The Analysis of Matter

Pg 338] All this represents a failure of correspondence between physical space-time and perpetual space and time. If we assume that the human body moves in a geodesic, perceptual time may be identified with the integral of ds taken along that geodesic, while perceptual space consists of certain relations between simultaneous percepts (the word "simultaneous" raises no difficulties, since all percepts are in our heads), partly themselves perceptual, partly inferred, but all just what they are, whatever physics may say. There are certain respects in which we can modify perceptual space to suit physics, and certain others in which we cannot. We can, for example, infer that percepts consist of imperceptible parts, if physics gives us ground for thinking so. But where we perceive some relation between percepts, we cannot deny that there is such a relation, however little physics may allow it to subsist between the objects said to be perceived. The rule is: We can infer extra complexity of structure in percepts if physics requires it, but, however much physics may require it, we cannot infer a smaller complexity than is demanded by the study of percepts on their own account. In the world of percepts, the distinction between space and time does really exist, and space does really have certain properties which relativity denies to physical space. Thus to this extent the correspondence between perceptual and physical space breaks down, and measurement, which has to do primarily with percepts, fails to give us quite such good data as we hoped to obtain for inferences as to the physical world. (2) I come now to the difference between a percept as it seems and a stimulus as it is inferred. But this is not the whole scope of the problem to be discussed. The word "perception" implies relation to a physical object; we are supposed to "perceive" a chair or a table or a person. If physics is correct, the relation of a percept to a physical object is very remote and curious. In ordinary cases, we see objects by[Pg 339] means of light which is reflected or scattered, which increases the complication. To take the simplest possible case, let us suppose that we are seeing a glowing gas. The percept seems to be a patch of bright colour of a certain shape, sensibly continuous in perceptual space, and approximately constant in perceptual time. Perception gives knowledge only in so far as this percept corresponds to what is really taking place in the gas. Now if physics is true, there are great differences between the apparent structure of the percept and the real structure of what is taking place in the gas. (Differences other than structural may be ignored.) Instead of something steady and continuous, such as the percept seems to be, the process in the gas is supposed to be a large number of separated sudden discrete upheavals. It is true that there are important similarities between the percept and the physical event. The shape of the percept corresponds to the shape of the region in which the upheavals are taking place, with the limitations mentioned just now in connection with measurement. The colour of the percept corresponds to the amount of energy lost by each atom in an upheaval. The constancy of the percept corresponds to the statistical constancy in the rate at which upheavals occur in any not too small portion of the gas. Thus everything in the percept represents a statistical fact about the gas, with the exception of the colour, which is supposed to represent a fact about each atom. This, by the way, is an odd reversal of Locke's dictum about secondary qualities: the colour is the most nearly objective of all the elements in the percept. These differences are all of one kind in a certain respect: they attribute more structure to the physical occurrence than to the percept. This is in line with the general principle that the relation of distant to near appearances is one-many, so that differences in the percept imply differences in the object, but not vice versa. The finer structure of the object is all, in[Pg 340] the last analysis, inferred from the grosser structure of percepts, but it involves the comparison of many percepts and the search for invariable causal laws, in the manner which we considered in Part II. There is therefore no inconsistency in the view that the physical event differs from the percept in the way suggested by physics, since the difference consists in attributing more structure to the physical event, not in denying to it those elements of structure which are possessed by the percept. It is possible, if we choose, to attribute to the percept the same structure as that possessed by the physical occurrence, or rather the same structure as that possessed by the immediate external stimulus. It cannot be proved that this hypothesis is untrue, but it is less useful than it might be supposed to be, because only what is known about percepts is epistemologically important, and such structure, if it exists, is certainly unperceived. What we only discover about percepts by means of inference does not belong to the part which affords premisses for science, but is, from the standpoint of theory of knowledge, in the same position as events in the external world. Therefore, although percepts may have an unperceived structure, this does not diminish the significance of the fact that the structure we perceive in percepts has only a one-many relation to that of their stimuli. The question must be faced: Is physical space-time perhaps much more unlike the space and time of perception than we have supposed? Have we been victims of imaginative laziness in our merely piecemeal modifications of common-sense prejudices? Dr Whitehead, most emphatically, is not open to such a charge; his "fallacy of simple location," when avoided, leads to a world-structure quite different from that of common sense and early science. But his structure depends upon a logic which I am unable to accept, namely the logic which supposes that "aspects" may be not quite alike, and[Pg 341] yet may be in some sense numerically one. To my mind, such a view, if taken seriously, is incompatible with science, and involves a mystic pantheism. But I shall not pursue this topic here, having treated it on former occasions. The question I wish to ask is: Without adopting heroic measures, what could we suppose about physical space-time, if we were anxious to preserve what is probably true in physics, but not anxious to keep as near as possible to common sense? In particular, can space-time itself be atomic, as the existence of the unit of action seems to suggest? And first, how are we to conceive "action"? Action is usually defined as the time-integral of energy; since energy can be identified with mass, "action" may also be defined as mass multiplied by time. Gravitational mass is a length; e.g. the mass of the sun is 1·47 kilometres.[69] Since gravitational and inertial mass are equal, we might regard action as length multiplied by time. Dr Jeans (Atomicity and Quanta, p. 8) says: "There can hardly be an atomicity of the continuum itself, for, if there were, a universal constant of the physical dimensions of space multiplied by time ought to pervade the whole of physical science. Nothing of the kind is even suspected, nor, so far as I know, has ever been so much as surmised. Thus science can to-day proclaim with high confidence that both space and time are continuous." In this passage, the "high confidence" seems to me to go beyond what is warranted. If there were a scientific gain in conceiving the space-time structure atomically, I do not believe that any theoretical arguments to the contrary could interpose a veto. Arguments from dimensions, such as Dr Jeans employs, have no longer the definiteness that they had before the introduction of relativity. As we have just seen, we could define "action" so that its dimensions would be length multiplied by time. Now there is a universal constant of action, namely . Perhaps, if we were to take action as one of the basic conceptions of physics, we might be able to construct a physics which would be atomistic all through, and yet would contain all that is verifiable. I do not "proclaim with high confidence" that this is possible; I only invite attention to the hypothesis, as worth investigating on the chance of its affording a simplification of the conceptual apparatus of physics. In the following chapters, this hypothesis is to be borne in mind. FOOTNOTES: [69] Eddington, op. cit. 87. [Pg 343] CHAPTER XXXIII PERIODICITY AND QUALITATIVE SERIES THE periodic character of many physical occurrences has been obvious ever since men observed their own respiration and the alternation of night and day, but it has acquired a quite new importance with the discovery of the quantum. The quantum characterizes a whole period of a rapid periodic process, not any one moment of the period; it thus requires us to consider the period as a whole, and in some sense reverses what has hitherto been the trend of physical laws, namely to proceed away from integrals towards differentials. It will be remembered that the quantum principle, as enunciated by Wilson and Sommerfeld, states: Given a periodic or quasi-periodic process, the kinetic energy of which has been expressed by means of "separated" co-ordinates, if is any one of these co-ordinates and is the kinetic energy, then where the integration is to extend over one complete period of , and is a small integer which is the quantum number associated with . This law is essentially concerned with a whole period, and thus makes periodicity fundamental in physics in quite a new way. Before going further, it will be well to consider how far periodicity retains this importance in the newer quantum mechanics inaugurated by Heisenberg. For this purpose, we may concentrate attention upon the one fundamental equation involving h in the new system. This equation takes the form:[70] [Pg 344] where and are matrices, being a Hamiltonian co-ordinate in the new sense, and the corresponding "impulse," also in the new sense; while is the unit matrix. This equation is asserted to hold for all motions, not only for such as are periodic. But in the case of motions which are not periodic, it gives a result which approximates to that of classical mechanics. Thus it remains the case that the new mechanics is only necessitated by periodic motions, although it is technically possible to find a quantum principle which is also applicable to non-periodic motions. Hence the importance of periodicity remains intact from an empirical point of view, though somewhat diminished from the point of view of a statement of fundamental laws. In any case, it remains sufficiently important to demand a separate discussion. Traditionally, periodicity in physics was a question of motion: a body described the same path in space over and over again. With the coming of relativity, it has become necessary to modify this account somewhat. In space-time, every point has a date, and cannot be occupied twice; neither the earth nor an electron can describe again the orbit it described on a former occasion. And periodicity will be relative to a given system of co-ordinates: if, in one system, a co-ordinate runs through a given range of values repeatedly, and always in equal times, it may happen that, in another system, even if there is an oscillating co-ordinate, its periods are not all equal. A change of axes may even take away all trace of periodic character from a process. Since, however, the quantum principle compels us to treat periodicity as physically important, it would seem that we must regard it as a character belonging to a process when referred to axes which move with it, since this would overcome the difficulties connected with relativity. If, in certain cases, this method is not open to us, some other must be found which equally avoids these difficulties. But