under the circumstances we should again be thrown back on the perplexing problem of whether there could exist any kind of universal objectivity holding for all observers in this universe.

One thing is certain. We could no longer attribute an invariant length to the pole. This length would no longer be immanent in the pole, since it is impossible to discover an invariant expression of spatial length holding for all observers, hence independent of their existence. We cannot, therefore, escape the conclusion that spatial length by itself can have no more universal existence than the apparent height or visual angle of classical science. Unless we abandon all hope of discovering a something universally objective, we much search for some substitute for that absolute spatial distance in which classical science believed.[72]

Minkowski found that such an absolute could be constructed; but it was made up of the relative length and duration under which every observer perceived any two instantaneous events. In exactly the same way as classical science had constructed the absolute spatial magnitude, so now Minkowski constructed the absolute space-time magnitude, i.e., the Einsteinian interval. Objectivity is at last rediscovered, though this objectivity refers neither to space magnitudes nor to durations, but to a combination of both. In other words, the analogue of the absolute objective length of the pole in classical science is now given by the absolute objective space-time interval. The analogue of the relative visual angle, or apparent height of the pole, of classical science is given by its relativistic length as measured by the observer; and this length is no more an illusion than was the visual angle. By omitting to analyse the meaning of his words, the critic has argued as though the visual angle, or apparent height, in classical science were an illusion. But the visual angle is not an illusion. The illusion arises only from faulty inferences, when, having identified visual angle with apparent height, we then proceed to confuse the apparent height with the real height of the pole, thereby crediting it with too short a length. It is this last confusion that is unjustified, for it amounts to confusing visual angle, or apparent height (which, though real for the individual, has no universal significance, hence which is relative) with real length (which is absolute in classical science).

In the same way the FitzGerald contraction is not an illusion. It can be measured, and manifests itself physically in every conceivable manner. But again it is a relative for the very concept of spatial magnitude is essentially a relative, since, according to our motion, it will have one value or another. That which is absolute, that which endures unchanged, is the Einsteinian interval; and unless we wish to continue to talk about such shadows as space and time, it is in the space-time world and there alone that we shall obtain universal objectivity.

Let us now state the precise nature of those modifications in lengths and durations which will arise as a result of relative motion. The Einstein-Lorentz equations show that a rigid material object, say a yardstick, which, when at rest in our frame, would measure out as one yard in length, would appear to contract more and more in value in the direction of its relative motion (FitzGerald contraction) as this relative velocity increased. Could the relative velocity reach that of light, the rod would become completely flattened down to nothing.

Likewise, an observer fixed to a clock would note that the durations between the successive second-beats of the clock were truly seconds. But with an increase in the relative motion existing between clock and observer, these beats would measure out as lengthened; and for a relative speed equal to that of light an infinite duration would separate two successive beats.

It must be noted that this lengthening in the durations defined by the tickings of the clock must not be attributed to the fact that the observer is moving farther and farther from the clock and therefore that longer and longer periods of time are necessary for him to take cognisance of these tickings. The results mentioned are those which would be found to hold after all the necessary corrections had been performed. It is solely the relative motion of the observer and the clock which is involved, and not the variations in their mutual distance. Our results would be exactly the same whether we were approaching or receding from the clock, so long as the same magnitude of our relative motion was maintained.