p The title of this section cannot now appear as extravagant from the standpoint of exact science as it undoubtedly would have been in the first twenty or thirty years of this century, let alone in past centuries. The problems of the relationship between the fundamental particle and the Universe have now left the unsure philosophical ground that at one time engendered them and have become burning issues in physics and astronomy.
p The reasons for this can be found in the development of science itself. The discovery of the electron and of radioactivity created real grounds for the solving of two of the great enigmas pertaining to the problem of matter in its micro- and mega-states, namely, atomic structure and the source of solar (stellar) energy. Discovery of the quantum of action gave rise to non-classical atomism and to 223 a new understanding of the relation, internally connected with it, between the fundamental and the complex, the part and the whole, the element and the system, which was unknown to the old science, and which could not help but embrace the problems of elementary particles and problems of the Universe, so combining them in one way or another.
p Major philosophical problems began to emerge in physics (now one can speak rather of the posing of them; they are still very far from being solved) and, as always in such cases, the posing of questions of the history of philosophical thought may prove useful here, in the sense that one might be able to extract pointers to possible solutions from it, though not, of course, in a concrete form.
p When we consider the great philosophers of the past who studied problems of the Universe when there was no science as such, we can, as a matter of fact, easily find ideas in them that are in the forefront of the modern science about nature.
p An outstanding philosophical predecessor of Giordano Bruno, the dialectician Nicolas of Cusa, with his theory about the coincidence of opposites (coincidentia oppositorum) expressed the proposition that the absolute ‘minimum’ (any, even the most insignificant object) coincided with the ’absolute maximum’ (the whole world).^^30^^
p According to Leibniz, the monads that he believed to form the basis of everything were both closed and connected with the whole world, themselves representing, as he put it, ’compressed Universes’.
p And for Democritus, the great materialist of Ancient Greece, one of the founders of atomism, atoms figure not only as indivisible microscopic formations but also as whole vast worlds. In their own way they very much resemble Markov’s ‘friedmons’—the fruit of ultramodern notions about the microworld and the Universe that have grown on the soil of the general theory of relativity (we shall discuss them below).
p Let us now consider ideas relating to the theme of this section more systematically. To that end, let us return to Berestetsky’s comment about the composition of strongly interacting particles (see Section 4 above).
p Let us assume that a strongly interacting particle (a hadron) A turns (‘decays’) into a combination (becomes 224 a system) of hadrons B and C:
p A^ B + C,
p the probability of such a transformation being very close to 1. Then, in accordance with the conservation laws, the sum of the corresponding quantum numbers of hadrons B and C should coincide with the quantum numbers of hadron A; this is a necessary condition of the above transformation of hadrons.
p Another condition, of course, is the existence of a mass defect. If the defect of particle A is small, i.e. if it has enough energy for the transformation (‘decay’ into particles B and C) in fact to take place, it is said that particle A consists of particles B and C. Let us assume that particles B and C consist, in turn, of particles with still smaller mass, and that these consist of particles of even smaller mass; then how far can this process of constructing a particle of a given mass out of particles with smaller and smaller masses be continued? An answer is provided by the uncertainty relation; it turns out that there is a limit to the process beyond which the total mass of the particles forming the structure of the initial particle begins to exceed the mass of that particle.
p If, on the other hand, the mass defect of the particle A is great, i.e. its energy is not sufficient for the transformation in fact to occur, it is said that particle A is composed of particles # and C. What, however, does that statement mean?
p In this case B and C appear as virtual particles, and the particle A has virtual structure. A particle of given mass is constructed, as it were, out of particles of larger mass. How is this to be understood?
p (1) If the process of combining particles B and C is accompanied, because of energy release, by a decrease in the sum of their masses, that is evidence precisely of the formation of a system (B + C) that differs qualitatively from the simple combination of particles B and C. (2) Although, during the formation of system (B + C) the energy radiated diminishes the sum of the masses of particles B and C according to Einstein’s equation of the relation of mass and energy, only strong interactions can lead to a big release of energy and, therefore, to a big mass defect of the system (B + C). In this case particles B and C cannot really exist 225 in the structure of particle A, and do riot; they exist only virtually, in a possibility that becomes actuality in certain new conditions when particle A receives a corresponding amount of additional energy.
p Such is the necessary concretisation of the material about the concepts ‘consist’, ‘elementary’, ‘complex’, etc., that were discussed in the preceding sections.
p Let us recall from this angle that any elementary particle can be regarded as complex, and a complex fundamental particle as an elementary one: the answer depends on the existence of the appropriate conditions for the transformation of the particles (the relativity of the concepts of elementary, complex, and structure in the world of elementary particles). From the same angle it is held that hypothetical quarks have a mass exceeding that of nucleons. In general, all such assumptions are based on the idea that strong interactions are responsible for the relevant mass defect created in particle systems.
p Let us now assume that known elementary particles are ‘composed’ of quarks, and the latter, of yet heavier particles, etc.; what conclusions would such reasoning lead to? Would we have to recognise the existence of fundamental particles of infinitely large mass?
p This problem was studied by M. A. Markov, who demonstrated that there is an upper limit for the masses of fundamental particles; he used the term ‘maximon’ to denote the heaviest fundamental particles. According to Markov, maximons, which are gigantic particles (on the microworld scale), are combined in smaller particles, a new mechanism beginning to operate in this combination, namely, gravitational collapse, by which astronomic phenomena are already explained.
p Gravitational collapse (increase of a system’s spatial density through the effect of the gravitational forces between the bodies composing it), which almost instantaneously increases the energy of particle coupling, leads to an enormous mass defect, to a tremendous difference between the sum of the masses of the maximons and the mass of the particle to which they are condensed by gravitational collapse. For the collapse to begin, there has to be a colossal density of matter that does not now exist in the part of the Universe known to us. Such density could have existed when the Universe (according to Friedmann’s theory) once 226 began to expand. From the angle of the idea of maximons the beginning of the appearance of the elementary particles now known thus coincides with the beginning of expansion of the Universe, which is still going on.^^31^^
p It was not our intention to go into the details of the maximon hypothesis, especially in view of its presentation here being very sketchy. Let us simply stress that it developed on the basis of the notions and principles of modern physical theories. Problems of this sort, it seems to us, will be solved more accurately on the basis of fundamental physical theories that are more general and profound than contemporary ones, and that do not contain the contradiction between quantum and relativistic physics existing at present. We would like to stress the idea that modern physical theories pose the problem of the unity of the elementary particle and the Universe, of the ultimately simple and the ultimately complex, in a quite concrete way. Research on the relevant plane continues and will do so in the future; new truths will undoubtedly be discovered along this path, which science is still only approaching without yet knowing how close it has come to them.
p Markov’s quite recent hypothesis of ‘friedmons’ provides confirmation that this is precisely the way matters stand. Let us consider it briefly.
p According to the general theory of relativity, there could be cases when gravitational interaction would lead to a large mass defect, i.e. play the role of strong interaction in the appropriate systems. Because of the large gravitational mass defect, for example, the total mass of a closed Universe is zero; to put it differently, the mass of all the bodies of the Universe is reduced to nothing by the gravitational interaction between them.
p If, on the other hand, Friedmann’s Universe is considered as not completely closed (‘nearly’ closed), its total mass, depending on the degree of this ‘nearly’, can be arbitrarily small, in particular, it can equal to the neutron’s mass, and for the external observer its behaviour will not differ from that of an elementary particle like the neutron ( although it may contain a whole system of galaxies).
p Note the following fundamental property of such universes: if a semi-closed universe emerged with an arbitrarily large electric charge, it would prove to be unstable; it would tend to reduce its total mass (by giving rise to various 227 kinds of pairs of charged particles and decreasing its total electric charge) and so to close as fully as possible. It turns out that the system tends to a certain identical limiting system with a total electric charge of a definite value regardless of the magnitude of the initial electric charge, which can be of any size.
p It is assumed that the final value of the limiting system’s electric charge may be close to that of an elementary particle. In its final state this system is called a friedmon. Markov points out that friedmon with its amazing properties is not a figment of poetic imagination; the EinsteinMaxwell system of equations contains friedmon solutions.^^32^^
p Contemporary physical theories thus make it possible to interpret the Universe as a micro-particle, while the microparticle may contain the whole Universe. In other words, modern physics unites the opposite properties of the superlarge and ultrasmall worlds.
p For all the hypothetical nature of these propositions and arguments, especially if we remember that they take only partially the quantum character of the laws of the microworld into account and regard the laws of the theory of relativity as applicable without limit to very small distances, it is still possible, in the present state of science, to consider it proved that the gulf created by the mind between the Universe and the microworld does not really exist, and that the problems of the Universe and those of the elementary particle are closely linked with one another. Besides, let us note once more that such a unity and connection are not the result of ‘foggy’ philosophical reasoning but are referred to by such a very rigorous science as physics in the precise language of its concepts.
p In conclusion let us discuss a statement of Zelmanov’s that is closely related to our theme. According to him, three concepts of the Universe should, apparently, be distinguished in cosmology, and the following expressions used to denote them: ’the Universe in general’, ’the Universe as a whole’, ’the whole Universe’. The first of these concepts, Zelmanov says, denotes the whole irrespective of its parts, the second the whole in relation to its parts and all the parts in their relation to the whole, and the third, finally, denotes all parts irrespective of the whole. Confusing of these concepts can lead to very serious misunderstanding.^^23^^
228p What Zelmanov has written ahout the relation between the whole and the parts in application to the Universe, it seems to us, can also be applied mutatis mutandis to the elementary particle.
p lu our view one should distinguish between three concepts of the elementary particle, for which we suggest the following labels: ’the elementary particle as an elementary particle’ (this resembles Zelmanov’s first concept of the Universe); ’the elementary particle as a system’ (this resembles the second concept of the Universe); ’the elementary particle as an elementary particle and at the same time as a system’ (this is a concept of the elementary particle which means that the existence of each elementary particle leads inevitably to the existence of others—- hadrons are implied—and resembles the third concept of the Universe).
p There is thus yet another aspect of the unity between the Universe and the elementary particle, which finds expression in their concepts.
p REFERENCES
p ^^1^^ See entry Entwicklung in Philosophisches Worterbuch, edited by Georg Klaus and Manfred Buhr (Verlag Enzyklopadie, Leipzig, 1964).
p ^^2^^ V. I. Lenin, Collected Works, Vol. 38 (Progress Publishers, Moscow), pp 355-364.
p ^^3^^ Ibid., p 361.
p ^^4^^ Ibid.
p ^^5^^ V. I. Lenin. Philosophical Notebooks. Collected Works, Vol. 38, p 151.
p ^^6^^ A. I. Uyomov. Veshchi, svoistva, otnosheniya (Things, Properties, Relations) (AN SSSR, Moscow, 1963), pp 19-28.
p ^^7^^ W. RossvAshby. An Introduction to Cybernetics (Chapman & Hall, London, 1956), p 40.
p ^^8^^ V. I. Lenin. Philosophical Notebooks. Op. cit., p 222.
p ^^9^^ N. Bourbaki. The Architecture of Mathematics. The A merican Mathematical Monthly, 1950, 57, 7: 225-226.
p ^^10^^ M. V. Lomonosov. Considerations on the Solidity and Liquidity of Bodies. Polnoye sobranie sochinenii, Vol. 3 (AN SSSR, MoscowLeningrad, 1952), p 387.
p ^^11^^ I. V. Obreimov. Molecules and Crystals. In: A. N. Nesmeyanov (Ed.). Glazami uchonogo (AN SSSR, Moscow, 1963), pp 238-239.
229p ^^12^^ See S. I. Vavilov. Newton’s Atomism. Uspekhi fizicheskikh nauk, 1947, 31, i: 7-18; idem. Sobranie sochinenii, Vol. 3 (AN SSSR, Moscow, 1956), pp 714-729.
p ^^13^^ Sir Isaac Newton. Optics (Encyclopaedia Britannica, Chicago, 1952), p 541.
p ^^14^^ S. I. Vavilov. Op. cit.
p ^^15^^ See D. I. Mendeleev. Specific Volumes. Sochineniya, Vol. 1 (AN SSSR, Leningrad, 1937), p 147; idem. An Attempt to Apply a Principle of Newton’s Natural Philosophy to Chemistry. In: D. I. Mendeleev. Periodichesky zakon. Klassiki nauki (Moscow, 1958), pp 529-554.
p ^^16^^ See, for example, Filosofskie problemy sovremennogo estestvoznaniya (Philosophical Problems of Modern Science) (AN SSSR, Moscow, 1978); I. V. Kuznetsov (Ed.). Problema prichinnosti v sovremennoi fizike (The Problem of Causality in Modern Physics) (AN SSSR, Moscow, 1960).
p ^^17^^ L. D. Landau and E. M. Lifshitz. Teoriya polya (The Theory of Field) (Fizmatgiz, Moscow, 1960), pp 57-59.
p ^^18^^ See, for instance, David Bohm. Causality and Chance in Modern Physics (Routledge & Kegan Paul, London, 1957).
p ^^19^^ Ya. B. Zeldovich. Modern Physics and Astronomy. In: Voprosy kosmogonii, Vol. 9 (Nauka, Moscow, 1963), p 22.
p ^^20^^ R. Hofstadter. Die Elektronenstreuung und ihre Anwendung auf die Struktur von Kernen und Nukleonen. Physikalische Blatter, 1962, 18, 5: 206.
p ^^21^^ Immanuel Kant. Critique of Pure Reason. Translated by Meiklejohn (Wiley Book Co., New York, 1900), p 246.
p ^^22^^ Frederick Engels. Dialectics of Nature (Progress Publishers, Moscow, 1972), p 263.
p ^^23^^ V. B. Berestetsky. Dynamic Symmetries of Strongly Interacting Particles. Uspekhi fizicheskikh nauk, 1965, 85, 3: 396.
p ^^24^^ Arthur March. Die physikalische Erkenntnis und ihre Grenzen (Viewog & Sohn, Brunswick, 1955), pp 102-105.
p ^^25^^ G. F. Chew and S. C. Frautschi. Principle of Equivalence for All Strongly Interacting Particles Within the S-Matrix Framework. Phys. Rev. Letters, 1961, 7, 10: 50-53.
p ^^26^^ P. A. Schilpp (Ed.). Albert Einstein. Philosopher-Scientist (Tudor Publishing Co., New York, 1951), pp 59-61.
p ^^27^^ Hans Reichenberg. Aus der Physik der Elementarteilchen. Physikalische Blatter, 1963,19, 3: 110. This paper contains a brief account of Heisenberg’s lecture An Introduction to the Theory of Elementary Particles read at Munich University in 1961.
p ^^28^^ The following popular scientific and philosophical publications give an idea of the emergence and development of concepts associated in one way or another with the relativity of the difference between the ‘elementary’ and the ‘complex’: N. N. Bogolyuhov and M. K. Polivanov. Fields and Quanta; and I. E. Taimn. Elementary Particles (papers published in the symposium Glazami uchonogo); G. F. Chew. The Crisis in the Conception of Elementarity in 230 Physics. In the international yearbook Budushcheye nauki. No. 2 (Nauka Publishers, Moscow, 1968); V. S. Barashenkov and D. I. Blokhintsev. Lenin’s Idea of the Inexhaustibility of Matter in Modern Physics. In Lenin and Modern Natural Science (Progress Publishers, Moscow, 1978); M. E. Omelyanovsky. The Problem of the Elementarily of Particles in Quantum Physics. In: Filosofskie problemy fiziki elementarnykh chastits (Mysl, Moscow, 1963); idem. The Problem of the Elementary and the Complex in the Physics of the Microworld. Voprosy filosofii, 1965, 10.
p ^^29^^ Pravda, 13 August 1972.
p ^^30^^ Nicolas of Cusa. Oeuvres choisies (Editions Montaigne, Aubier, 1942), p 70. It should be recalled that he had a deity in mind both embracing the whole world and existing in every object.
p ^^31^^ On maximons see M. A. Markov. Was 1st oder was hedeutet das? Maximonen. Physikalische Blatter, 1969, 25, 8: 361-362.
p ^^32^^ M. A. Markov. On the Concept of Primordial Matter. Voprosy filosofii, 1970, 4.
^^33^^ A. L. Zelmanov. On the Formulation of the Cosmological Problem. Trudy vtorogo s’ ezda Vsesoyuznogo astronomo-geodezicheskogo obshchestva (AN SSSR, Moscow, 1960), pp 82-83.
Notes