p Physics, like its mother, philosophy, has always striven, but in its own ways, to penetrate the most fundamental laws of nature. Its founders, Galileo and Newton, and the physicists of the classical period who continued and developed Newton’s main ideas, assumed that-science had cognised the laws underlying the universe. Lagrange aptly expressed this typical feature of classical physics when he called Newton the happiest of mortals since he had discovered great truths which, Lagrange considered, could only be discovered once.

p Had classical physics, however, comprehended the most fundamental laws of nature? The development of twentieth century physics has given an answer to that question which does not agree at all, of course, with Lagrange’s view: fundamental laws of nature in the sense that this was understood by the creators of classical physics, were not discovered by classical science and its understanding of the structure of matter, nor by all the developed versions of the system of principles of classical mechanics, nor by classical field theory, nor by Lorentz’s theory of electrons.

p The problem of studying the laws of nature that underlie all the physical phenomena now known is resolved by quantum theory. It emerged and developed on a broad empirical foundation; that is its strength and the guarantee that its principles and concepts are not in the least a priori constructions, in spite of their being far removed from the ‘visualisable’ ideas and theories of classical physics.

p Even in its historically first forms (Bohr’s atomic model, modern quantum mechanics), quantum theory successfully resolved many of the problems that confounded classical science (though by no means in the ‘classical’ spirit). When chemistry was establishing itself as a science, for instance, the concept of a chemical element (with its smallest part, the atom) and the law of the conservation of mass linked chemical phenomena into a single chain. But is there a connection between chemical elements? This question, which is very important for the theory of the structure of matter, came to the fore in the nineteenth century when a great many elements were discovered.

p Mendeleev’s periodic law linked all chemical elements together; it received deeper substantiation, however, in the nuclear model of the atom, by which it was possible to explain exactly why chemical elements (resp. ati ms) are the elementary structural units in chemistry, and to understand that chemical properties are associated with electron shells and are determined by the electrical charge of the atomic nucleus.

p The nuclear model of the atom in the original form in which it was proposed by Rutherford served in physics rather as a scout than as an established theory: the atom, regarded as a classical electromagnetic system, could riot exist as a stable material formation. The stability of atoms (preserving the nuclear model) was explained in terms of quantum laws (Niels Bohr). The principles of quantum theory as applied to the forces of electrical origin that connected atoms also made it possible to explain the various connections between atoms and the formation of molecules and crystals. Thanks to quantum theory, chemistry became an exact science in the full sense of the term; at the same time it became clear (and no longer simply on the basis of general considerations) that chemical laws cannot be reduced to mechanical ones, as was assumed by nineteenth century scientists.

p On the other hand, the classical approach to the relationship between matter and field remained to some extent unaltered in chemistry, or rather in the theory of the structure of matter transformed in accordance with quantum laws. From the angle of quantum mechanics, fields still remained ‘classical’ but the behaviour of particles acquired features of wave motion which created an affinity between matter and field.

p This last circumstance found reflection in quantum mechanics’ understanding of structure. On the one hand, quantum mechanics radically revised the concept of physical system (structure) as a system of particles capable of strict localisation and connected by forces, the behaviour of which was governed by the principle of Laplacian determinism. On the other hand, quantum mechanics preserved the classical separation of matter and field, and accordingly the kinds and number of elementary particles were regarded as invariable.

p Quantum mechanics, it is true, following the theory of 211 relativity introduced a new element (compared with classical mechanics) into the question of the extension of fundamental particles. Whereas fundamental particles could be regarded as absolutely solid bodies according to classical mechanics, from the standpoint of the theory of relativity there are no such bodies, and elementary particles therefore had to be regarded as points. Although quantum mechanics has altered the situation, it too approaches the problem of the extension of fundamental particles in accordance with the principles of the theory of relativity.^^17^^

p New possibilities of solving this problem have been given by the latest development of quantum theory and experiment (this point will be discussed below; here we would note once more that, according to quantum mechanics, elementary particles are stable formations whose number and type are invariable during their interaction).

p The problem of the elementarity of particles in quantum physics was radically altered with the development of quantum field theory (which, like quantum mechanics, originated from Planck’s quantum hypothesis). This branch of quantum physics combines the ideas of quantum mechanics and the theory of relativity and in essence is a relativistic quantum theory of elementary particles. In its general form quantum field theory is still far from complete; it has already, however, reached a most important position, the experimental conclusions from which are now well known, and the philosophical implications of which can hardly be exaggerated.

p Quantum field theory considers elementary particles from the angle of their emergence and disappearance and of their reciprocal transformations in accordance with certain principles (conservation laws). It contains no statement about invariance of the number of interacting particles. Fundamental particles are produced and annihilated during interaction with each other. In other words, modern atomism which has grown on the soil of quantum physics, is something new in principle compared with the atomistics of classical science.

p The ideas and methods of quantum electrodynamics, i.e. the quantum theory of electromagnetic field, led quite a long time ago to the discovery of anti-particles and mesons. Hyperons were detected for the first time in cosmic rays. The establishing of various types of interaction between 212 elementary particles during their transformations (strong, electromagnetic, weak), and the discovery of certain symmetries and conservation laws that govern the scattering, creation, annihilation, and reciprocal transformation of particles were of great significance.

p Research in the field of high energy physics has added new knowledge and posed new problems in the theory of elementary particles. Without going into an analysis of the many points relating to this, let us consider those that are directly concerned with our theme.

p Not so long ago (1960) about 30 particles were known (among them, the electron, proton, neutrino, and photon were classed as stable;’the rest were unstable). Now, since the discovery of groups of so-called resonances (particles with an extremely short half-life, even in terms of nuclear time), the number of known types of elementary particles considerably exceeds 100, and physicists suggest that this is not the limit. New, unexpected properties of strong interactions have been discovered, and the new data on weak interactions may possibly lead to a radical change in physical notions about the symmetry of space and time that once seemed unshakable. The concept of the structure of an elementary particle is becoming more and more important, with a content unusual from the standpoint of classical theory; physics is now more and more departing from the notion of a point particle.

p One of the most significant problems posed by all these discoveries and others is that of elementarily. How do matters stand with the elementarity of the particles that are usually called elementary, if there are so many of them? Are they indeed elementary? Is their number finite? What is the relationship between the elementary and the complex (if there is one) in the world of fundamental particles? Is the posing of the question of structure to be preserved in this world in the form in which it was expressed before the theory of elementary particles?

p In pre-quantum physics the problem of the elementarity of particles was solved, of course, in the following way: matter consisted at bottom of stable, indivisible particles capable of quite accurate localisation in space and time, which formed the structure of the more complex forms of matter. This idea was realised to some extent in chemistry: Prout’s hypothesis that chemical elements consisted of 213 hydrogen is realised in one way or another, only the role of hydrogen is being played by the charge of the atomic nucleus, which determines the number of electrons in the atomic shell, and the element’s place in Mendeleev’s periodic system. It must be remembered, however, that the atom as a system (its structure and properties) is governed by quantum laws: the parameters of the simplest atoms are calculated by means of quantum mechanics, while those of complex atoms are calculated by approximate methods.

p The problem of elementarity has arisen again in connection with the discovery by modern physics of a great number of elementary particles and their various types of interaction and a whole set of diverse quantum properties. Can it be solved as was acceptable before the discovery of elementary particles? Or are new approaches needed? In order to clarify the situation, we must allow for its being impossible, for instance, to consider stable particles that do not decay without an external influence (the group includes, as was noted above, the proton, electron, photon, and neutrino) as truly elementary and to regard all the remaining elementary particles (metastable ones and resonances), which decay spontaneously, as compound. Thus, a neutron does not consist of a proton, an electron and an anti- neutrino, although in its free state it decays into these three particles.

p It would seem reasonable to reduce the problem of elementarity to the existence of a certain sequence in the levels of matter in which each of them is an ‘elementary’ stage for the next higher level and a ‘compound’ stage for the preceding deeper level. This idea of the hierarchy of elementarity found one of its embodiments, in particular, in the Newtonian conception of matter as a system of particles of a mounting degree of complexity; it also finds expression, to a certain extent, in the contemporary understanding of the structure of matter (the level of elementary particles— the level of atomic nuclei and atoms—the molecular level, the series being continued toward the macroscopic world and, in the opinion of some authors, toward the microscopic world).^^18^^

p Will the idea of a hierarchical system really serve as the key to solve the problem of elementarity in modern physics?

p Assume that the sequence of levels begins from the ’ elementary’ side. Then matter will be represented as an ordered 214 set of elementary particles and systems (particles) of various degrees of complexity that consists ultimately of these same elementary particles. Thus, we face a version of classical atomistics. The scheme of the Japanese physicist Sakata, which consists of three fundamental particles, namely, the proton, the neutron, and the lambda-hyperon (together with their anti-particles), from which all strongly interacting particles are constructed, can serve as a novel expression of this version among contemporary conceptions of elementary particles.^^19^^ We must, however, remember (1) that in Sakata’s scheme it is not so much, in fact, a matter of three particle-bricks as of the three laws of the conservation of the electric charge, of the baryon charge, and of strangeness being valid in the processes of strong interaction; and (2) that the choice of the three main particles is not unambiguous—they may be xi-hyperons (S- ) and (S-°) or lambda-hyperons (A). These peculiar features of Sakata’s scheme diverge from classical atomistics.

p More recently other physicists have returned again to the notion of three fundamental particles, having altered and refined Sakata’s scheme. It has been established that the quantum numbers of these particles (known as ‘quarks’) have to be represented by fractions. Only experiment, of course, can settle the matter of the existence of quarks. Yet another scheme has been suggested, according to which all particles are constructed of four fundamental particles.

p Now let us assume that the sequence of the levels of matter is infinite (i.e. has no beginning) from the ’ elementary’ side, this infinity representing a constantly recurring transition from the compound to the elementary and vice versa. According to this assumption, the ‘elementarily’ of objects is only relative, and the objects themselves are something compound (complex). We arrive at the idea that there are no ‘elementary’ objects as such, i.e. that matter does not consist of elementary particles.

p Many physicists today hold this view of matter in one way or another. Hofstadter, for instance, who discovered the structure of the nucleon, suggests that ’the search for ever smaller and more fundamental particles will go on so long as man is thirsty for knowledge’.^^20^^

p In their logical essence the remarks above on the elementary and the compound resemble Kant’s second 215 antinomy: there exists nothing that is not either itself simple, or composed of simple parts (thesis); in general there does not exist in the world any simple substance (antithesis).²¹ From his argumentation Kant drew agnostic conclusions. A dialectical critique (Hegel, Marxist philosophy) corrected his argument and resolved his antinomies.

Dialectical principles, it seems to us, make it possible to outline an approach to the problem of elementarily that excludes both the concept of purely relative elementarity and the point of view of classical atomism. This approach (matters relating to it will be analysed in the next section) wholly corresponds, in our view, to the trends of development of the physics of elementary particles.