Even Newton speculated on the cause of gravitation, attributing it to some species of ether pressure, yet in spite of his illustrious name these ideas were not even mentioned by subsequent scientists. Why? Because they afforded no quantitative treatment and were so vague as to be worthless. It is the same when we consider the hypotheses that have been suggested in order to account for the origin of the solar system: we find these to be extremely numerous and varied. But not one of them carried any weight until it had been submitted to mathematical investigation, and then, according to the results obtained, it was declared possible or impossible. And it is precisely this mathematical work that is the crux of the difficulty, calling for the genius of a Laplace or a Poincaré. In much the same way, we may guess that the sequence of prime numbers will eventually be included in a concise mathematical formula, or that some day interplanetary communications will be established. The difficulty resides not in the guess, not in the desire, but in its realisation. As a matter of fact, it is questionable whether loose guesswork has ever been of any use in science. Jules Verne’s idea of ships that travelled under water can scarcely be claimed to have contributed to the invention of submarines, any more than his story of a trip to the moon can be of much assistance in enabling us to set foot on our satellite. Taking a more scientific example, Democritus’ guess about atoms most certainly never advanced their discovery by a single hour.[149]
And so it is with Mach’s guess (we can scarcely dignify it with any other name). Indeed, in Mach’s day, it would have been quite impossible for any one to justify his idea, since the necessary material, i.e., space-time, was then unknown. When we realise the important rôle played by space-time in our attempts to avoid a belief in absolute rotation, we can well understand that the doctrine of the relativity of all motion would have been absurd in Newton’s day. In fact, any thinker prior to, say, the year 1900 could never have anticipated the discovery of space-time, for its sole justification arose from the negative experiments in optics and electrodynamics attempted at about that time. As for Newton, not only did he know nothing of the non-mechanical negative experiments, but in addition, the equations of electrodynamics had not been discovered in his day. Furthermore, even had he conceived of space-time through some divine inspiration, he could never have utilised it for the purpose of establishing the relativity of all motion. His ignorance of non-Euclidean geometry would have rendered the task impossible. In fact, space-time, in the seventeenth century, would have been a hindrance, and the sole result of its premature introduction into science would have been to muddle everything up and render the discovery of Newton’s law of gravitation well-nigh impossible.
And this brings us to another point which is often true in physical science. Premature discoveries are apt to do more harm than good. For instance, had the astronomers of the seventeenth century possessed more perfect telescopes, had they recognised that the planets (Mercury, in particular) did not obey Kepler’s laws rigorously, Newton’s law might never have been discovered. At all events, its correctness would have been questioned seriously and mathematicians might have lost courage and doubted their ability to discover natural laws. Leverrier, for example, might have lacked the necessary assurance to carry out his lengthy calculations leading to the discovery of Neptune. In short, physical science proceeds by successive approximations, and too rapid jumps in the accretion of knowledge are liable to be disastrous.
We may now follow up Einstein’s investigations step by step and see how Newton’s absolute rotation was gradually eliminated from science. The situation facing Einstein was somewhat different from the one that had confronted Newton. In Newton’s time, there was no a priori reason why motion through empty space should be regarded as absolute rather than relative. Whichever way experiment pointed would therefore be equally acceptable. But when motion through the ether was considered there was every reason to anticipate that it could not be meaningless. The fact was that the ether seemed to present the properties of an elastic material medium, so that it was difficult to anticipate a marked difference between motion through the ether and motion through matter. More important still, the equations of electromagnetics proved that phenomena should be affected by motion through the ether. It followed that when the negative experiments in electrodynamics were being performed, there was every reason to suppose that absolute velocity through the ether would be detected. Had this been the case, the stagnant ether would, in all probability, have been identified with Newton’s absolute space. And it might have been claimed that absolute velocity, which had always escaped mechanical detection, had been revealed at last by electromagnetic and optical tests.
Yet, as we know, absolute velocity, even through the ether, obstinately refused to reveal itself. The situation was similar to the one we mentioned when discussing space. There also, absolute velocity through space appeared to elude us, in spite of the fact that, owing to the absoluteness of rotation, space could not help but be absolute. But, in the case of space, this duality entailed by the Newtonian principle of relativity was accounted for immediately by the mathematical form of the equations of mechanics. The fundamental law of mechanics, stating that a force is equal to a mass multiplied by an acceleration, makes no mention of velocity; hence, absolute velocity is obviously irrelevant to mechanical processes. In the case of the ether, the elusiveness of velocity was much more disquieting; among other reasons, because the equations of electromagnetics contained a velocity explicitly in the form of the electric current.
And so, when account was taken of the supposedly semi-material nature the ether was thought to have, and when the lack of covariance of the equations of electromagnetics was considered, the course of least resistance obviously suggested that we assume velocity through the ether to be a reality, but that its effects were concealed by compensating influences. At any rate, we need not be surprised to find that chronologically this was the attitude first considered. It was, as we remember, the attitude championed by Lorentz. But when Lorentz had succeeded in accounting for the negative experiments under this view, his theory appeared so patently artificial that scientists recognised that something was wrong somewhere.
If, with Einstein, we adopt a very general attitude, neglecting to consider the why and wherefore of things, and if we restrict our attention solely to what experiment has revealed, we cannot fail to be struck by the following fact: Every time we have sought to detect absolute velocity, whether through space or through the ether, our attempts have failed. Even certain classical scientists, on the strength of mechanical experiments alone, had felt compelled to banish the thought that absolute velocity through space had any meaning. How much stronger, then, was the suspicion that some general principle was involved, when the same situation confronted us once more in the case of the ether! Under the circumstances, it can scarcely be said that Einstein followed a very revolutionary course when he postulated his special principle of relativity, claiming that absolute velocity through space or the ether was a meaningless concept. In so doing, he was merely stating in abstract form the result of experiment. Einstein’s special principle can be expressed, as follows:
“No experiment, regardless of its nature, whether mechanical, optical or electromagnetic, can ever enable us to detect our absolute velocity through space or ether.”
We see that the only difference between Einstein’s principle and the Newtonian principle of relativity is that henceforth the relativity of velocity holds for all manner of experiments, or, again, that ether and space are identified. Apart from this difference nothing is changed. As before, space or ether remains absolute, in that though relative for velocity, it still manifests itself as absolute for accelerated or rotationary motions, just as in Newton’s day.
Against Einstein’s stand, the metaphysician may object to absolute velocity being cast aside as meaningless, merely because no experiment seems capable of demonstrating its existence. But science, as we know, is not metaphysics; it is based on experience. An a priori rejection of absolute velocity would sin against the scientific method; but an absolute velocity which, though supposedly present, no experiment can reveal, and for which, in addition, no useful function can be found, plays no part in the workings of nature. Were future experiment to detect this absolute velocity, it would of course have to be reintroduced; but to retain it on general principles against the verdict of experiment would be very poor science.