p The infinite sequence of levels of matter, as Engels pointed out, is ’various nodal points which determine the various qualitative modes of existence of matter in general’.^^22^^ From this standpoint matter is not just elementary particles and their combinations and is also not just substance that does not consist of elementary particles; matter in general has simultaneously the properties of both the elementary and the compound or complex.

p There are grounds in classical physics for abstracting the unity of the elementary and the complex and considering them in isolation from one another (and this understanding is confirmed by experiment). In quantum physics the situation is fundamentally different, the reason being that the further physics penetrates into the heart of matter the more strongly its theory is bound to be affected by discovery of the reciprocal transformability of all elementary particles. In modern atomistics the concept ’transformation of the one into the other’ has come to the fore, to the plane on which the problem of elementarity and complexity is posed and solved in a way quite different from that in classical atomistics (in which transformation is understood in the final analysis as ’the combination and dissociation of certain constant particles’).

p The concepts of the elementary and the complex, as applied to elementary particles, have lost their abstract opposition to one another and so their literal meaning. Elementary particles are not elementary in the classical sense; they resemble but are not classical complex systems. The properties of the elementary and the complex are united in them, i.e. an elementary particle is simultaneously both an elementary entity and a system.

p The concept ’to consist of has accordingly also changed its meaning as regards elementary particles. It had already undergone a certain metamorphosis in nuclear physics. In the statement ’an atomic nucleus consists of neutrons and protons’, the concept ’consists of has a meaning rather different from that in the statement ’a molecule of water consists of oxygen and hydrogen atoms’; the neutron and proton are considered as two states of the same particle, the nucleon, while it is quite a different matter with oxygen and hydrogen atoms.

p The change in the concept ’consists of is especially striking as regards resonances. A lambda (1520)-particle can decay into a sigma-particle (2) and a pion (n), or into a neutron (N) and a kaon (x ), or finally, into a lambdaparticle (A) and two pions (n); but that does not mean that the lambda (1520)-particle literally ’consists of the particles into which it ‘decays’.

p These examples emphasise that ‘elementarity’ and ’ complexity’ are not inherent in the interacting elementary particles by themselves, irrespective of the conditions in which their transformations occur, but in their intrinsic link with these conditions.

p For a particle involved in an interaction to decay, certain conservation laws have to be observed, which in this case operate as the conditions of the possibility of decay. In strong interactions, for example, only those decays can occur the initial and final particles of which have identical values of all the quantum numbers conserved. For the possibility of decay to become actual, the initial particle must have total energy (rest energy plus kinetic energy) at least equal to the sum of the total energies of the particles into which it should decay, i.e. the law of the conservation of energy must be observed.

p The above may be illustrated in a certain sense by the set of experimental data from which it was possible to infer 217 the existence of the omega-hyperon (Q ). A high energy kaon colliding with a proton produces an omega-hyperon (Q ), and two kaons (a K⁺-meson and a ^T -meson); then the omega-hyperon decays into a pion (jt "-meson) and a xi- hyperon (S°); the last decays into two gamma-quanta and a lambda-hyperon (A°), which in turn decays into a proton and a pion (n-meson).

p In this reaction the kaon and the omega-, lambda- and xi-hyperons (Q , A°, S°) behave as compound systems only because the total energy of each of them is sufficient for them to decay into the corresponding particles without violating certain conservation laws. In other reactions the total energy of one or more of these particles may not satisfy this requirement; the corresponding particles are then no longer compound formations.

p An interacting particle thus cannot be regarded as elementary or complex without mentioning the total energies of all the particles involved in the reaction. In that sense the concepts of ‘elementary’ and ‘complex’ are relative as regards elementary particles.

p This understanding of elementarity has nothing in common with its understanding in the sense of pure relativity. ’Purely relative elementarity’ is unimaginable without a supplementary statement that the object by itself is complex. From the point of view developed here the situation, as we have seen, is quite different. The relativity of the ‘elementarity’ and ‘complexity’ of elementary particles is similar to the relativity of size of a body and duration of a process in Einstein’s theory, or the relativity of particle and wave characteristics in quantum mechanics, in spite of the different content of these ‘relativities’. Without relativity in this sense, it would be impossible to employ classical concepts with the necessary refinement to describe those phenomena of nature that do not fit into, or cannot, in general, be made to fit into classical theories.

p In conclusion, let us consider the notion of structure in elementary-particles physics. If a fundamental particle can be complex, it can consequently have a structure. And as the concept of the ‘complex’ has no ‘classical’ meaning as regards elementary particles, the concept of ‘structure’ should not be identical in relation to elementary particles to the classical understanding of structure. Since Hofstadter’s experimental proof of the structure of a nucleon, the 218 existence of structure in elementary particles has ceased to be a matter of debate anfl has become an object of research in modern physics.

p The concept of structure is inseparable from those of set and element, i.e. from the concept of discontinuity. As materialist dialectics has demonstrated, however, the concept of discontinuity is one with its opposite, continuity, i.e. the opposition between these concepts is not absolute, as metaphysical philosophy considers. On this fundamental question quantum theory has followed the path of dialectics: in quantum mechanics the corpuscular concept (pertaining to discontinuity) and the wave concept (pertaining to continuity) are considered in their internal connection. Niels Bohr developed this interpretation of quantum mechanics most fully; it has been developed further in quantum field theory.

p The specific quantum concepts of virtual process, virtual state, and virtual particle also have a direct bearing on the problem of the structure of elementary particles.

p On this plane Berestetsky’s remarks on the composition of strongly interacting particles are of great interest. He distinguishes between the concepts ‘consists’ and ’composed of. If, for example, it is said that ’the nucleus consists of nucleons’ it is implied (1) that a nucleus with quantum numbers A and Z can be formed of Z protons and A-Z neutrons and (2) that its mass defect is small. There are systems, however, for which the first proposition is true and the second is not. In that case, according to Berestetsky, we should say ’may be composed of or ’is composed of instead of ‘consists’; for instance, non-strange mesons are composed of nucleons and anti-nucleons.^^23^^

p In this scheme the particles of which a system is composed are virtual. For them the law of the conservation of energy, it is said, does not hold or rather it is meaningless to apply the law of conservation of energy to them. From this angle elementary particles constitute a part of other elementary particles not in their real form but in a virtual state; in other words, elementary particles have virtual structure.

p The concept of a particle’s virtual structure was developed in quantum theory quite long ago. Underlying it is the idea that an interacting particle is the source of a field whose quanta transfer interaction. In an interaction particles 219 exchange virtual quanta of the field; a nucleon, for example, with a baryon charge produces and absorbs virtual n-mesons, quanta of the nuclear field.

p It can be shown that the probability of two or more it-mesons being produced at the same time in strong interaction is quite big. As a result, the nucleon proves to be on average (in time) in an atmosphere consisting of virtual it-mesons. This atmosphere of virtual mesons (which has certain dimensions) cannot be separated from the nucleon, and from this angle it must be said that the latter has a jt- meson structure.

p A nucleon is a source of ^T-mesons or kaons, in addition to n-mesons or pions. The corresponding argument leads to the conclusion that a nucleon engenders kaons when hyperons are formed. It is also possible for a nucleon to engender virtual nucleon-antinucleon pairs. They, too, contribute to the general virtual structure of a nucleon.

p Thus, a nucleon has virtual structure as a consequence of its interaction with other elementary particles. Virtual processes occur within it: the nucleon spends part of the time in the state of a nucleon with pions, part of the time in the state of a hyperon with kaons, and part of the time in the state of a nucleon with nucleon-antinucleon pairs. The superposition of sets of virtual particles of different kinds (various virtual structures) also gives the nucleon’s general structure that can be observed in the experiment.

p The structure of the nucleon was first observed in Hofstadter’s experiments on the scattering of fast electrons by protons. Its structure becomes real after being virtual through the transfer of energy to it by the moving electrons. It has been demonstrated in experiments that the proton scatters electrons as if its charge were distributed in space and not as if it were a charged point particle.

p Hofstadter’s experiments, in particular, left no stone standing of March’s philosophical construction, by which an elementary particle is quite without structure so that, therefore, the concepts of extension and shape are inapplicable to it. March said that there was no experiment that would resolve whether an elementary particle was point-like or had extension, since all the relevant data were based on hypotheses. Analysis of these hypotheses led March to infer that the application of conventional spatial concepts to elementary particles resulted in contradictions; the way 220 out of these contradictions March saw in the thesis that modern physics excludes the concept of matter.^^24^^

p Hofstadter’s experiments were the experiments whose possibility March had denied. They showed that the elementary particles do possess structure but that this structure is not the ‘classical’ structure of normal bodies.

p In the light of these ideas about the structure of elementary particles, the ‘bootstrap’ hypothesis put forward by Chew and Frautschi is of great philosophical interest.^^25^^ According to this hypothesis every strongly interacting particle helps create other particles which in turn form the particle itself.

p Chew and Frautschi’s hypothesis, according to which no single particle can exist without the existence of other particles interacting with it, is interesting philosophically in that it puts forward the idea of freeing fundamental theory of purely empirical quantities not related to its postulates, and tries to connect these quantities with the postulates of the theory and so explain them and understand the necessity of their existence. In short, this hypothesis has a resemblance to the ideal of a perfect physical theory, in which, as Einstein thought, there would be no purely empirical constants and all the physical constants would admit of theoretical definition and follow from a theoretical principle reflecting the harmony of the universe.^^26^^

p Modern atomistics thus does not at all require the diversity of known particles to be reduced to a few elementary entities or, on the contrary, elementary entities to be excluded in general from scientific use. Elementary particles, which form the deepest level of matter at present known, unite the properties of the discontinuous (particles) and the continuous (fields). The number of the various types of particles is unlimited; at the same time they are one; this feature of the level of elementary particles distinguishes it from the higher levels of matter, in the consideration of which the intrinsic unity of the discontinuous and continuous can be abstracted in certain conditions.

p Heisenberg held the view that ’there is no difference in principle between "elementary" and "non-elementary" microparticles’.^^27^^ From everything said above about the elementarily of particles it is clear where one can agree with Heisenberg and where one cannot. There is a difference between the ‘elementary’ and the ‘non-elementary’ in the world 221 of elementary particles but it is relative in nature and not absolute (as in the sphere of macroscopic phenomena).

p As noted above in Section 2, classical atomism linked the fact that there is a constancy in the development of nature (sameness of its forms; recurrence of its phenomena; repetitions) with its basic propositions (in particular, with that about the finite diversity of types of elementary entities). From that angle there could be no constancy in nature if the number of types of elementary particles were infinite.

p This line of reasoning of classical atomism, however, has no justification in the light of the modern data on elementary particles. The latter are transformed into one another in accordance with certain laws of conservation (which do not permit arbitrary reactions between elementary particles). It is on these conservation laws, which at the same time are laws of the transformation of elementary particles, that constancy in nature rests (and also the relativity of this constancy).

p In conclusion we would like to draw attention to the following. The concept of the relativity of the difference between the ‘elementary’ and the ‘complex’ or, say, the radical alteration of the classical concept ’to consist of, etc. (discussed above), from being a kind of a regulative idea, has now become an idea of action leading the theory of elementary particles to new advances.^^28^^ This can be seen from the work of Soviet scientists, in which dispersion relations for the photoproduction of mesons were first formulated and demonstrated (in terms of the fundamental principles of quantum field theory). The physical characteristics of the processes of photoproduction of pions were linked with those of the strong interaction of pions and nucleons, and reliable quantitative results were obtained for photoproduction processes in a quite wide energy range.

p This work was discussed in an article in Pravda by N. Bogolyubov and Bruno Pontecorvo (members of the USSR Academy of Sciences), ’A Major Contribution to Particle Physics’. It is of interest to note that, analysing the presentday development of the physics of elementary particles, they wrote: ’The old naive conceptions about matter’s being divisible into parts and the very concept "consists of" thus prove to be inconsistent.’^^29^^

In summing up this section we would like once more 222 to stress that the concepts of discontinuity and continuity, possibility and actuality, and the infinite and the finite are becoming closely interwoven within the problem of the elementarily and structure of matter in contemporary physics. Physics, which reflects eternally developing nature, has followed the path of materialist dialectics in solving this problem. New perspectives in understanding the structure of matter are also being opened up on this path. Modern quantum field theory is full of difficulties and paradoxes. It was not possible to unite the various types of interaction, and the particles involved in them, on its basis, although physicists have not given up looking for approaches to a solution. Modern physics is also far from linking the world of cosmic dimensions and the atomic and subatomic world up into a single theory. The problems emerging, one must suppose, will necessitate new physical principles and basic concepts, and that will lead to deeper knowledge of the structure of matter. The idea of the inexhaustibility of the electron expressed by Lenin long before discovery of the abundance of the elementary particles and of the laws of the microworld is also stimulating the development of physical theory today.