p Works have appeared of late by physicists in which the meaning of the concepts of actuality and possibility as employed to deal with the philosophical problems of quantum 172 theory is clarified. Heisenberg has written much—in the spirit of Plato’s idealism, however—on possibility as an objective category and on its important role in analysis of the concept of quantum state.^^43^^ There are several important statements by Max Born about actuality and possibility as applied to atomic physics.  [172•*  A major role in understanding the significance of the idea of possibility for quantum mechanics was played by V. A. Fock’s paper On the Interpretation of Quantum Mechanics,^^44^^ and by his more recent publications discussed in other chapters of our book (they indicated from various aspects that it was impossible, without the category of objective possibility as it is understood by dialectical materialism, to deal properly with the philosophical problems posed by quantum mechanics).

p Different meanings are often attached to the concepts of actuality and possibility, and to many other general concepts used in philosophy and science. Max Born, for instance, drew attention to the fact that the concept ‘actuality’ is often used with the meaning of ‘truth’. This concept also has other meanings. Much confusion rises from the multiple meanings of concepts, about which more than enough has been said in the philosophical literature. We shall consider ‘actuality’ and ‘possibility’ as categories that reflect objective reality and material objects and processes from certain definite aspects (the specific nature of these aspects will be defined later). In this way we emphasise, first of all, that we do not intend to identify the concepts ’objective reality’ and ‘actuality’; cognition of actuality is a higher stage in the cognition* of phenomena and processes of objective reality.  [172•** 

p Let. us look more closely ‘actualiuy’ and ‘possibility’.

p Hegel defined actuality as the unity of essence and existence, or of the inner and the outer, that has become immediate.^^45^^ This contains the profound idea that immediate or direct phenomena and the essence, law, etc., found in them are in fact inseparable, that cognition of objects, processes, etc., in their actuality, is cognition of the unity of their essence and existence. The actuality of an object combines in itself both the mediation of its essence and the immediacy of its being.

p Possibility is a moment of actuality, the inner of actuality; whether it or the other is possible, i. e. the possibility of the one or the other being realised, is determined by the whole aggregate of the moments of actuality. In the appropriate conditions possibility passes into actuality, and this means disappearance of one actuality and at the same time the birth of another actuality, with its possibilities. Generally speaking, the categories of actuality and possibility come to the fore when one studies the development of an object, the passing of a certain something into a different something, the process of the disappearance of the old and simultaneous origin of the new.

p The possibility of something (an object, event, property) is such a being of something as is equivalent to its nonbeing. The concept of the possibility of an event implies that this event may occur in one way or another but not just in the one way and not in another. Otherwise possibility would not be a moment of actuality but actuality itself; in other words, realisation of a possibility in just this way and not in another one, in exactly such a form and not in another one, would have been predetermined for ages. It follows from this that the possible and the chance are connected with one another, because, as we know, the existence of objective chance reduces acceptance of the fatal necessity in nature to nought.

p The concept of probability developed by the physical and mathematical sciences has a major role in understanding objective, law-governed, necessary connections in nature. It is a concept of the same order as that of possibility; it is not one that characterises the degree of our knowledge; similarly, possibility is not a concept that characterises conceivability, though just these meanings can and should be ascribed to the concepts of probability and possibility in certain cases. The probable is an objective category representing the possible in its, so to say, quantitative aspect; probability is the measure of the possibility of a certain event’s taking place in such and such definite conditions, which can be repeated as often as you wish.

p In classical physics whose object of study made it possible within certain limits to ignore the transformability of material realities into one another, the concepts of possibility and actuality could be treated as independent of 174 each other. ’Theoretically this meant that only one actuality was recognised as an object of sciencej.in scientific practice this led to possibility existing alongside actuality and being opposed to it.

p Thus, there was a thesis in classical mechanics that events in the future were predetermined by events in the present, and possibility consequently should be realised exactly in the form in which it was realised.The possibility of an event’s occurring did not differ in classical mechanics from necessity; probability, consequently, was out of the question on the plane of principle in classical mechanics (compare Laplacian determinism). On the other hand, the impossibility of predicting events in classical mechanics beyond certain limits, including temporal ones, was interpreted as due to the incompleteness of our knowledge of the initial conditions; random events were therefore admitted in practice and probability concepts introduced.

p The statistical theories of classical physics also presented no exception. Gibbs, for example, believed that the application of probability concepts in physics was due to the crudity of the human sense organs and of measuring instruments. On the other hand, when problems relating to mass phenomena of a certain type were being dealt with, they could not be solved without employing probability concepts. Ideas associated with these concepts arose inevitably in classical physics, but in the form of assumptions supplementing the principles of a, so to say, dynamic type on which a given theory rests. The kinetic theory of gases, for example, added the hypothesis of molecular chaos to the principles of classical mechanics.

p In summing up our brief analysis of the problem of the possibility in classical physics, we would like to emphasise the fact that in classical physics this question could not be answered in the aspect of its connection with actuality, since from the angle of classical physics probabilities could not be included in basic laws but developed in theory independently of them.

p The coexistence within classical theories of assumptions associated with the notion of probability and dynamic principles, determined to some extent the content of the so-called theory of levels (Louis de Broglie, David Bohm, J. P. Vigier), the philosophical ideas of which were developed by Bohm.^^46^^ Let us briefly consider these ideas.

p It is well known that the irregular fluctuations of the Brownian motion of a particle have their basis in the effect of chaotic molecular motion. Bohm stated that ’all the factors determining the irregular changes in the Brownian motion were not assumed to exist at the level of the Brownian motion itself, but rather, most of them were assumed to exist at the level of atomic motions’. If, therefore, the level of the Brownian motion itself were considered, only statistical regularities would be treated, ’but for a study of the] precise details of the motion this level will not be sufficient’ (p 80).

p To explain ’a very strange combination’ (as Bohm put it) ’of determinate and statistical aspects’ (p 78) that physics encountered in the atomic domain, a similar assumption was introduced. In order, for instance, to consider all the details of the motion of an individual electron or quantum of light, we would transfer to a certain, deeper level as yet unknown, the relation of which to the atomic level is the same as the relation of the latter to that of Brownian motion. In that case it would be quite possible that those properties which are determinate at the atomic level are determined by factors existing at the atomic level itself, while other properties of a statistical nature are determined by factors existing at an even deeper level. From this angle, for instance, one could ’conceive of the division of these "indivisible atoms of energy" at a more fundamental level’ (p 81).

p Thus, according to Bohm, there is a ’sub-quantum mechanical level of continuous and causally determined motion, which could lead to the laws of quantum mechanics as an approximation holding at the atomic level’ (p 94). If only those entities are considered that can be defined at one quantum-mechanical level, their motion will be indeterministic in the full sense, ’because determining factors that are important . . . simply cannot be defined at this level’ (p 106).

p From the standpoint of the statement of Bohm’s ’causal laws’ and ’laws of chance’ coexist, representing two aspects of one and the same real process. Or, as Bohm put it: ’The various kinds of things . . . have been found to be organised into levels. Each level enters into the substructure of the higher levels, while, vice versa, its characteristics depend on general conditions in a background’ (p 140). That is why the system of purely deterministic laws cannot be absolutely valid, because it covers only a finite number 176 of objects and does not take into account the infinite number of factors contained at levels below and above that which includes these objects. As a result, ’causal laws’ and ’laws of chance’ should be regarded ’as effectively furnishing different views of any given natural process, such that at times we may need one view or the other to catch what is essential, while at still other times, we may ha veto combine both views in an appropriate way’ (p 143).

p Although the theory of levels is free from such a radical drawback of mechanical determinism as the denial of objective chance (in spite of the fact that this theory criticises indeterminism and develops an important dialectical idea about the qualitative infinity of nature), there are serious flaws in it, in the form it is expounded by Bohm.

p First of all, Bohm isolates necessity from chance and in fact opposes them to each other. He says, in particular, that ’it is not the existence of indetermination and the need for a statistical theory that distinguishes our point of view from the usual one [meaning the Copenhagen interpretation—M.O.].... The key difference is that we regard this particular kind of indeterminacy and the need for this particular kind of statistical treatment as something that exists only within the context of the quantum-mechanical level’ (p 106).  [176•*  One cannot be agreed with all that. Dynamic and statistical regularities operate in their inseparable connection at the levels of macroscopic processes, atomic phenomena, and subatomic processes, and physics reflects them in their unity with one degree of completeness and depth or another depending on the specific nature of a given level, allowing for its connections with other levels, the research conditions, and the special features of the objects studied.

p Furthermore, from the standpoint of Bohm’s theory of levels the chance is not by any means explained by the necessary. According to this theory an approach to a phenomenon from the aspect of the category of chance is only corrected and supplemented by allowing for the necessary connection, and vice versa, an approach from the aspect of the category of necessity should be corrected and supplemented by allowing for the random insignificant factors. Bohm writes, for example: ’A causal law can arise as a 177 statistical approximation to the average behaviour of a large aggregate of elements undergoing random fluctuations, a law of chance can arise as a statistical approximation to the effects of a large number of causal factors undergoing essentially independent motions’ (p 143).

p When it is a matter of a ’causal law’, however, the question arises of explaining the basis of the random fluctuations, i.e. to accept either the primary determinacy or the primary indeterminacy of elements. When, however, it is a matter of a law of chance, it is necessary to remember that ’a large number of causal factors undergoing essentially independent motions’ represents a statistical ensemble, i.e. the same dilemma arises again: the elements of a statistical ensemble are either primarily deterministic or primarily indeterministic. The theory of levels, instead of resolving this dilemma, sidesteps it, since, according to Bohm, although the necessary and the random are mutually connected, this connection is exclusively external and represents only a coexistence of the random and the necessary.

p Certainly, Bohm’s statement that ’actually neither causal laws nor laws of chance can ever be perfectly correct’ (p 143) is valid, but its validity follows not from the fact that ’each inevitably leaves out some aspect of what is happening in broader contexts’ (p 143), but from the necessary being as chance as chance is necessary.

p Finally, the theory of levels does not contain the idea of objective possibility, and in that respect does not differ from the conception of mechanistic determinism. In classical physics the fact that the apparatus of the theory of probability is accepted not so much from the angle of reflection of objective reality by probability concepts as from the angle of its serving statistical regularities was also validated by this, that classical theory studied the patterns of mass random phenomena on the assumption that the individual particles forming statistical ensembles moved according to the laws of Newton’s mechanics. The theory of levels endeavours in fact to extend the same approach to include the laws of quantum mechanics, and quantum physics in general, although, as is clear from the content of quantum theory (with which we are concerned throughout our book), there are actually no grounds for such an approach to atomic phenomena. Micro-particles are not the corpuscles of classical mechanics; their dual particle-wave nature 178 means that the problem of the probability and statistics in quantum theory cannot be solved in the spirit of classical notions.

p In this case Bohm holds another point of view, which can be formulated as follows. It is assumed that every elementary particle is connected with a body that ’in most applications at the atomic level ... can be approximated as a mathematical point’ (p 111). The body is associated with a wave that ’is assumed to be an oscillation in a new kind of field’ described by the ^-function; ’the i|j-rield and the body are interconnected in the sense that the op-field exerts a new kind of “quantum-mechanical” force on the body, a force that first begins to manifest itself strongly’ only at the atomic level but that ’has not previously turned up in the study of the large-scale domain’. The body in turn acts on the op-field, and this reciprocal action, which may be significant ’in the sub-quantum mechanical domain’, is ’small enough to be neglected in the quantum-mechanical domain’ (pp 111-112).

p It is assumed, furthermore, that the op-field undergoes ’random fluctuations about an average that satisfies Schrodinger’s equation and that these fluctuations communicate themselves to the body. The details of these fluctuations would then represent properties of the field associated with a sub-quantum mechanical level (p 113), while at the quantum-mechanical level the behaviour of micro-particles would be regarded only statistically. The assumed fluctuations ’produce a tendency’ for more or less random motion of the body, a tendency opposed by the ‘quantum-force’, ’which pulls the body into the places where op-field is most intense’(p 113). In the end ’a mean distribution in a statistical ensemble of bodies’ results ’which favours the regions where the op-field is most intense, but which still leaves some chance for a typical body to spend some time in the places where the op-field is relatively weak’ (p 113).

p Thus, in any process ’both wave and particle could be present together in some kind of interconnection’, as Bohm writes (p 111).

p The ’interconnection of waves and particles’ in the theory of levels is thus not a dialectical unity of the opposite particle and wave properties of matter but a certain ’ combination of particle and field’ (p 116), a coexistence of waves and particles in a certain mechanical picture. It is 179 understandable that such an interpretation of a micro-particle inevitably leads to the already known notion of the coexistence of’causal laws’ and ’laws of chance’. Hence the natural absence of possibility and probability from the theory of levels as objective categories.

p In summarising Bohm’s point of view on probability and statistics in physics, we must add that it opens up the way to identifying probability with the statistical concept of ‘frequency’, the illegitimacy of which is well known. He considers probability and statistics in quantum physics in the aspect of mechanical classical concepts, and says, for instance, that the results of the theory of levels show ’that mechanical concepts can go further in the quantum domain than had hitherto been thought possible’ (p 128).

p In our view one cannot agree with statements of that kind. The theory of levels does not reflect what in quantum mechanics is called the symmetry of particles and waves, and, in particular, an essential feature of quantum mechanics is left out: namely, the quantum state is described by a wave function in a coordinate representation, and with the same justification by a wave function in a momentum representation, while in fact only the particle interpretation, ‘corrected’ in the spirit of the mechanical ideas of classical physics, is legitimated.

To sum up, Bohm’s theory of levels solves the problem of the nature of probability in quantum mechanics in the spirit of classical ideas, which contradicts the content of quantum theory.