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p Causality or a causal relation, as noted above, is an objectively real genetic connection between (at least) two events or phenomena occurring in different places. If it has been determined that, in such and such conditions, event A is the cause and event B is the effect, it is concluded that event B occurred after event A. In classical mechanics it is assumed that the changes in a system produced by an external factor may (but not necessarily because of longrange forces) form a causal chain. If one allows for the fact that a causal relation is by necessity a connection in time, then this thesis about causality is expressed in the form known in physics: namely, a signal cannot be transmitted to the past but only to the future. The laws of classical mechanics, however, since they describe reversible mechanical processes, do not contain any statement about causality pertaining to the signal. This statement is an addition to the laws of classical mechanics, which by themselves do not determine the direction of time.

p The situation is quite different in the theory of relativity and in quantum mechanics, which accept the thesis about causality in the sense above but with a new element that is essential to the theory of relativity, namely, that in it the velocity of light in a vacuum is the limiting velocity of a signal.

p The separation of events into those consecutive in time and the quasi-simultaneous, which is closely related to causality, follows as a consequence of the existence of a limiting velocity in the theory of relativity. As it turns out, if two events are connected with each other by a causal relation, only then is their sequence absolute, i.e. the temporal sequence of these two events is preserved in all inertial reference frames. As to quasi-simultaneous events, i.e. 190 events that cannot be connected through interaction, their sequence is relative, i.e. it depends on the frame of reference. The well-known philosophical dictum ’post hoc can never justify propter hoc^^1^^ is thus given a novel and clear expression by the theory of relativity.

p In this connection Einstein’s remark about events connected by a signal with a velocity greater than that of light (W > c, where W is the velocity of propagation of a certain signal, and c is the velocity of light) and the time T necessary for transfer of the signal from A to B, presents interest. Einstein wrote: ’The velocity v [i.e. the velocity of the observer—M.O.] can assume any value less than c. If, therefore, W > c, as we have assumed, v can always be so selected that T <; 0. This result means that we must take a transmission mechanism as possible by which the effect obtained precedes the cause. If this result also does not, in my view, contain any contradiction, taken purely logically, it still contradicts the character of our whole experience to such an extent that the impossibility of the assumption W > c seems adequately proved thereby. ’^^49^^

p The question of causality in quantum field theory, it seems to us, should be considered from a rather different plane than in pre-quantum physics and (non-relativistic) quantum mechanics.

p With the so-called axiomatic approach to the construction of quantum local field theory, the latter adopts the principle of relativistic invariance and the unitariness and locality principles (let alone certain other requirements that we ignore). Quantum fields are associated with elementary particles, and the process of interaction between (very high energy) elementary particles is described by the socalled scattering matrix, which is an operator translating the wave function (state) of particles before the reaction (scattering) into their state after the reaction.

p In descriptions employing the scattering matrix, it is important to remember (and this is the source of the new approach to causality in quantum field theory compared with classical physics) that the point consists not in elucidating the behaviour of particles when they are brought very close together but in the problem of the final ( postreaction) states, and the probabilities of their arising.

p From this point of view the concept in the theory of high energy particle interaction (only now being constructed) 191 of details of behaviour of particles when the distances between them are small does not make sense (is unobservable in principle).^^60^^

p The assumption that this concept is unobservable in principle opens up certain perspectives for non-local quantum field theory (this theory has developed in its initial form soon after physics came up against the paradoxes of the divergencies inherent in modern quantum theory with its postulate of the localisation of field interaction). In ’ normal’ quantum theory, in fact, the postulate of an interaction’s localisation is borrowed from the classical theory of point particles. It requires that field interactions pertain to one and the same point of space-time. This requirement accords with the theory of relativity, which rejects an assumption about the dimensions and structure of elementary particles because it has to be supposed otherwise that a signal can be propagated at a velocity greater than that of light, and therefore (as was noted above) to assume that the effect-event could precede the cause-event.

p It is thus impossible to separate the postulate of an interaction’s localisation from the thesis of causality that the cause-event cannot follow the effect-event.

p Non-local quantum field theory was intended to rid modern quantum physics of difficulties with divergencies. It abandons the postulate of locality of field interaction and tries to do so in various ways; consequently more than one variant of non-local theory is being developed. We shall not dwell on these variants or forms or on the difficulties of non-local theory (it now appears that the last are not so fundamental).^^61^^ We are interested in the philosophical essence of the theory: is it true that there is nothing left of the principle of causality in it, and that it leads to a need to reject the space and time concepts as applied to the world of elementary particles, as some authors assert? Or rather, how do things stand with the principle of causality and with space and time at that level of matter known as the elementary particle?

p Let us recall that, from the standpoint of materialist dialectics, causality is only a tiny part of the objectively real universal connection. Lenin gave a very positive estimate of the fact that Hegel had paid comparatively little attention to the theme of causality so dear to Kant’s followers. For Hegel as a dialectician, Lenin wrote, ’causality 192 is only one of the determinations of universal connection, which he had already covered earlier, in his entire exposition, much more deeply and all-sidedly; always and from the very outset emphasising this connection, the reciprocal transitions, etc.’^^52^^ It is on this plane that the problems posed in regard to non-local theory incorporate something unusual.

p This theory, first of all, should satisfy the possibility of meeting the condition of macroscopic causality, i.e. it should not lead to experimentally observable consequenceo disagreeing with the statement of causality on the macroscopic (including atomic) scales of space and time. This means, in essence, that when non-local theory is generalised for the large scales of space and time it turns into ‘conventional’ local quantum theory (in accordance with the correspondence principle).

p A new universal constant appears in non-local theory, that of the dimension of length (or elementary length), which ‘separates’ (as it were) the domain of ultra-small dimensions in which causality is ‘violated’ and perhaps a radical revision of physical notions about space and time is called for, from the space-time domain in which the principle of causality and the laws of geometry hold. A specific constant for high energy physics is thus added to the universal constants c and h on which quantum field theory is based; it links (or should link) short-range and long-range interactions into something united.

p The introduction of elementary length,  [192•*  with certain assumptions, puts the question of revising geometry in its usual form on a physical basis; metric space-time geometry ceases to exist; the concepts ‘nearer’ and ’more remote’, ‘before’ and ‘after’, ‘length’ and ‘duration’ lose their macroscopic meaning in the ultra-small. The separation of phenomena into cause-events and effect-events should, of course, 193 also become invalid, and the theory’s mathematical apparatus should reflect this situation.

p Does this mean that the philosophical foundation of non-local quantum field theory contains a certain idealist and fideist line on causality? The answer to that question becomes quite clear as soon as we consider how materialist dialectics understands the causal relation.

p In its usual interpretation the causal relation does not exhaust the forms of connection and mutual dependence. The present-day development of quantum physics is leading to the discovery of new forms of connection and mutual dependence between the phenomena of inanimate nature which cannot be fitted into the schemes of existing physical theories. This once more confirms, in particular, the objective nature of the universal connection, its inexhaustibility, the transformation of some of its forms into others that are deeper and more general. Causality, as it is usually understood, may have no meaning in the ultra-small; in this domain a deeper, more general form of connection—- interaction—comes into prominence in conditions of mutual transformation according to certain laws of the fundamental particles of matter. It appears, however, not as a constant change of cause and effect but as their foundation and the whole generating them.

p In abstract reasoning one is not forbidden, of course, to regard interaction as cause^^83^^; in this case, however, we are not dealing with cause as it is conventionally understood. The latter is an individual cause which acts at an individual moment of time and at individual location, i.e. such form of connection which was called causa efficiens (efficient cause) in the old philosophical systems. But interaction as a cause is not a causa efficiens but rather, to use the old philosophical concepts, causa finalis (final cause); Spinoza’s well-known dictum substantia est causa sui is concerned with ’final cause’.

p There is no reason, however, to pour the wine of modern science into old philosophical bottles. It was Engels who noted that ’already in Hegel the antithesis of causa efficiens and causa finalis is sublated in reciprocal action’.^^54^^

p In the world of the large (including atomic dimensions) the abstraction of individual phenomena taken out of their universal connection and consequently considered separately (with respect to space and time) is internally justified; as 194 We Can see from what has been said, the principle of causality implies the legitimacy of this abstraction. In the ultra-small world, however, or the world of high energy elementary particles interacting with and transforming into one another, such abstraction loses its meaning and the thesis of causality in its usual understanding is also deprived of confidence and status.

p Experiment undoubtedly has the last word in clarifying these points, which are very important for high energy physics; at the same time one must not neglect the fact that objectively applied, comprehensive, universal flexibility of concepts is of great importance in the quest for their correct solution.^BB Strictly speaking, it is experiment also that confirms that the flexibility of concepts has been objectively applied, i.e. is a correct reflection of the eternal evolution of the world.

p The development of quantum physics and theory of elementary particles is opening up new forms of the universal connection, that are not covered by the schemes of existing physical theories. The points discussed above reflect the round of ideas of the transition from one form of connection and reciprocal dependence to another that is deeper and more general. On that plane the work of Tamm, Bogolyubov, and Blokhintsev devoted to space-time and causal relations in the microworld, various aspects of which have been discussed in this chapter, present special interest from the angle of dialectics.^^68^^ Modern physics is providing remarkable confirmation of Lenin’s words: ’From coexistence to causality and from one form of connection and reciprocal dependence to another, deeper and more general.’^^67^^

p REFERENCES

p  ^^1^^ See, for example, Hans Reichenbach. Philosophic Foundations of Quantum Mechanics (Univ. of Gal. Press, Berkeley and Los Angeles, 1965).

p  ^^2^^ Werner Heisenberg. The Development of the Interpretation of the Quantum Theory. In: W. Pauli (Ed.). Niels Bohr and the Development of Physics (Pergamon Press, London, 1955), pp 26-28.

p  ^^3^^ Werner Heisenberg. Das Naturbild der heutigen Physik (Rowohlt, Hamburg, 1955), p 25.

p  ^^4^^ See, fer instance, Werner Heisenberg. Die Plancksche Entdeckung und philosophischen Grundfragen der Atomlehre. Naturwissenschaften, 1958, 45, 10: 230.

p 5 Hans Reiehenbaeh. Op. cit., p 1. • Ibid., p 4.

195

p 7 P. W. Bridgman. Reflections of a Physicist (Philosophical Library
New York, 1955), p 225.  ^^8^^ Ibid., p 215.

p  ^^8^^ Henry Margenau. The Nature of Physical Reality (McGraw-Hill, New York, 1950), p 96.

p  ^^10^^ Ibid., p 421.

p  ^^11^^ Ibid., p 422.

p  ^^12^^ Max Born. Statistical Interpretation of Quantum Mechanics. Phys-

p ics in my Generation (Pergamon Press, London, 1956), p 186.

p  ^^13^^ Max Born. Op. cit., p 97.

p  ^^14^^ V. I. Lenin. Philosophical Notebooks. Collected Works (Progress Publishers, Moscow), Vol. 38, p 160.

p  ^^15^^ Frederick Engels. Dialectics of Nature (Progress Publishers, Moscow, 1972), p 243.

p  ^^16^^ Arthur March. Das neue Denken der modernen Physik (Rowohlt, Hamburg, 1957), p 122.

p  ^^17^^ Arthur March. Die physikalische Erkenntnis und ihre Grenzen (Vieweg, Brunswick, 1955), p 36.

p  ^^18^^ Werner Heisenberg. Das Naturbild der heutigen Physik, p 25.

p  ^^19^^ Ibid., p 25.

p  ^^20^^ Leon Brillouin. Scientific Uncertainty and Information (Academic Press, New York, 1964), p 69.

p  ^^21^^ Ibid.

p  ^^22^^ Arthur March. Die physikalische Erkenntnis und ihre Grenzen, p 33.

p  ^^23^^ Ibid., p 34.

p  ^^24^^ Ibid., p 35.  ^^26^^ Ibid., p 37.

p  ^^26^^ Paul Langevin. La Notion de corpuscules et d’atomes (Hermann et C^ie, Paris, 1934), p 35.

p  ^^27^^ V. A. Fock. Comments on Bohr’s Article About His Discussions with Einstein. Uspekhi fizicheskikh nauk, 1958, 66, 4: 601.

p  ^^28^^ Ya. P. Terletsky. Dinamicheskie i statisticheskie zakony fiziki ( Dynamic and Statistical Laws of Physics) (Moscow, 1950), p 93.

p  ^^20^^ Karl Marx. Difference Between the Democritean and Epicurean Philosophy of Nature (Doctoral Dissertation). In: Karl Marx and Frederick Engels. Collected Works, Vol. 1 (Progress Publishers, Moscow, 1975), pp 46-53.

p  ^^30^^ Plutarch, Reply to Colotes, 1111. See also Diogenes Laertius. De clarorum philosophorum, vitis, dogmatibus et apophthegmatlbus libri decem, Book X, 4. Cited by Karl Marx. Op. cit., p 39.

p  ^^31^^ Max Born. Op. cit., pp 164-170.

p  ^^32^^ Werner Heisenberg. Art cit., p 230.

p  ^^33^^ M. V. Lomonosov. The Theory of Air Pressure. Polnoye sobranie sochinenii, Vol. 2 (AN SSSR, Moscow, 1951), p 111.

p  ^^34^^ Max Born. Op. cit., p. 168.  ^^36^^ Ibid., pp 166-167.

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p  ^^36^^ D. I. Blokhintsev. Osnovy kvantovoi mekhaniki (Fundamentals of Quantum Mechanics) (Nauka Publishers, Moscow, 1963), pp 590- 591.

p  ^^37^^ L. I. Mandelstam. Lectures on the Fundamentals oi Quantum Mechanics. Polnoye sobranie sochinenii, Vol. 5 (AN SSSR, Moscow, 1950), pp 358-359.

p  ^^38^^ Werner Heisenberg. Die Plancksche Entdeckung und die philosophischen Probleme der Atomphysik. Universitas, 1959, 14, 2: 135- 149.

p  ^^39^^ Werner Heisenberg. Das Naturbild der heutigen Physik, p 28. « Ibid., p 29.

p « Ibid., p 30.

p ^4a Niels Bohr. Essays 1958-1962 on Atomic Physics and Human Knowledge (N. Y., London, Interscience Publ., 1963), p 6.

p 43 \verner Heisenberg. The Development of the Interpretation of the Quantum Theory. In: W. Pauli (Ed.). Op. cit., pp 12-14.

p  ^^44^^ See Uspekhi fizicheskikh nauk, 1957, 62, 4.

p  ^^46^^ See Hegel’s Science of Logic. Translated by W. H. Johnston and L. G. Struthers (Allen & Unwin, London, 1929), Vol. 2, pp 173-174.

p  ^^46^^ David Bohm. Causality and Chance in Modern Physics (Routledge & Kegan Paul, London, 1957). (The page numbers in the text refer to this book.)

p  ^^47^^ P. A. M. Dirac. The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1958), p 9.

p  ^^48^^ N. N. Bogolyubov, D. V. Shirkov. Vvedenie v teoriyu kvantovykh polei (Introduction to the Theory of Quantum Fields) ( Gostekhizdat, Moscow, 1957), p 143.

p  ^^49^^ Albert Einstein. Uber das Relativitatsprinzip und die aus demselben gezogenen Folgerungen. In: Jahrbuch der Radioaktivitat und Elektronik, Vol. IV (1907) (S. Hirzel Verlag, Leipzig, 1908), p 424.

p  ^^60^^ I. E. Tamm. Elementary Particles. In: A. N. Nesmeyanov (Ed.). Glazami uchonogo (AN SSSR, Moscow, 1963), pp 187-188.

p  ^^61^^ D. A. Kirzhnits. Non-local Quantum Field Theory. Uspekhi fizicheskikh nauk, 1966, 90, i.

p  ^^62^^ V. I. Lenin. Op. cit., p 162.

p  ^^53^^ G. A. Svechnikov. Causality and the Relation of States in Physics (Progress Publishers, Moscow, 1971).

p  ^^64^^ Frederick Engels. Dialectics of Nature, p 243.

p ?^^5^^ On the dialectical requirement of flexibility of concepts, see V. I. Lenin. Op. cit., p 222.

p  ^^56^^ In addition to the works already referred to, see also: V. S. Barashenkov, D. I. Blokhintsev. Lenin’s Idea of the Inexhaustibility of Matter in Modern Physics. In: Lenin and Modern Natural Science (Progress Publishers, Moscow, 1978); D. I. Blokhintsev. Prostranstvo i vremya v mikromire (Space and Time in the Microworld) (Nauka, Moscow, 1970).

^^57^^ V. I. Lenin. Op. cit., p 222.