Mathematical Matter

MATHEMATICAL MATTER J. K. RoBERTSON I T HE nature of the -ultimate structure of matter underlies most of the questions with which physics, or indeed any branch of natural· science, has to deal. Neither the geologist with his rocks and fossils, nor· the chemist with his compounds, nor the botanist with his plants can get away from matter. Life itself is associated with matter, and even such intangible entities as light and electricity do not manifest themselves except through matter. It is not surprising,_therefore, that from times which almost antedate history, natural philosophers have sought to interpret, in terms of a few common constituents, all the various forms of matter. In this search philosophers were early led to the view that matter is discontinuous, is coarse-grained in structure, a vie\v which culminated in the atomic theory of the nineteenth century. According to th1s theory, as it was held by such famous physicists as_ Maxwell, atoms, ·uncuttable and indivisible, were "the foundation stones of the universe." They were the bricks with which Nature constructs her infinitely varied types of architectur~. A. piece of stone, a flower, man himself are but a collection of atoms. A few substances, ·some ninety-two in number, are built up entirely of the same kind of atoms. They are called elements. The vast majority of substances, however, are compounds, that is, they are combinations of two or more elements. 'The smallest part of a compound, called a molecule, except in rare cases, is a union of only a few atoms. A molecule of common salt, for example, con56 MATHEMATICAL MATTER tains on~ atom of the element sodium and one of the element chlorine. So small are molecules that in a piece of salt the size of a small pin-head, there are a few thousand million million million of them. With such a background the physicist of the nineteenth century had enormous success in exp]aining the natural phenomena which occur in the physical world. The pressure of a gas was shown to be nothing but the bombardment of the walls of the containing vessel by moving molecules; heat was but molecular motion. No man had ever seen an atom, for it was beyond the power of the most powerful microscope, but it was as real to the nineteenth -century professor of physics as the individual grains of sand on the sea-shore. Toward the end of that c·entury a radical change took place in the physicist's conception of the atom. Indeed, etymologically it ceased to be an atom at all, for it was·shown that it had structure, that ·there were sub-atomic particles. As a result of researches dealing with the passage of electricity- through gases, unmistakable evidence was provided of the existence of electrons, negatively charged particles so small that the mass of each is only about one two-thousandth of that of the atom of hydrogen , the lightest known substance. For the first time a materia prima· was found, because the electron proved to be a common constituent of all atoms. About the same time the discovery of radioactivity provided additional evidence that the atom has structure. Certain - elements have the remarkable property of spontaneously and continuously shooting off three kinds of rays: (I) alpha rays, positively charged particles four times as heavy. as the hydrogen atom; (2) beta rays, negatively charged particles w.Q.ich are just high-speed electrons; and (3) gamma rays, an invisible kind of light very similar to 57 THE UNIVERSITY OF TORONTO QUARTERLY X-rays. Investigations in this field, notably by Lord Rutherford, showed that the emission of these rays is the result of an atomic explosion in the cou.11se of which an atom of one element changes into another, and led to a "picture'' of the atom which in its essential features is accepted to-day. The Rutherford atom, as it is sometimes called, consists of a positively charged core or nucleus accounting for practically the whole ·mass of the atom, surrounded by one or more electrons whose n. egative charge just neutralizes the positive 'charge on the core. In the case of ·hydrogen, there is but one electron...