Berkeley’s criticisms appear to have arisen from some such argument as the one we have just discussed. Thus, he tells us that absolute motion cannot be imagined and for that reason should be banished from science. He then proceeds to point out that motion can only mean a displacement with respect to something sensible and that, space being suprasensible, motion through space is meaningless. Now it is perfectly correct to claim that men originally came to conceive of motion through visual experience by observing the motion of one body with respect to another. In other words, the phoronomic conception of motion is the natural one.
But when these points are granted, it still remains a fact that we cannot force our scientific co-ordinations into a mould which would satisfy too narrow a phenomenological attitude. In physics, as in pure mathematics, we are often confronted with conceptions which it may be difficult to imagine. Thus, although our understanding of continuity is derived from experience, for instance by passing our finger over the table, yet the concept of continuity has had to be extended and elaborated profoundly by mathematicians. Continuous curves with no tangents are not easy to imagine; yet we cannot deny their existence merely because it puts too great a strain on our imagination. Neither can we deny that there are as many points in a cube as on one of its sides, for Cantor has proved that such is indeed the case.
It is the same in physics. Experiment presents us with certain facts which we may often interpret in various ways. But we cannot ignore the facts merely because they happen to conflict with our own particular philosophy. All that we may do is to repeat the saying of a certain king of Spain, that had we been God, we should have constructed the universe with greater simplicity. Not being God, however, we must make the best of a bad job. Now, in the case of motion, any philosophy which starts to rule out absolute motion is forthwith confronted with the difficulty of accounting for centrifugal force. Berkeley, as might be expected, falls down on this point completely. His arguments reduce to a criticism of absolute space without affording us any better solution. Furthermore, his premises are scientifically incorrect.
For instance, when criticising Newton’s proof of absolute space as illustrated by the experiment of the rotating bucket of water, he remarks that owing to the earth’s velocity along its orbit, the particles of water cannot possibly be describing circles. And so Newton’s argument purporting to have detected absolute circular motion would thus be at fault. Berkeley’s argument reveals that same ever-recurring confusion between velocity and acceleration; he fails to realise that velocity through absolute space is not claimed by Newton to be detectible by mechanical experiments; the Newtonian principle of relativity states this point explicitly. Acceleration alone gives rise to forces. Now, so far as the particles of water are concerned, they possess exactly the same acceleration, whether they be whirling in circles or describing cycloids. Hence, Newton’s experiment discloses absolute acceleration, and this is all it was ever intended to disclose. A further argument presented by the same critic is based on the tangential force which he claims to be acting on the revolving water particles. He hopes thereby to account for centrifugal force without introducing absolute rotation. The reasoning is so obscure that we do not pretend to have fathomed it, but one thing is quite certain—the premises are totally incorrect; for there is no tangential force acting on uniformly revolving water particles, and centrifugal force manifests itself in this case. Obviously Berkeley is confusing momentum and force.
Other critics have speculated on the possibility of our space revolving in a more embracing one, this other in still another, etc. But what if it does! A hypothesis of this sort would never endanger the Newtonian position. Suppose, for argument’s sake, that our universe of space were likened to a bubble of ether rotating in a super-space; this bubble of ether would still represent absolute space. In every case the essential feature of absolute space and motion resides in the empirical fact that a certain definite set of dynamical axes appears to be present in nature; and the above-mentioned argument could never banish the existence of these absolute axes. All it could do would be to prove that nothing could be predicated of the motion of these axes in the super-space. But in any case the axes would be non-rotating in the ether bubble. This would thereby assume the position of absolute space as understood by science, and we should have to conceive of the more embracing space as rotating round it. Needless to say, the entire speculation is unscientific in the extreme since it reduces to a hypothesis ad hoc, beyond the control of experiment conceived of for the sole purpose of complicating a co-ordination o facts; whereas the only possible justification for this type of hypothesis is to permit us to introduce simplicity into our co-ordinations.
We may mention yet another type of argument because it brings out an important point of terminology. It is asserted, for instance, that acceleration must be relative since we measure it relatively to an inertial frame or to space. But here, of course, we have a mere confusion of words. The critic is assuming that absolute motion should mean motion with respect to nothing. But absolute motion in science does not mean this at all. It means motion which cannot be regarded as relative to something observable, such as matter; hence it becomes automatically motion with respect to something suprasensible, i.e., to space. Were it not for this interpretation placed on absolute motion in science, the expression would become meaningless, for motion with respect to nothing is itself nothing.
We may summarise the scientific attitude towards space and motion as follows: If motion can be detected otherwise than in relationship to things observable, or, more precisely, if a co-ordination of scientific facts renders it simpler to assume that such is the case, then motion, and hence space, must be considered absolute. If, on the other hand, no trace of absolute motion, as defined above, can be detected by experiment, two courses are open to us. Either we may assume that absolute motion has no scientific significance and that motion is always motion between observable existents, in which case motion and space are held to be relative; or else we may follow Lorentz’s method of dealing with the ether and claim that absolute motion would be detected were it not for a number of compensating physical effects which just happen to conceal its presence from our experiments. But if we adopt this very artificial attitude, it is imperative that we follow up our argument as Lorentz has done, and succeed in specifying the precise mode of action of these compensating effects and also their precise numerical magnitudes—and this would entail a considerable knowledge of advanced mathematics. So much for the scientific status of the problem of space and motion.
Now metaphysicians have a habit of confusing this scientific aspect of the absoluteness or relativity of motion and space with that other problem dealing with the essence of space. But, as Euler pointed out two centuries ago in the passage quoted previously, this metaphysical problem is of a totally different order, and has no bearing on the one that scientists are discussing. Even if we were prepared to attribute any meaning to such metaphysical inventions as Leibnitz’s monads, and agreed that space might be conceived of as the result of a relationship between them—even so, in view of the dynamical facts stressed by Newton, motion and space would still be absolute. It would be of no avail to hold that motion was relative since it was relative to the monads, for these, whether fictitious or real, are at all events suprasensible. Conversely, even were we to accept the metaphysician’s claim that, metaphysically speaking, space is an absolute existent, nevertheless, were it impossible to detect any trace of absolute motion, we should have to say that motion and space were scientifically relative, or else follow Lorentz’s method of dealing with the ether.
When, in addition to all these facts, we remember that the metaphysician’s theories reduce to mere expressions of opinion affording no possibility of proof or disproof, we can well understand that the scientific attitude towards space and motion has been governed solely by the empirical evidence.
And now the query will naturally be raised: If the dynamical facts of motion impose the belief in absolute rotation, how is it that Einstein, and even before him Mach, should have considered it possible to escape Newton’s solution? Let us first consider Mach’s argument. Mach’s aim was to co-ordinate the dynamical facts of motion in terms of sensible factors alone and thus obviate the introduction of that suprasensible entity, absolute space. And so he was led to conceive of rotation as rotation with respect to the universe, hence with respect to the stars. In contrast to Berkeley, however, Mach realised the great difficulty of accounting for centrifugal forces under this view. He, at least, made an attempt to solve the puzzle by attributing a direct dynamical influence to the relative rotation of the star-masses. But, since his attempt was not followed up mathematically, it was nothing more than a loose, unsupported suggestion. The fact is that in physical science the only convincing theories are those we can defend with quantitative arguments; mere undeveloped guesses are of no value.