. It can be shown that Planck’s constant
is not a mere number; it represents some definite abstract mathematical entity, and that entity is action.
We must assume, therefore, that there exist atoms of action in nature, just as there exist atoms of matter. But what is the deeper significance of this atom of action? First of all, has it any deep significance, or is its discovery on a par with that of some new variety of flower, or some new mineral? But to decide on a question of this sort we must possess a fairly thorough understanding of what is meant by action, as also of the part this important entity plays in science. Now, action is a highly abstruse concept taken from analytical dynamics. It would be absurd, therefore, to criticise the conclusions of scientists, whatever these might be, unless we were in a position to discuss the numerous facts which were involved in their arguments.
The verdict of scientists is that the atomicity of action entails a gigantic revolution in our understanding of nature. In the first place, the laws of mechanics, whether those of classical science or those of relativity, issue in a principle of action; so that by tampering with action, we are tampering with the basic laws of mechanics. Hence, it would appear that our insight into the laws of nature, even in spite of the great advance due to relativity, was still far too crude. We should have observed merely macroscopic average effects; the deeper laws, the underlying microscopic ones, would have escaped us completely. Conclusions of this sort had, of course, already been arrived at in other ways, as, for example, in the kinetic theory of gases; but the atomicity of action extends these views still farther. It suggests that change is always discontinuous; that a system passes from one state to another, not in a continuous way, but by a series of jerks or jumps. When we wish to decide how the jumps will follow one another, no exact laws can be formulated; and we are compelled to appeal to statistical considerations and probabilities. No rigid deterministic scheme is apparent in nature, or, in Weyl’s words, “no causality of physical nature which is founded on rigorously exact laws.” In the realm of the microscopic, we appear to be confronted with total chaos and anarchy. The past does not entail the present, as it would in a purely deterministic scheme. Free will appears to be rampant; and our sole means of prevision is to establish averages, just as a life-insurance company does when it fixes its premiums. Statistics and probability, blind chance and uncertainty, take the place of rigid determinism. Of course it may be that a further advance in our knowledge will enable us to rediscover a deterministic scheme beneath the chaos which is now confronting us. But the point we wish to stress is that in the present state of our knowledge no definite stand can be assumed.
Even this is not all. There is every reason to suspect that the atomicity of action is closely related to the atomicity of matter, though what the precise connection may be remains a total mystery. Furthermore, when we realise that “action” contains the product of space and time, or, if we prefer, “elements of space-time,” and when we realise that what mathematicians call “the domains of probability” are now of finite extent instead of reducing to points, the possibility of space-time turning out to be atomic suggests itself strongly. There is no telling where we may be led, for our entire understanding of nature is at stake. As Weyl expresses it: “Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution.” As we have mentioned, it may be that space and time will turn out to be atomic, or, again, that we shall have to recognise them as approximate concepts which will have to be abandoned when the infinitely small is contemplated. In much the same way, the conception of temperature as due to an agitation of molecules loses its meaning when the molecules themselves are considered.
What the future may hold in store is any one’s guess at the present time. But one thing is certain: we are faced with a gigantic revolution; and the new ideas will undoubtedly conflict with the common-sense instinct which the rationalist often erroneously attributes to “reason.” But what if they do? Did not the existence of men walking upside down at the antipodes conflict with the crude common sense of our ancestors? Or, again, consider the less trivial illustration of the wave theory of light. When Fresnel defended it, Poisson pointed out that it would imply the existence of a bright shadow behind a body of a certain size situated at a certain distance from a wall. On the strength of this argument Poisson dissented from Fresnel’s views. Yet when the experiment was actually performed, the bright shadow was seen to be there. And why did Poisson regard his argument as valid? Because it was based on common sense; but we see that this common-sense instinct that was misleading him was by no means the product of reason; it was founded merely on partial and crude experience.[132] It is probable that the more we study of nature, the more the common sense of our day will be submitted to disagreeable jolts; and this is only natural, since the more refined our investigations, the farther we shall be wandering from the familiar world of common experience.
To revert to the new ideas that suggest themselves as a result of the quantum theory, we see that starting from facts which by common consent it is the function of the physicist to establish, we are gradually led through a series of theoretical deductions to considerations which border on metaphysics. But whereas the metaphysician will claim a priori knowledge or else, whether he admits it or not, will be deducing his knowledge from the crudest facts of daily experience, the theoretical scientist will base his deductions on extremely accurate observations embracing all the phenomena known to science.
For this reason, these deductions will constitute knowledge; for knowledge springs from an accurate investigation of a large number of facts, not excluding those revealed by ultra-refined experiment. More precisely, a knowledge of nature consists in the co-ordination of all known facts, and this co-ordination must be performed so as to account for phenomena not merely in some vague qualitative way, but with the utmost accuracy. Only after this preliminary synthesis has been accomplished can general philosophical conclusions be forthcoming. Until then all we can do is guess, and past experience proves that ninety-nine times out of a hundred our guesses will be wrong.