The Analysis of Matter

process disintegrates the helium nucleus, and because of the loss of mass involved. (If the mass of the helium atom is taken as 4, that of a hydrogen atom is not 1, but 1·008.) This latter argument depends upon considerations connected with relativity, and must therefore be discussed at a later stage. Various suggestions have been made as to the way in which the protons and electrons are arranged in the helium nucleus, but none, so far, has yielded the necessary stability. What we may call the geometry of nuclei is therefore still unknown. It may be that, at the very small distances involved, the law of force is not the inverse square, although this law is found perfectly satisfactory in dealing with the motions of the planetary electron in the two cases in which the mathematics is feasible. This, however, is merely a speculation; for the present we must be content with ignorance as regards the arrangement of protons and electrons in nuclei other than that of hydrogen (which contains no electron in the nucleus). So long as an atom remains in a state of steady motion, it gives no evidence of its existence to the outside world. A material system displays its existence to outsiders by radiating or absorbing energy, and in no other way; and an atom does not absorb or part with energy except when it undergoes sudden revolutionary changes of the sort considered by the theory of quanta. This is of importance from our point of view, since[Pg 27] it shows that no empirical evidence can decide between two theories of the atom which yield the same result as regards the interchanges of energy between the atom and the surrounding medium. It may be that the whole Rutherford-Bohr theory is too concrete and pictorial; the analogy with the solar system may be much less close than it is represented as being. A theory which accounts for all the known facts is not thereby shown to be true, this would require a proof that no other theory would do the same. Such a proof is very seldom possible; certainly it is not possible in the case of the structure of the atom. What may be taken as firm ground is the numerical part of the theory. Certain quantities, and certain whole numbers, are clearly involved; but it would be rash to say that such and such an interpretation of these quantities and whole numbers is the only one possible. It is proper and right to use a pictorial theory as a help in investigation; but what can count as definite knowledge is something much more abstract. And it is quite possible that the truth does not lend itself to pictorial statement, but only to expression in mathematical formulæ. This, as we shall see, is the view taken by what we may call the Heisenberg theory. It may be worth while to linger a moment over this question of the nature of our read knowledge concerning atoms. In the last analysis, all our knowledge of matter is derived from perceptions, which are themselves causally dependent upon effects on our body. In sight, for example, we depend upon light-waves which impinge upon the eye. Given the waves, we shall have the visual perception, assuming no defect in the eye. Therefore nothing in visual perception alone can enable us to distinguish between two theories which give the same result as regards the light-waves which reach human eyes. This, as stated, seems to introduce psychological considerations. But we may put the matter in a way that makes its physical significance clearer. Consider an oval surface, which is liable[Pg 28] to continuous motion and change of shape, but persists throughout time; and let us suppose that no human being has ever been inside this surface. In illustration, we might take a sphere surrounding the sun, or a little box surrounding an electron which never forms part of a human body. Energy will cross this surface, sometimes inward, sometimes outward. Two views which lead to the same results as to the flow of energy across the boundary are empirically indistinguishable, since everything that we know independently of physical theory lies outside the surface. We may enlarge our oval surface until its "inside" consists of everything outside the body of the physicist concerned—to wit, ourselves. What we hear, and what we read in books, comes to us entirely through a flow of energy across the boundary of our body. It may well be maintained that our direct knowledge is less than this statement would imply, but it is certainly not greater. Two universes which give the same results for the flow of energy across the boundary of A's body will be totally indistinguishable for A. My object in bringing up these considerations is partly to give a new turn to the argument about solipsism. As a rule, solipsism is taken as a form of idealism—namely, the view that nothing exists except my mind and my mental events. I think, however, that it would be just as rational, or just as irrational, to say that nothing exists outside my body, or that nothing exists outside a certain closed surface which includes my body. Neither of these is the general form of the argument. The general form is that first given above—namely, that, given any region not containing myself, two physical theories which give the same boundary conditions all over this region are empirically indistinguishable. Electrons and protons, in particular, are only known by their effects elsewhere, and so long as these effects are unchanged we may alter our views of electrons and protons as much as we please without making a difference in anything verifiable. The question of the validity of the inference to things outside ourselves is logically quite distinct from the question whether the stuff of the world is mental, material, or neutral. I might be a solipsist, and hold at the same time that I am my body; I might, conversely, allow inferences to things other than myself, but maintain that these things were minds or mental events. In physics, the question is not that of solipsism, but the much more definite question: Given the physical conditions at the bounding surface of some volume, without any direct knowledge of the interior, how much can we legitimately infer as to what happens in the interior? Is there good ground for supposing that we can infer as much as physicists usually assume? Or can we perhaps infer much less than is generally supposed? I do not propose as yet to attempt an answer to this question; I have raised it at this stage in order to suggest a doubt as to the completeness of our knowledge concerning the structure of the atom. FOOTNOTES: [6] Professors F. Paneth and K. Peters claim to have transformed hydrogen into helium. If this claim is substantiated, it disposes definitively of the possibility that the helium nucleus is an independent unit. See Nature, October 9, 1926, p. 526. [Pg 30] CHAPTER IV THE THEORY OF QUANTA THE atomicity of matter is a hypothesis as old as the Greeks, and in no way repugnant to our mental habits. The theory that matter is composed of electrons and protons is beautiful through its successful simplicity, but is not difficult to imagine or believe. It is otherwise with the form of atomicity introduced by the theory of quanta. This might possibly not have surprised Pythagoras, but it would most certainly have astonished every later man of science, as it has astonished those of our own day. It is necessary to understand the general principles of the theory before attempting a modern philosophy of matter; but unfortunately there are still unsolved physical problems connected with it, which make it improbable that a satisfactory philosophy of the subject can yet be constructed. Nevertheless, we must do what we can. As everyone knows, the quantum was first introduced by Planck in 1900 in his study of black-body radiation. Planck showed that, when we consider the vibrations which constitute the heat in a body, these are not distributed among all possible values according to the usual law of frequency which governs chance distributions, but on the contrary are tied down by a certain law. If is the energy of a vibration, and its frequency, then there is a certain constant ,[7] known as Planck's constant, such that is or , or , or some other small integral multiple of h. Vibrations with other amounts of energy do not occur. No reason is known for their non-occurrence, which remains so far of the nature of a brute[Pg 31] fact. At first, it was an isolated fact. But now Planck's constant has been found to be involved in various other kinds of phenomena; in fact, wherever observation is sufficiently minute to make it possible to discover whether it is involved or not. A second field for the quantum theory was found in the photo-electric effect. This effect is described as follows by Jeans:[8] "The general features of the phenomenon are well known. For some time it has been known that the incidence of high-frequency light on to the surface of a negatively charged conductor tended to precipitate a discharge, while Hertz showed that the incidence of the light on an uncharged conductor resulted in its acquiring a positive charge. These phenomena have been shown quite conclusively to depend on the emission of electrons from the surface of the metal, the electrons being set free in some way by the incidence of the light. "In any particular experiment, the velocities with which individual electrons leave the metal have all values from zero up to a certain maximum velocity , which depends on the conditions of the particular experiment. No electron is found to leave the metal with a velocity greater than this maximum . It seems probable that in any one experiment all the electrons are initially shot off with the same velocity , but that those which come from a small distance below the surface lose part of their velocity in fighting their way out to the surface. "Leaving out of account such disturbing influences as films of impurities on the metallic surface, it appears to be a general law that the maximum velocity depends only on the nature of the metal and on the frequency of the incident light. It does not depend on the intensity of the light, and within the range of temperature within which experiments are possible it does not depend on the temperature of the metal.... For a given metal this maximum velocity increases regularly as the frequency of the light is increased, but there is a certain frequency below which no emission takes place at all." [Pg 32] The explanation of this phenomenon in terms of the quantum was first given by Einstein[9] in 1905. When light of frequency falls on the conductor, it is found that the amount of energy absorbed by an electron which the light separates from its atom is about five-sixths of , where is Planck's constant. It may be supposed that the other one-sixth is absorbed by the atom, so that atom and electron together absorb exactly one quantum . When the light is of such low frequency that is not enough to liberate an electron, the photo-electric effect does not take place. Explanations not involving the quantum have been attempted, but none seem able to account for the data. Another field in which the quantum hypothesis has been found necessary is the specific heat of solids at low temperatures. According to previous theories, the specific heat (at constant volume) multiplied by the atomic weight ought to have the constant value 5·95. In fact, this is found to be very approximately correct for high temperatures, but for low temperatures there is a falling off which increases as the temperature falls. The explanation of this fact offered by Debye is closely analogous to Planck's explanation of the facts of black-body radiation; and as in that case, it seems definitely impossible to obtain a satisfactory