130

p The experimental data about corpuscular and wave properties of micro-objects (particle tracks in a cloud chamber and the diffraction of particles, e.g. electrons or molecules) 131 are beyond doubt and are not rejected by any physicist. But how can these data—the particle-wave duality— be interpreted in a theory? This point is by no means trivial, because classical physics considers corpuscular and wave theoretical constructions as mutually exclusive. On the philosophical plane, the question of the ontological status of ‘waves’ and ‘particles’ arises first of all: does objective reality correspond to the experimental data on the micro-objects, which we denote by words classed as ’ particles’ and ‘waves’? Is Philipp Frank, say, right when he states that ’the “electron” is a set of physical quantities which we introduce to state a system of principles from which we can logically derive the pointer readings on the instruments of measurement’?^^10^^

p One can speak of a certain analogy between Zeno’s paradoxes relating to motion and the particle-wave duality. In the first case the point is not so much the sensual certainty of the motion, of whether there is motion, as how to express it in the logic of concepts.^^11^^ In the second case one also has in mind the need to understand the empirical certainty of corpuscular and wave properties of the microobjects because the certainty alone is not enough. The corresponding problems in the two cases are solved by dialectics; the cases differ, however, as regards the nature of the dialectical unities that emerge. In the case of motion (mechanical displacement) the latter does not directly lead to the idea of contradictoriness, and even now one cannot help feeling amazed at the virtuosity of Zeno’s dialectical mind (a virtuosity not yet conscious in many modern scientists),¹² when he, so to say, ’divided the single into two’. In the case of particle-wave duality, on the contrary, the ‘split’ is usual and it is the empirical fact of electron diffraction that causes surprise, or visual experiments with light of low intensities, which mean that the particle and wave aspects merge together.

p How can the mutually contradictory particle and wave aspects be combined? More than one approach to a solution of this problem is possible.

p Attempts used to be made to treat the wave phenomenon as one in a medium formed of particles. J. J. Thomson’s theory, according to which ’the electron behaves as if it were within an atmosphere containing charges of electricity’, can serve as an example.^^13^^ Such a theory, in which 132 only the particle is ascribed fundamental meaning and the waves are represented as something derivative, is being reborn in modern physics in one form or another.

p When quantum mechanics was being created Schrodinger tried to interpret particles as ’wave packets’. This interpretation did not agree with the facts (it can be shown that ’wave packets’ should ‘spread’ in the course of time, which does not happen to micro-particles); in addition it came up against insuperable difficulties when it had to explain the interaction between two ’wave packets, in physical, three-dimensional space.

p Of late theories are being offered (David Bohm and others) that treat particles and waves as equally fundamental aspects of matter, emphasising primarily the idea of the joint existence of corpuscular and wave properties of moving objects in a certain classical type of model. This model preserves the classical concept of a trajectory, and in essence eliminates the symmetry between particles and waves that is inherent in quantum theory.

p Those interpretations and other like them are typically based on the application of certain classical concepts and schemes to phenomena of atomic scale. In this way the classical concepts and schemes are understood in the corresponding conceptions as invariable and absolute. On the methodological plane, this feature is the main source of weakness of these conceptions: in the last resort they ‘explain’ post factum results that have already been obtained on the basis of Bohr’s conception which rests on non-classical principles. Let us turn now to a point of view on the unifying of the particle and wave aspects that differs in principle from those noted above.

p Bohr called the method of unifying the corpuscular and wave aspects based on the idea of transferring the concept of wave from classical optics to particle mechanics an irrationality. Although the attacks on his conception of unifying the corpuscular and wave points of view, and on his use of the term irrationality in this case not only still continue but have also become unjustifiably bitter,^^14^^ one must nevertheless agree with Bohr about the essence of the matter. The method of unifying the particle and wave aspects in quantum mechanics resembles to some extent the introduction of irrational and imaginary numbers into mathematics, or the concept of the interval into the theory 133 of relativity. One cannot get far in analysing issues related to such unification on the basis of any system of formal logic. Dialectical logic, which may appear, and actually seems irrational to the metaphysical mind, but which is in fact beyond reproach on the plane both of formal logic and of its own dialectics, appears on the scene.

p In each of the ‘rational’ approaches noted above a segment of the line of cognition that reflects the state of things as it is is stressed in a one-sided way. Materialist dialectics, on the contrary, excludes one-sided cognition. It provides everything necessary and sufficient to clarify whether the supposedly absolutely incompatible particle and wave pictures of the behaviour of the micro-objects have objective meaning.

p Matter, i.e. substance and field, is not, on the whole, particles or waves in the sense of classical theories, or unification of the two in a certain macroscopic (classical) model. Particle and wave properties are united in their opposition. In other words, matter simultaneously has the properties of particles and waves, but only in the sense that the motion of micro-objects can only approximately be regarded as translation of particles and propagation of waves. When the limiting cases are taken into account, micro-objects behave approximately like waves in some experimental conditions, and approximately like particles in others. The so-called relativity with respect to the means of observation (which realise the conditions in which the mutually exclusive properties of the micro-objects are manifested) is a typical feature of the description in quantum theory that follows from acceptance of the dual particlewave nature of micro-objects.

p These ideas have been developed in their clearest and most systematic form by scientists who are conscious adherents of dialectical materialism.^^16^^ Idealist and metaphysical views primarily influenced a certain interpretation of the problem of uniting the particle and wave pictures of the behaviour of micro-objects, viz. by denying the objectively real nature of the unity of the particle and wave properties of matter at its atomic level and by subjectivising relativity to the means of observation. This interpretation is expressed most clearly in the idea of the uncontrollability in principle of the interaction between the microscopic object and the means of observation.

134

p ’Uncontrollability in principle’, in the proper sense of the term, contains no truth, because processes and phenomena in nature are in principle cognisable, and, therefore, in principle controllable. Among the physicists who used this term, however, it frequently had no definite meaning and played the role of a kind of notation for the fact that quantum laws are qualitatively different from the laws of classical mechanics. The opponents of materialism, however, used this philosophically mistaken term in a subjectivist manner.

p The concept has disappeared from the scientific literature of late, especially in the works of those physicists who oppose the principles of positivism in science (i.e. not only those scientists who are the conscious adherents of dialectical materialism). Niels Bohr, for example, in his last works on the philosophical aspects of atomic physics (as mentioned in earlier chapters), did not employ the concept and made it clear that the description of atomic phenomena had’a perfectly objective character’.^^16^^ The term ’ complementarity’, which he retained, signifies a novel kind of relation of the experimental evidence about micro-objects, obtained by mutually exclusive means of observation. This evidence, Bohr remarked, though it appears mutually contradictory, in fact ’exhausts all conceivable knowledge about the object’.^^17^^

p Let us now go into greater detail about certain aspects of the meaning of a conception that stems from recognition of the dual particle-wave nature of micro-objects.

p The particle—a basic notion of classical mechanics (like its other basic notions)—can be defined indirectly by Newton’s law. Such a definition signifies that a particle has both momentum and position.  [134•*  The classical concept, however, cannot be applied on the atomic scale because it does not correspond to the quantum laws established by experiment that are expressed by quantum formalism. In this case the uncertainty relation plays a most important role not only determining the limits of the applicability of the classical concept of particle, but also allowing us to generalise the particle concept and make it more profound by giving it a new content unknown to classical theories. 135 This new content follows from the need to allow for the wave properties of micro-objects in the theory.

p In the definition of a particle of classical mechanics, of course, its momentum and position are unrelated to each other by their very nature, and must be considered separately. In quantum mechanics it is impossible to consider the position and momentum of a particle separately; they have to be understood in their deep interrelation, because microobjects have wave properties that are inseparable from their corpuscular ones. This becomes clear, in particular, from the imaginary experiments that accompany the exposition of the uncertainty relation; they provide obvious evidence that one cannot isolate the particle’s position from its momentum in quantum mechanics precisely because of the dual particle-wave nature of micro-objects.

p In quantum formalism, which differs qualitatively from the formalism of classical theories, the state of things in physics internally linked with recognition of the dual particle-wave nature of micro-objects is described mathematically. In it symbols figure that denote not numbers (as in classical formalism) but more abstract mathematical concepts (operators) that are not, generally speaking, governed by the commutative law of multiplication. Each physical quantity in quantum mechanics corresponds to its operator in such a way that the eigenvalues of the latter give the possible values of the former, and its eigenfunctions describe the corresponding states of the object (system). Even the definitions of the operators of momentum and position potentially contain the uncertainty relation (for momentum and position), which means that in no quantum state ( mathematically described by a wave function) there exist the eigenvalues of the operators of position and momentum at the same time together, i.e. it is affirmed in essence that quantum mechanics does not deal with the ‘classical’ particle.

p In quantum mechanics (and this is demonstrated above all by its mathematical apparatus) corpuscular and wave notions thus cannot be combined in the manner of classical physics. From the standpoint of classical physics the expression ’particle-wave dualism’ can be used, as follows from what has been said, in the following senses: 1) either a particle or a wave, 2) both a particle and a wave. From the standpoint of quantum formalism, however, both these 136 meanings lose significance. It remains to find, as Bohr put it, the ‘irrational’ form of uniting the particle and wave concepts. If such a form exists, what is its logical meaning?

p The novel form of the combination of the particle and wave concepts in quantum mechanics is concentrated in the novel feature of quantum probability, one of the fundamental concepts of quantum theory. This concept, introduced by Born and developed further by Bohr, means that the processes in material systems are governed by probability ( stochastic) laws. According to this interpretation, the translation of a particle is associated with a wave process that represents the propagation of a probability wave.

p Probabilities differ radically in quantum mechanics from those in classical theories. In the latter they express the existence of circumstances that are random for the phenomena being studied and therefore do not enter directly into the laws of these phenomena. The hypertrophy of this state of affairs that is typical of metaphysical ideology leads to a subjectivist interpretation of chance and probability (Laplacian determinism). Things are quite different in quantum mechanics: in it probabilities are considered as occurring in the basic laws of nature, and their introduction reflects the potentially possible objectively existing in certain real conditions. The probability laws of quantum mechanics are the laws of behaviour not of ‘classical’ particles and not of ‘classical’ fields, but of material systems that combine the properties of particles and waves in a novel way.

p The idea of the ’probability wave’ of quantum mechanics as a mode of uniting the particle and wave concepts may appear artificial, but when one analyses certain experiments that are by no means imaginary, its naturalness is obvious.

p In an experiment, say, with a machine gun, we can judge the statistics of the bullets by their pattern on the target. In an experiment on the diffraction of successive electrons we learn about the statistics of electron behaviour on the basis of the specks on a screen (traces of the electrons hitting it), which form a diffraction pattern in a sufficiently long experiment. Comparing these two experiments, we are justified in saying that the probability behaviour of the electron is governed by the wave law (which cannot be said of the behaviour of the bullet). The diffraction 137 pattern formed by the traces of electrons hitting the target is evidence that the electron moves not as a ‘classical’ particle but as one possessing both corpuscular and wave properties. Indeed, we conclude from a spot on the screen that the electron possesses particle properties; from the diffraction pattern formed by the spots we infer that the electron that has passed through a diffracting system has interacted not with a single atom, or a small number of them (as a ‘classical’ particle would have done), but with the diffracting system as a whole (i.e. it behaves as a wave). Thus, an electron passing through a diffracting system moves neither as a ‘classical’ particle nor as a ‘classical’ wave but as an object that has inseparable particle-wave properties.

p It is very important to clarify what the inseparability of the electron’s particle-wave properties means or what is understopd by dialectical unity of the particle and wave properties of matter when the question is posed more broadly. It can be demonstrated by the following example. By performing Young’s interference experiment (assuming that the screen used is made of material that emits photoelectrons easily) we can observe the particle nature of light. Born denied that in this experiment light appears in its two forms simultaneously as particles and as waves.^^18^^

p When one thinks over Bern’s arguments, however (he says, in particular, that ’to speak of a particle means nothing unless at least two points of its path can be specified experimentally; and similarly with a wave, unless two interference maxima are observed’^^19^^), it becomes clear that he essentially had in mind the ‘classical’ particle and wave. Indeed, in order to understand the corresponding phenomena in Young’s experiment one must not employ the classical concept of particle and wave—it was just that which Bern’s argument demonstrated, as a matter of fact, although he meant to show something else. Here one must already employ the concepts of quantum theory which differ qualitatively from the classical ones. The concept of particle in quantum theory undoubtedly differs from its classical analogue, and in its own way Young’s experiment demonstrates this circumstance.

p The difference between the quantum concepts of parlicle and wave and the analogous classical ones is that the quantum concepts are relative within the limits of their theory, 138 while the classical ones are absolute within the limits of their theory. This means that it is necessary, in order to describe the behaviour of a micro-object, to consider the means of observation (relativity with respect to them), whereas this consideration can be omitted in the description in classical physics.^^20^^ This difference rests on recognition of the fact that in quantum theory the moving objects are regarded from the standpoint of the unity of their opposing particle and wave properties, while in classical theory the unity of waves and particles, if permitted at all, is only so from the standpoint of their coexistence or parallel existence in a certain model governed by the laws of classical theory.

p We are justified in inferring that the dialectical unity in which relative opposites must be and are combined differs radically from the uniting of opposites in the sense of their conjunction, when they remain absolute and immobile. The combination of opposites in a dialectical unity does not lead to a formal-logical contradiction (as follows from the definition of dialectical unity). Such a combination implies that a more profound theory than that in which absolute opposites figure is being, or has been born, a theory with corresponding new basic concepts and principles. The opposites combined in this theory become aspects of a new concept. The quantum-mechanical concept of particle thus ‘preserves’ the element of discreteness of the classical concept but ‘loses’ the properties of motion along a trajectory and of individuality. These ‘losses’ actually mean that, whenever it is a matter of quantum-mechanical objects, wave properties are combined with particle ones (which is expressed in quantum mechanics itself concretely by the uncertainty relation for momentum and position).

p Summarising what has been said on the logical plane about dialectical unity, we can note that this unity is governed, generally speaking, by the formula ’both yes and no’, reand as regards particle-wave duality by the formula ’both particle and wave’, but posed as an antinomy problem.  [138•*  This formula neither can nor does lead to a formal logical misunderstanding, because, when the antinomy problem is resolved, the quantum mechanics means by ’particle’ 139 and ‘wave’ mutually relative concepts, while in classical physics they are absolute concepts. In the terms of modern logic it becomes especially clear that the formula ’both particle and wave does not lead to any logical nonsense. This expression belongs to the metalanguage, while the expression ’either particle or wave’ belongs to the object language, and moreover to the language of classical theories, and this is admissible only on condition that the problem is formulated in the metalanguage and resolved in the object language. From that point’of view quantum mechanics is also, in a certain respect, the metatheory of classical mechanics. It is quantum mechanics that enables the limits of applicability of classical mechanics and of its principles and basic concepts to be established, and other matters relating to classical mechanics as a whole as a theory to be considered (e.g. the matter of the adequacy of the concepts admissible in classical mechanics to objective reality).

p The limitations imposed in quantum mechanics on the classical concept of particle are neither a limitation of knowledge! nor confirmation of the positivist thesis that the objective significance of the empirically observed is a question quite without scientific meaning. This ‘limitation’ is in fact a deeper understanding of the corpuscular properties of matter allowing for the wave properties that are inherent in it and that are neglected by classical theories of matter in their study of particles. The concept of particle is generalised and deepened in accordance with this ’ limitation’ when it drops its classical form, so to say, in this generalisation.

p Let us sum up. When physics comes to understanding the world of atomic phenomena and of the subatomic world, or when it passes to cognition of the world of stellar systems and galaxies, it has to take into account the all-round, universal flexibility of concepts reflecting the eternal development of the objectively real world when synthesising in the truly philosophical sense of the term the physical knowledge gained about the macroworld and the microworld. Lenin’s fragment On the Question of Dialectics which is extremely ‘coimpressed’ and very profound in its content, and which summarises everything basic that he said in his Philosophical Notebooks, clearly indicates that such an allround flexibility of concepts is inherent only in dialectical thinking.

140

p The splitting of a single whole and the cognition of its contradictory parts is ... thee s s e n c e... of dialectics,’ he said. ’The condition for the knowledge of all processes of the world in their "self-movement", in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the “struggle” of opposites.’

p ’ The second alone [the conception of development as a unity of opposites—M. 0.] furnishes the key to the “self-movement” of everything existing; it alone furnishes the key to the “leaps”, to the "break in continuity", to the "transformation into the opposite", to the destruction of the old and the emergence of the new.’^^21^^

p It is as if this fragment had been intended by Lenin for the new physics, for the quest for a solution of the philosophical problems arising in it. Striking confirmation of this is the transformation of the original quantum ideas into a logically consistent, developed physical theory—quantum mechanics.

p REFERENCES

p  ^^1^^ Frederick Engels.Anti-Diihring (Progress Publishers, Moscow, 1975), p 31.

p  ^^2^^ Karl Marx. Capital, Vol. I. Translated by S. Moore and E. Aveling (Progress Publishers, Moscow, 1977), p 163.

p  ^^3^^ I. S. Narsky. Problema protivorechiya v dialekticheskoi logike (The Problem of Contradiction in Dialectical Logic) (Moscow University Publishers, 1969); idem. Dialekticheskoye protivorechiye i logika poznaniya (Dialectical Contradiction and the Logic of Cognition) (Nauka Publishers, Moscow, 1969).

p  ^^4^^ This is noted, in particular, by Heisenberg in his Physics and Philosophy (George Allen & Unwin, London, 1959), p 99.

p  ^^5^^ H. Minkowski. Raum und Zeit. Physikalische Zeitschrift, 1909, 10, 3: 104.

p  ^^6^^ P. A. Schilpp (Ed.). Albert Einstein: Philosopher-Scientist (Tudor Publishing Company, New York, 1951), p 57.

p  ^^7^^ Albert Einstein. Zur Elektrodynamik der bewegter Korper (Ann. Phys., 1905).

p  ^^8^^ H. Minkowski. Op. cit., p 104.

p  ^^9^^ Ibid.

p  ^^10^^ Philipp Frank. Foundations of Physics. In: International Encyclopedia of Uniflied Science, Vols. I & II. Foundations of the Unity of Science, Vol. 1, N’o. 7 (Univ. of Chicago Press, Chicago, 1946), p 54.

141

p  ^^11^^ See V. I. Lenin. Philosophical Notebooks. Collected Works, Vol. 38 (Progress Publishers, Moscow), p 256.

p  ^^12^^ S. A. Yaiiovskaya. Has Modern Science Overcome the Difficulties Known as Zeno’s Aporia? Problemy logiki (AN SSSR, Moscow, 1963).

p  ^^3^^ J. J. Thomson. Beyond the Electron (CUP, Cambridge, 1929), p 23.

p *^^4^^ See, for example, Studies in the Foundations of Methodology and Philosophy of Science, Vol. II: Quantum Theory and Reality (Springer Verlag, Berlin, 1967).

p  ^^15^^ A. D. Alexandrov. On the Meaning of the Wave Function. Doklady AN SSSR, 1952, 85, 2; D. I. Blokhintsev. Osnovy kvantovoi mekhaniki (Fundamentals of Quantum Mechanics) (Gostekhizdat, Moscow-Leningrad, 1949); idem. A Critique of the Idealist Understanding of Quantum Theory. Uspekhi fizicheskikh nauk, 1951, 45, 2: 195; S. I. Vavilov. Development of the Idea of Matter. Sobranie sochinenii. Vol. Ill (AN SSSR, Moscow, 1956), p 41; V. A. Fock. On the Interpretation of Quantum Mechanics. In: I. V. Kuznetsov and M. E. Omelyanovsky (Eds.). Filosofskie voprosy sovremennoi fiziki (Gospolitizdat, Moscow, 1959); idem. Quantum Physics and the Structure of Matter. In: M. E. Omelyanovsky (Ed.). Struktura i formy materii (Nauka Publishers, Moscow, 1967), p 161.

p  ^^16^^ Niels Bohr. Quantum Physics and Philosophy. In: Niels Bohr. Essays 1958-1962 on Atomic Physics and Human Knowledge (N. Y., London, Interscience Publ., 1963), p 3.

p  ^^17^^ Ibid., p 4.

p  ^^18^^ Max Born. Atomic Physics (Blackie & Son, Glasgow, 1963), p 103.  ^^18^^ Ibid.

p  ^^20^^ On the concept of relativity to the means of observation, see V. A. Fock. On the Interpretation of Quantum Mechanics. In: Filosofskie problemy sovremennogo estestvoznaniya (Proceedings of the Ail-Union Conference on Philosophical Aspects of Science) (AN SSSR, Moscow, 1959).

 ^^21^^ V. I. Lenin. On the Question of Dialectics. Collected Works, Vol. 38, pp 359-360.