p On the point in the title of this section there is no unanimity among scientists. If that is a minus from the standpoint of the strictness of a system of ideas, it is a plus from the standpoint of the history of views on the problem of causality and determinism, a plus in that the various statements about the problem cover diverse aspects of the universal connection in nature. Philosophy once experienced something similar. In ancient philosophy, for instance, the concept of cause was more general and undefined than it is in our day, and Aristotle, that great encyclopaedic mind of antiquity, distinguished four kinds of causality: causa formalis, causa materialis, causa efficiens, and causa finalis.

p The concept causa finalis was used in particular by Engels in his Dialectics of Nature, though in another sense than Aristotle’s. In general, all these terms can be found in modern philosophical literature, but the meanings given to them by Aristotle are now referred to other, more accurately denned categories. Only the term causa efficiens (the efficient cause) has to some extent retained its meaning, which corresponds approximately to the modern meaning of the word ‘causality’.

p In the first section of this chapter we considered the relationship of determinism and the principle of causality in its general form. Here we shall add some details and definitions in connection with our theme.

p Causality is a category for denoting a necessary connection in time for processes occurring in it. If in given constant conditions phenomenon A generates, causes, or determines (in this context these concepts are identical) another phenomenon 5, then the connection between the two phenomena is a causal one in which phenomenon A is the cause and phenomenon B is the effect.

p A causal connection is a necessary connection between different phenomena precisely in time. There are the most varied connections between the phenomena of nature, including a necessary connection in the space in which various phenomena occur at one and the same time. The statement ’a charge is the source of an electromagnetic field’, for example, expresses a necessary connection between the values of certain quantities existing simultaneously; in other words, the connection between the electrical and magnetic fields is a necessary one but, like the connection mentioned in the first example, it does not represent a causal connection. An infinite number of such examples can be adduced; they illustrate the idea that a causal connection is only a tiny part of the world connection between phenomena.

p The categories of cause and effect have an inherent meaning only as applied to phenomena that in given conditions are regarded independently of the phenomena around them and in that sense represent an isolated system. As soon, however, as these phenomena are considered in connection with the phenomena around them, cause and effect are united with each other in the notion of universal interaction in which they never remain the same: what is the cause 150 in some conditions becomes the effect in others, and vice versa.

p The category of causality implies a connection between two phenomena. A certain phenomenon M can be a cause of a certain phenomenon N and an effect of phenomenon K; no phenomenon, however, can be the cause of itself. Engels, it is true, said that matter and its inherent motion were causa finalis (the final cause), but did not do so in the ordinary meaning of the term ‘cause’.^^15^^

p A change of any object or phenomenon, and its transformation into ’its other’, is a splitting of the whole into contradictory parts, into mutually exclusive opposites, and the unity of these opposites is sometimes called the cause of change and development. That is done, however, so as to make the argument easier to follow, and the term •cause’ is not used here in its proper meaning; the category of dialectical contradiction underlies the other categories of logic and dialectics, including that of causality, so that it is wrong to explain the category of contradiction by the category of causality.

p At the same time we must not ignore the fact that a phenomenon can change and at the same time remain basically the same; in this case the concept of state is used. This concept plays an important role in physics, especially in matters relating to causality. Without it, it is impossible to solve problems relating to the theme of this section.

p Many physicists, regardless of their philosophical views, understand by the principle or law of causality in physics a proposition about a necessary connection between a system’s state (an isolated system is implied, which may be a single particle) at an initial moment of time and its state at any other succeeding moment of time. The Austrian physicist Arthur March, for instance, who said that ’the spirit of materialism’ and ’the materialist mode of thought’ were ‘bankrupt’,^^16^^ at the same time has written that ’in quantum mechanics, too, there is causality, and this, as in classical physics, consists in the basic proposition that it is possible to deduce the future state of a system from its state at a given time and under given influences’.^^17^^

p From this point of view the principle of causality is valid in quantum mechanics because in it, the initial value of the state of a system characterised by a wave function 151 allows one to determine the state, i.e. the wave function i|), at any other moment of time by means of the so-called wave
equation ih -^ = Iffy, where H is the energy operator, or Hamiltonian.

p This understanding of the principle of causality, however, actually means an extension of the concept of causality, its incorrect identification with the idea that phenomena are mutually connected and reciprocally caused. It seems to us that one cannot agree with that interpretation of causality, when it performs the function of other categories reflecting aspects of the universal world connection. The principle of causality, of course, consists only in the following: under certain conditions a phenomenon (cause) generates another phenomenon (effect). In the case of causal relation between phenomena we ignore their connection with the world whole and consider them independently of it. Consequently, as we have already noted, the infinite diversity of necessary connections cannot be reduced to just one causal connection, i.e. the connection between cause and effect.

p Let us turn to classical mechanics. In the case of uniform motion in a straight line the change in a particle’s position at a certain moment of time is not the result of the action of a force. Newton’s first law directly expresses the connection between phenomena relating to uniform motion in a straight line and therefore it makes it possible, given knowledge of the initial position and the velocity of a particle moving uniformly along a straight line, to calculate its position at any other moment of time.

p In the case of non-uniform motion, however, a change in a moving particle’s velocity results from the action of a force that functions in this case as the cause; Newton’s second law expresses this causal connection. In classical mechanics, however, the state of motion of a particle at a certain moment of time is not a cause of its state at a subsequent moment of time. If the initial- state allows one to calculate the particle’s position and velocity at any other moment of time, this circumstance is evidence only that the particle’s state of motion at a given moment and its state at any other moment are necessarily connected with each other, and this connection is a regular pattern of the phenomena of motion studied by classical mechanics and expressed in Newton’s laws.

p The problem of causality and determinism is similarly solved in quantum mechanics. If the value of the wave function at any moment of time can be calculated from its value at any initial moment, this means only that the connection established by quantum mechanics between the values of the wave function at different moments of time is a regularity of quantum mechanics, and this regularity is expressed by the wave equation (which was formulated by Schrodinger).

p Quantum mechanics thus resembles classical mechanics in the sense that they both unambiguously determine the connection between a state at time t₀ and a state at time t.

p Although in both classical and quantum mechanics the state of a system at a future moment can be determined unambiguously from the state of this system at a given moment, the nature or type of the connection between the two states differs fundamentally in classical and in quantum mechanics.

p The connections between a particle’s states at two different moments of time that are considered by classical mechanics resemble the connections of the states, say, of an electromagnetic field to which Maxwell’s theory applies, in this respect, that value of the quantities describing the state of an object at any moment of time can be calculated from the values of the quantities describing its state at an initial moment. This common feature of the given connections exists, in spite of Newton’s laws being different from Maxwell’s equations, and in spite of the states of an electromagnetic field being characterised by quantities other than position and momentum. Such connections have something to do with dynamic regularity, and many authors believe the latter to be the sole, so to say,?> representative of determinism and causality in physics.

p In quantum mechanics, as follows from what has been said, the type of connection between the values of a particle’s state in time is different in principle from that in classical physics. The wave function describing the state of a particle describes not the particle ’by itself but the potential possibilities of its interaction with instruments, i.e. definition of the wave function at the initial moment of time makes it possible to obtain probabilities of results 153 of measurements of each quantity, measurements that can be made of a particle in a given state.  [153•* 

p We would be justified to draw the following general conclusion from what has been said: the wave function determines the probabilities and at the same time satisfies the Schrodinger equation; this means that there is an inner necessary connection in quantum mechanics between its probability (statistical) and dynamic regularities.

p The connections between the quantities of quantum mechanics relating to the time variation of a state thus do not have solely a statistical or solely a dynamic regularity. This is the novel feature of the statistical (probability) laws of quantum mechanics. Its laws inseparably combine the statistical and dynamic aspects of the mechanism of atomic phenomena (which is most adequately expressed in the operator equations of quantum mechanics).

p It follows from everything said above that quantum mechanics, like every scientific theory, is deterministic, although its determinism differs^^1^^ from the Laplacian determinism of classical mechanics and from the wave determinism of classical field theory. And as regards the question of causality in quantum mechanics, i.e. whether quantum mechanics is a, so to say, causal theory, the answer suggests itself. Quantum mechanics recognises force effects on micro-objects; it is therefore a causal theory, since these effects or actions necessarily generate corresponding changes in the objects’ further motion. These force^^1^^ effects are therefore a cause. The temporal connections (i.e. the course of atomic processes in time) that are reflected by the wave equation also include these causal connections.

p To conclude this section, let us consider the statements of contemporary physicists about the relation between determinism and the principle of causality.

p In Heisenberg’s view the principle of causality gradually, as philosophy and physics developed, proved to be ’ tantamount to the expectation that the event in nature is uniquely determined, that exact knowledge of nature or of a certain sector is sufficient in principle at least to predict the future’.^^18^^ He believed that this was exactly the situation in Newtonian physics, in which a system’s state at 154 a certain time makes it possible to calculate its future motion. ’If we interpret the word “causality” so narrowly, we also use “determinism” and mean by it that there are firm laws of nature by which the future state of a system can be predicted unambiguously from its present state.’^^19^^

p Heisenberg thus did not distinguish between causality and determinism, and understood the latter in the spirit of a mechanistic outlook.

p Max Born drew a line between causality and determinism in physics. According to him, determinism coincided with Laplacian determinism. Hence one can understand why Born fought for indeterminism in quantum mechanics, as we said in the first section.

p There is much in common between Born and Leon Brillouin in their understanding of causality and determinism. In Brillouin’s opinion, ’determinism assumes a “must”: the cause must produce such and such effect (and very often one adds, "right away"!).’^^20^^

p ’Causality,’^^1^^ he continues, ’accepts a statement with a “may”: a certain cause may produce such and such effects, with certain probabilities and certain delays.’^^21^^

p Brillouin thus rejects dynamic regularity (and thejmechanical determinism associated with it) and accepts statistical regularity only, formulating the concept of causality accordingly.

p And yet, Brillouin’s probabilistic formulation of causality not only does not disprove determinism (which, of course, cannot be reduced to mechanical determinism, i.e. to a determinism such as corresponds, in spite of its limitation, to a certain domain of connections between the phenomena of nature) but, on the contrary, enables one to comprehend it deeply. Indeed, his formulation essentially does not cancel the genetic connection between cause and effect, as would appear at the first glance; this idea remains, but effect appears in it as a multitude of certain potential possibilities that are realised in certain conditions. Interpreted in this way causality is close to the idea of transformability in the modern theory of elementary particles.

p March understood by causality in physics ’the concept of order in application to natural processes’.^^22^^ In his interpretation a causal relation connects a present event not with a past event as its cause but connects it, in his words, ’with the whole past of the world’.^^23^^

p This understanding of causality led him to accept causality in both classical theory and quantum mechanics. ’ Every physicist,’ he wrote, ’must believe in the possibility of drawing inferences about the future from the present; abandonment of this principle would be tantamount to an interpretation that natural events take place quite anarchically, which would deprive physics of any content. A causality also exists in quantum mechanics, and it consists in the principle, as in classical physics, that it is possible to infer from the state at the moment of a system that is under a given influence what its future state will be. The difference from classical physics lies solely in the interpretation of the concept “state”, which quantum mechanics does not understand in the same way as classical physics.’^^24^^

p Consideration of the concept of state led March to conclude that there is ’strict causality’ in classical mechanics and ’statistical causality’ in quantum mechanics with no essential difference between the two and statistical causality including the strict one as its special case.^^25^^ He did not use the concepts of determinism and indeterminism.

p March’s reasoning, which touches in one way or another upon the question of the relation between determinism and causality in physics boils down, as a matter of fact, to his calling statistical regularity in the processes of nature causality and assuming that probability underlies all laws of phenomena occurring in time.

p With physicists who hold to dialectical materialism the matter of the relationship between determinism and causality is also not quite determined. They have demonstrated the incorrectness of mechanical determinism as applied to the processes of nature, emphasised the acceptability of Laplacian determinism for phenomena within the domain of classical mechanics, and rejected it for the atomic processes with which quantum theory is concerned. As for the terms for denoting objectively real, necessary connections in time between atomic phenomena, however, they have not yet developed a generally accepted point of view. Langevin, for example, preferred the term ‘determinism’ to describe the temporal course of the atomic phenomena that are reflected by quantum mechanics, drawing attention to the various forms of determinism in various physical theories and to the need for new concepts and new formulations of the problem when new phenomena were being studied.^^26^^

p Fock, Blokhintsev, and Terletsky prefer the term ‘causality’ to denote necessary connections in time, and point out the need for new forms to express causality in nature and, correspondingly, for new concepts.

p Fock, for instance, says: ’We need to introduce two terms, for example, "Laplacian determinism", which means a conviction of the possibility in principle of infinitely precise forecasts, and a more general term “causality” in the sense of the existence of laws of nature. Laplacian determinism is actually disproved by quantum mechanics, but causality is fully retained, only with its expression acquiring new forms.’²⁷ The question under consideration was treated quite clearly in Terletsky’s Dynamic and Statistical Laws of Physics (1950). He distinguished between a general law of causality that manifests itself in the ’existence of an objective reciprocal connection and the conditionality of phenomena and objects’ and the two main forms of its expression in physics: (a) classical determinism understood ’as a notion of the full reflection of a physical process by a certain set of quantities that are completely determined at any moment of time when the initial conditions are given’, and (b) a statement to the effect that ’every successive event is always a consequence of certain preceding events, or causes’.²⁸ It will readily be noted that Terletsky used the term ‘causality’ in the sense of ‘determinism’. And when he uses the term ’general law of causality’, he means by it what we, following the philosophical tradition, have called ’ determinism’. In this case it would be better to use ’the law or principle] of causality’ to denote what figured with Terletsky as the second main form of manifestation of the ’general law of causality’.

Which terminology is more appropriate and accurate? That can only be answered correctly in connection with the history of philosophy and the development of its concepts, which have found their highest result and summary in dialectical materialism. The term ‘determinism’ signifies determinacy, reciprocal conditionality, an all-sided connection between phenomena of the material world; the term ‘causality’ signifies a certain part of the world connection; the terms ’dynamic regularity or laws’ and ’ statistical regularity or laws’ signify various manifestations of the world connection in the sphere of phenomena studied by physics.