PART II
THE PHYSICAL WORLD
In all that we have said hitherto on the subject of man from without, we have taken a common-sense view of the material world. We have not asked ourselves: What is matter? Is there such a thing, or is the outside world composed of stuff of a different kind? And what light does a correct theory of the physical world throw upon the process of perception? These are questions which we must attempt to answer in the following chapters. And in doing so the science upon which we must depend is physics. Modern physics, however, is very abstract, and by no means easy to explain in simple language. I shall do my best, but the reader must not blame me too severely if, here and there, he finds some slight difficulty or obscurity. The physical world, both through the theory of relativity and through the most recent doctrines as to the structure of the atom, has become very different from the world of every day life, and also from that of scientific materialism of the eigthteenth-century variety. No philosophy can ignore the revolutionary changes in our physical ideas that the men of science have found necessary; indeed it may be said that all traditional philosophies have to be discarded, and we have to start afresh with as little respect as possible for the systems of the past. Our age has penetrated more deeply into the nature of things than any earlier age, and it would be a false modesty to over-estimate what can still be learned from the metaphysicians of the seventeenth, eighteenth and nineteenth centuries.
What physics has to say about matter, and the physical world generally, from the standpoint of the philosopher, comes under two main heads: first, the structure of the atom; secondly, the theory of relativity. The former was, until recently, the less revolutionary philosophically, though the more revolutionary in physics. Until 1925, theories of the structure of the atom were based upon the old conception of matter as indestructible substance, although this was already regarded as no more than a convenience. Now, owing chiefly to two German physicists, Heisenberg and Schrödinger, the last vestiges of the old solid atom have melted away, and matter has become as ghostly as anything in a spiritualist séance. But before tackling these newer views, it is necessary to understand the much simpler theory which they have displaced. This theory does not, except here and there, take account of the new doctrines on fundamentals that have been introduced by Einstein, and it is much easier to understand than relativity. It explains so much of the facts that, whatever may happen, it must remain a stepping-stone to a complete theory of the structure of the atom; indeed, the newer theories have grown directly out of it, and could hardly have arisen in any other way. We must therefore spend a little time in giving a bare out line, which is the less to be regretted as the theory is in itself fascinating.
The theory that matter consists of "atoms", i.e. of little bits that cannot be divided, is due to the Greeks, but with them it was only a speculation. The evidence for what is called the atomic theory was derived from chemistry, and the theory itself, in its nineteenth-century form, was mainly due to Dalton. It was found that there were a number of "elements", and that other substances were compounds of these elements. Compound substances were found to be composed of "molecules", each molecule being composed of "atoms" of one substance combined with "atoms" of another or of the same. A molecule of water consists of two atoms of hydrogen and one atom of oxygen; they can be separated by electrolysis. It was supposed, until radio-activity was discovered, that atoms were indestructible and unchangeable. Substances which were not compounds were called "elements". The Russian chemist Mendeléev discovered that the elements can be arranged in a series by means of progressive changes in their properties; in his time, there were gaps in this series, but most of them have since been filled by the discovery of new elements. If all the gaps were filled, there would be 92 elements; actually, the number known is 87, or, including three about which there is still some doubt, 90. The place of an element in this series is called its "atomic number". Hydrogen is the first, and has the atomic number 1; helium is the second, and has the atomic number 2; uranium is the last, and has the atomic number 92. Perhaps in the stars there are elements with higher atomic numbers, but so far none have been actually observed.
The discovery of radio-activity necessitated new views as to "atoms". It was found that an atom of one radio- active element can break up into an atom of another element and an atom of helium, and that there is also another way in which it can change. It was found also that there can be different elements having the same place in the series; these are called "isotopes". For example, when radium disintegrates it gives rise, in the end, to a kind of lead, but this is somewhat different from the lead found in lead-mines. A great many "elements" have been shown by Dr. F. W. Aston to be really mixtures of isotopes, which can be sorted out by ingenious methods. All this, but more especially the transmutation of elements in radio-activity, led to the conclusion that what had been called "atoms" were really complex structures, which could change into atoms of a different sort by losing a part. After various attempts to imagine the structure of an atom, physicists were led to accept the view of Sir Ernest Rutherford, which was further developed by Niels Bohr.
In this theory, which, in spite of recent developments, remains substantially correct, all matter is composed of two sorts of units, electrons and protons. All electrons are exactly alike, and all protons are exactly alike. All protons carry a certain amount of positive electricity, and all electrons carry an equal amount of negative electricity. But the mass of a proton is about 1835 times that of an electron: it takes 1835 electrons to weigh as much as one proton. Protons repel each other, and electrons repel each other, but an electron and a proton attract each other. Every atom is a structure consisting of electrons and protons. The hydrogen atom, which is the simplest, consists of one proton with one electron going round it as a planet goes round the sun. The electron may be lost, and the proton left alone; the atom is then positively electrified. But when it has its electron, it is, as a whole, electrically neutral, since the positive electricity of the proton is exactly balanced by the negative electricity of the electron.
The second element, helium, has already a much more complicated structure. It has a nucleus, consisting of four protons and two electrons very close together, and in its normal state it has two planetary electrons going round the nucleus. But it may lose either or both of these, and it is then positively electrified.
All the later elements consist, like helium, of a nucleus composed of protons and electrons, and a number of planetary electrons going round the nucleus. There are more protons than electrons in the nucleus, but the excess is balanced by the planetary electrons when the atom is unelectrified. The number of protons in the nucleus gives the "atomic weight" of the element: the excess of protons over electrons in the nucleus gives the "atomic number", which is also the number of planetary electrons when the atom is unelectrified. Uranium, the last element, has 238 protons and 146 electrons in the nucleus, and when unelectrified it has 92 planetary electrons. The arrangement of the planetary electrons in atoms other than hydrogen is not accurately known, but it is clear that, in some sense, they form different rings, those in the outer rings being more easily lost than those nearer the nucleus.
I come now to what Bohr added to the theory of atoms as developed by Rutherford. This was a most curious discovery, introducing, in a new field, a certain type of discontinuity which was already known to be exhibited by some other natural processes. No adage had seemed more respectable in philosophy than "natura non facit saltum", Nature makes no jumps. But if there is one thing more than another that the experience of a long life has taught me, it is that Latin tags always express falsehoods; and so it has proved in this case. Apparently Nature does make jumps, not only now and then, but whenever a body emits light, as well as on certain other occasions. The German physicist Planck was the first to demonstrate the necessity of jumps. He was considering how bodies radiate heat when they are warmer than their surroundings. Heat, as has long been known, consists of vibrations, which are distinguished by their "frequency", i.e. by the number of vibrations per second. Planck showed that, for vibrations having a given frequency, not all amounts of energy are possible, but only those having to the frequency a ratio which is a certain quantity h multiplied by 1 or 2 or 3 or some other whole number, in practice always a small whole number. The quantity h is known as "Planck's constant"; it has turned out to be involved practically everywhere where measurement is delicate enough to know whether it is involved or not. It is such a small quantity that, except where measurement can reach a very high degree of accuracy, the departure from continuity is not appreciable.[1]
Bohr's great discovery was that this same quantity h is involved in the orbits of the planetary electrons in atoms, and that it limits the possible orbits in ways for which nothing in Newtonian dynamics had prepared us, and for which, so far, there is nothing in relativity-dynamics to account. According to Newtonian principles, an electron ought to be able to go round the nucleus in any circle with the nucleus in the centre, or in any ellipse with the nucleus in a focus; among possible orbits, it would select one or another according to its direction and velocity. But in fact only certain out of all these orbits occur. Those that occur are among those that are possible on Newtonian principles, but are only an infinitesimal selection from among these. It will simplify the explanation if we confine ourselves, as Bohr did at first, to circular orbits; moreover we will consider only the hydrogen atom, which has one planetary electron and a nucleus consisting of one proton. To define the circular orbits that are found to be possible, we proceed as follows: multiply the mass of the electron by the circumference of its orbit, and this again by the velocity of the electron; the result will always be h or 2h, or 3h, or some other small exact multiple of h, where h, as before, is "Planck's constant". There is thus a smallest possible orbit, in which the above product is h; the radius of the next orbit, in which the above product is 2h, will have a length four times this minimum; the next, nine times; the next, sixteen times; and so on through the "square numbers" (i.e. those got by multiplying a number by itself). Apparently no other circular orbits than these are possible in the hydrogen atom. Elliptic orbits are possible, and these again introduce exact multiples of h; but we need not, for our purposes, concern ourselves with them.
When a hydrogen atom is left to itself, if the electron is in the minimum orbit it will continue to rotate in that orbit so long as nothing from outside disturbs it; but if the electron is in any of the larger possible orbits, it may sooner or later jump suddenly to a smaller orbit, either the minimum or one of the intermediate possible orbits. So long as the electron does not change its orbit, the atom does not radiate energy, but when the electron jumps to a smaller orbit, the atom loses energy, which is radiated out in the form of a light-wave. This light-wave is always such that its energy divided by its frequency is exactly h. The atom may absorb energy from without, and it does so by the electron jumping to a larger orbit. It may then afterwards, when the external source of energy is removed, jump back to the smaller orbit; this is the cause of fluorescence, since, in doing so, the atom gives out energy in the form of light.
The same principles, with greater mathematical complications, apply to the other elements. There is, however, with some of the latest elements, a phenomenon which cannot have any analogue in hydrogen, and that is radio-activity. When an atom is radio-active, it emits rays of three kinds, called respectively α-rays, β-rays, and γ-rays. Of these, the γ-rays are analogous to light, but of much higher frequencies, or shorter wave-lengths; we need not further concern ourselves with them. The α-rays and β-rays, on the contrary, are important as our chief source of knowledge concerning the nuclei of atoms. It is found that the α-rays consist of helium nuclei, while the β-rays consist of electrons. Both come out of the nucleus, since the atom after radio-activity disruption is a different element from what it was before. But no one knows just why the nucleus disintegrates when it does, nor why, in a piece of radium, for example, some atoms break down while others do not.
The three principal sources of our knowledge concerning atoms have been the light they emit, X-rays, and radio-activity. As everyone knows, when the light emitted by a glowing gas is passed through a prism, it is found to consist of well-defined lines of different colours, which are characteristic for each element, and constitute what is called its "spectrum". The spectrum extends beyond the range of visible light, both into the infra-red and into the ultra-violet. In the latter direction, it extends right into the region of X-rays, which are only ultra-ultra-violet light. By means of crystals, it has been found possible to study X-ray spectra as exactly as those of ordinary light. The great merit of Bohr's theory was that it explained why elements have the spectra they do have, which had, before, been a complete mystery. In the cases of hydrogen and positively electrified helium, the explanation, particularly as extended by the German physicist Sommerfeld, gave the most minute numerical agreement between theory and observation; in other cases, mathematical difficulties made this completeness impossible, but there was every reason to think that the same principles were adequate. This was the main reason for accepting Bohr's theory; and certainly it was a very strong one. It was found that visible light enabled us to study the outer rings of planetary electrons, X-rays enabled us to study the inner rings, and radio-activity enabled us to study the nucleus. For the latter purpose, there are also other methods, more particularly Rutherford's "bombardment", which aims at breaking up nuclei by firing projectiles at them, and sometimes succeeds in making a hit in spite of the smallness of the target.
The theory of atomic structure that has just been out lined, like everything in theoretical physics, is capable of expression in mathematical formulæ; but like many things in theoretical physics, it is also capable of expression in the form of an imaginative picture. But here, as always, it is necessary to distinguish sharply between the mathematical symbols and the pictorial words. The symbols are pretty sure to be right, or nearly so; the imaginative picture, on the other hand, should not be taken too seriously. When we consider the nature of the evidence upon which the above theory of the atom is based, we can see that the attempt to make a picture of what goes on has led us to be far more concrete than we have any right to be. If we want to assert only what we have good reason to believe, we shall have to abandon the attempt to be concrete about what goes on in the atom, and say merely something like this: An atom with its electrons is a system characterised by certain integers, all small, and all capable of changing independently. These integers are the multiples of h involved. When any of them changes to a smaller integer, energy of a definite amount is emitted, and its frequency will be obtained by dividing the energy by h. When any of the integers concerned changes to a larger integer, energy is absorbed, and again the amount absorbed is definite. But we cannot know what goes on when the atom is neither absorbing nor radiating energy, since then it has no effects in surrounding regions; consequently all evidence as to atoms is as to their changes, not as to their steady states.
The point is not that the facts do not fit with the hypothesis of the atom as a planetary system. There are, it is true, certain difficulties which afford empirical grounds for the newer theory which has superseded Bohr's, and which we shall shortly consider. But even if no such grounds existed, it would be obvious that Bohr's theory states more than we have a right to infer from what we can observe. Of theories that state so much, there must be an infinite number that are compatible with what is known, and it is only what all of these have in common that we are really entitled to assert. Suppose your knowledge of Great Britain were entirely confined to observing the people and goods that enter and leave the ports; you could, in that case, invent many theories as to the interior of Great Britain, all of which would agree with all known facts. This is an exact analogy. If you delimit in the physical universe any region, large or small, not containing a scientific observer, all scientific observers will have exactly the same experiences whatever happens inside this region, provided it does not affect the flow of energy across the boundary of the region. And so, if the region contains one atom, any two theories which give the same results as to the energy that the atom radiates or absorbs are empirically indistinguishable, and there can be no reason except simplicity for preferring one of them to the other. On this ground, even if on no other, prudence compels us to seek a more abstract theory of the atom than that which we owe to Rutherford and Bohr.
The newer theory has been put forward mainly by two physicists already mentioned, Heisenberg and Schrödinger, in forms which look different, but are in fact mathematically equivalent. It is as yet an impossible task to describe this theory in simple language, but something can be said to show its philosophical bearing. Broadly speaking, it de scribes the atom by means of the radiations that come out of it. In Bohr's theory, the planetary electrons are supposed to describe orbits over and over again while the atom is not radiating; in the newer theory, we say nothing at all as to what happens at these times. The aim is to confine the theory to what is empirically verifiable, namely radiations; as to what there is where the radiations come from, we cannot tell, and it is scientifically unnecessary to speculate. The theory requires modifications in our conception of space, of a sort not yet quite clear. It also has the consequence that we cannot identify an electron at one time with an electron at another, if, in the interval, the atom has radiated energy. The electron ceases altogether to have the properties of a "thing" as conceived by common sense; it is merely a region from which energy may radiate.
On the subject of discontinuity, there is disagreement between Schrödinger and other physicists. Most of them maintain that quantum changes—i.e. the changes that occur in an atom when it radiates or absorbs energy—must be discontinuous. Schrödinger thinks otherwise. This is a matter in debate among experts, as to which it would be rash to venture an opinion. Probably it will be decided one way or other before very long.
The main point for the philosopher in the modern theory is the disappearance of matter as a "thing". It has been replaced by emanations from a locality—the sort of influences that characterise haunted rooms in ghost stories. As we shall see in the next chapter, the theory of relativity leads to a similar destruction of the solidity of matter, by a different line of argument. All sorts of events happen in the physical world, but tables and chairs, the sun and moon, and even our daily bread, have become pale abstractions, mere laws exhibited in the successions of events which radiate from certain regions.
- ↑ The dimensions of h are those of "action", i.e. energy multiplied by time, or moment of momentum, or mass multiplied by length multiplied by velocity. Its magnitude is about 6.55 × 10-34 erg secs.