The Problem of “Physical Reality” in the Copenhagen School

S. G. Suvorov

1. In this issue there is published a translation of the philosophical article by the outstanding physicist Max Born, “Physical Reality.” This article deserves close attention, for in it one of the most acute epistemological problems in contemporary physics—the problem of physical reality—is discussed, and it is discussed from a standpoint unusual for the school of physicists to which the author belongs*).

There is no doubt that the works of Bohr, Heisenberg, Born, and the whole brilliant constellation of scholars associated with them played an exceptional role in the development of contemporary physics, leading to significant practical results. Even opponents of the interpretation of atomic processes given by this school cannot fail to take this fact into account. A. Einstein, who to the end of his life regarded this interpretation as unacceptable in principle and stubbornly sought other paths in physics, nevertheless had to acknowledge that “it contains a considerable share of truth”). J. P. Vigier, who likewise seeks the possibility of a new, anti-Copenhagen interpretation of atomic processes, in describing the situation of the struggle in physics, admits that “the new theory (the Copenhagen one.—S. S.*) opened up exceptionally rich possibilities and paths for decisive progress in physics”).

It is also quite evident that the Copenhagen school not only discovered new physical relations in atomic physics, but also reflected on the paths of cognition and discussed epistemological questions. It is known, for example, that the concept of complementarity is regarded by the Copenhagen school as “an absolutely new scientific method of thinking,” as “the most important result for philosophy that has crystallized out of contemporary physics”; but it is now superfluous to prove the existence of such tendencies and evaluations—it would be breaking down an open door: they may be found in no small number in the articles of Bohr, Heisenberg, Born, Jordan, and others.

) Some authors, apparently for about a quarter of a century now, have called this school the Copenhagen school; others dispute the legitimacy of this name, bearing in mind that not all the scientists usually assigned to it worked together in Copenhagen; W. Heisenberg prefers the name “Copenhagen interpretation of quantum theory” (see his article “The Development of the Interpretations of the Quantum Theory” in the collection Niels Bohr and the Development of Physics*, Pergamon Press, London, 1955). If by a school one understands a tendency in science, then this established name may quite well be retained for the sake of brevity, and no one has substantiated its legitimacy so well as W. Heisenberg in the aforementioned historical survey of the formation of quantum theory.

) See the letters of A. Einstein to M. Born, UFN, LIX, no. 1, p. 131, 1956.

*) J. P. Vigier, “On the Question of the Behavior of Individual Micro-objects,” Voprosy filosofii 6, p. 92, 1956.

It is also indisputable that this “new method of thinking” is linked by the representatives of the Copenhagen school themselves with the development of positivism. P. Jordan, a student and formerly the closest collaborator of M. Born, directly identifies the positivist conception with the ideas of the new physics*). Whether the results of the new physics actually coincide with positivism is another question. It is beyond doubt, however, that an influential part of the founders of the Copenhagen interpretation seeks to give them an interpretation in a positivist spirit. The attempts of some of our authors to “defend” the Copenhagen school against “accusations of positivism” are naïve and harmful: naïve because, in the eyes of this school, positivism is a progressive philosophy, the only one that resolves the epistemological difficulties of modern physics; harmful because they prevent us from seeing the tasks that confront materialism in physics.

In the Copenhagen school of physicists, the positivist interpretation of “physical reality” received broad development. This was promoted by the extremely abstract character of contemporary conceptions of the object of physical investigations, the complex path from experimental results to the concept of an “elementary particle.” The physicist judges the presence of an antiproton in his experimental apparatus by the observed peaks on an oscillogram; these peaks acquire a definite meaning only as a result of a theoretical deciphering of the complex interaction of “traps,” arranged by him, in the form of magnetic fields, counters of various types, etc. In many of his articles W. Heisenberg repeatedly and not accidentally returns to the history of how the visualizability of conceptions of the atom (elementary particle) is gradually breaking down: first the sensuously perceptible properties attributed to it disappear, then its geometrical forms are lost, and the concept of the atom becomes more and more abstract. W. Heisenberg sees in this course of history a lawful process, which he identifies with the collapse of materialism, thereby showing that modern materialism has remained unknown to him, for the latter is by no means connected with any particular conception of the atom. W. Heisenberg believes that, since sensuously perceptible properties disappear in the concept of the atom (elementary particle), the atom thereby ceases to be a real formation in nature; the concept of it becomes an auxiliary concept, a symbol convenient for calculations. Of the elementary particle of modern physics W. Heisenberg writes: “In essence, it is not a material formation in time and space, but only a symbol, the introduction of which gives

*) “Among contemporary quantum physicists,” wrote P. Jordan, “there has been adopted, in essence quite unanimously, an epistemological conception that is under the strong influence of positivism; this epistemological conception cannot be rejected without also rejecting quantum mechanics itself (or, in any case, without considering it as still unfinished and unexplained). The inevitability of this conclusion is fully acknowledged also by the above-mentioned physicists (Planck, Laue, and also Einstein), who reject ‘positivism’ and therefore consistently regard contemporary quantum physics as unfinished, placing their hope in a future restoration of a ‘mechanical,’ strictly causal picture of the world. Bavink, who for his part welcomes the overcoming of the mechanical worldview, by virtue of his rejection of positivism turns against the new physics, which precisely accomplished the task of overcoming mechanism. We must regard the propositions as inseparably connected: the new physics is inconceivable without the influence of the positivist theory of knowledge; conversely, positivism first received its stabilization and clarification precisely in physics thanks to the fact that thinking by means of objective processes was replaced by a new form of thinking in categories of complementarity.” See Pascual Jordan, Die Physik des 20. Jahrhunderts (Einführung in den Gedankeninhalt der modernen Physik), Braunschweig, 1936, p. 132.

laws of nature an especially simple form”*). In this simplicity of the form of the laws W. Heisenberg sees the justification for introducing this “auxiliary concept.” Seeking to emphasize still more strongly the symbolic meaning of the concept of the atom, he continues: “For a clearer idea of the symbolic character of the modern concept of the atom, one may perhaps refer to the fact that the question of the existence of the atom in modern physics has a certain formal similarity to the mathematical problem of the existence of the square root of minus one. Although elementary mathematics teaches that among ordinary numbers there is no such square root, nevertheless the most important mathematical propositions first received their simplest form only after the introduction of this root as a new symbol, and thereby its existence was justified. In a similar way, the data of modern physics show that atoms do not exist as simple corporeal objects, but that the introduction of the concept of the atom makes possible a simple formulation of the interrelations that determine all physical and chemical processes”**).

V. I. Lenin expressed the profound thought that idealism is only nonsense from the point of view of metaphysical materialism; in reality it grows on the living tree of knowledge, one-sidedly turning one of the elements of the spiral of cognition into a straight line which, under certain conditions, leads into priestcraft. Of course, W. Heisenberg’s judgments, too, rest on something real at their basis. If into his words “exist as” one puts the meaning “possess the same properties, connections,” then his assertion that “atoms do not exist as simple corporeal objects” will prove correct, although also trivial. However, when gnoseological problems are posed, the dispute is not about this. Modern materialism asserts that atoms exist as certain material, objective formations, and that concepts of atoms are abstract images of these objective formations, and not symbols whose meaning consists in simplifying calculations. In this philosophical sense atoms exist just as simple corporeal objects exist, i.e., the existence of both is objective.

Thus, according to Heisenberg, the historical course of cognition gradually reveals that the concept of the atom contains nothing except a mathematical symbol that orders and simplifies the formulation of the interrelations of physical processes. W. Heisenberg proceeds from the view that in modern quantum physics attempts to find a transition from experimental results to the microparticle as an object, whose existence is spoken of by materialists, encounter fundamentally insurmountable obstacles. These obstacles arise from the unusual properties that it proves necessary to ascribe to microparticles if one wishes to fit the results of experiments with them into a logical system. Thus, it proves necessary to assume that microprocesses obey quantum laws of an essentially statistical character; that for microparticles there exists a law so unusual for classical objects as the uncertainty relation of coordinates and momenta. The measuring instruments which we inevitably have to use in investigations, in the final analysis, themselves consist of microparticles of the same

*) Die Antike, Bd. XIII. Quoted from the collection: W. Heisenberg, Philosophical Problems of Atomic Physics, Foreign Literature Publishing House, 1953, p. 49.

**) Ibid., p. 50. Another prominent representative of the Copenhagen school, P. Jordan, writes about the object of modern physics in the same spirit: “The atom, characterized as a system of formulas, is, like a geometric drawing on the ground, only an auxiliary concept for the ordering of experimental facts,” Pascual Jordan, Die Physik des 20. Jahrhunderts, 1936, p. 123.

of the order to which the particles being measured belong; the interactions of the instruments and the measured particles are subject to the same quantum regularities of a statistical character; by virtue of the uncertainty relation they always possess features of partial uncontrollability. Every measurement radically changes the “situation,” from which in quantum physics there is no unambiguous transition to a “situation” independent of measurement, to the “situation in itself.” Nothing of the kind was encountered in classical physics, for in it the “situation before measurement” could be calculated unambiguously. In quantum physics the concept of the “situation in itself” loses practical and theoretical meaning. A situation independent of measurement is regarded as something “in principle unobservable,” as nonexistent. “Physical reality” exists only in the experimental arrangement.

Similar views were developed in the Copenhagen school over the course of thirty years. Quite recently W. Heisenberg repeated them, speaking in defense of the “Copenhagen interpretation of quantum theory.” In formulating the spirit of the Copenhagen interpretation, W. Heisenberg draws a distinction between the concepts “objective” and “real.” By “objective” he understands that which exists in isolation from man and his instruments, in a form not altered by any connections with the external world. This is a purely formal device for defining the objective. Naturally, the “objective” defined in this way is unattainable, since any attainment is possible only through the establishment of a connection, and the establishment of a connection destroys the “objective”*). The attempt to disclose the properties of the “objective” is as hopeless as chasing the blue bird: one need only catch it, and it at once ceases to be blue.

The concepts of the “objective” and the “real,” as has been said, do not coincide for W. Heisenberg**). The picture that is reflected in instruments is not objective, but “real.” W. Heisenberg believes that the criticism of the Copenhagen interpretation of quantum theory is based on the fear that it removes the concept of the real from physics. “As we have shown here exhaustively,” writes W. Heisenberg, “this fear is groundless, since the ‘real’ in quantum theory plays the same decisive role as in classical physics.” From W. Heisenberg’s point of view, the “objective” is only the possible as described by mathematical equations, and not the real. The mathematical equations of quantum theory govern precisely only the possible, and not the real. The transition from the possible to the real is always discontinuous, and this leap is not reflected in the mathematical equations describing the possible. Connected with this is the conclusion that “knowledge of the ‘real’ is by its very nature incomplete knowledge.” Such are the views of W. Heisenberg, repeated once again quite recently.

Physicists discuss the question of what reality is not by chance and not as a matter of leisure; they are compelled to reflect on it because it is necessary to comprehend new experimental facts. The latter confront the investigator with many problems. If the electron before pass—

*) “In this case (if the system is closed.—S. S.) the representation is completely ‘objective,’ i.e. it no longer contains features connected with our knowledge of the observer; but at the same time it is completely abstract and unattainable, since the various mathematical expressions \(\psi(q)\), \(\psi(p)\), etc. have no relation to real space or to real properties; thus, so to speak, it contains no physics at all.” See the above-mentioned article by W. Heisenberg in the collection: Niels Bohr and the Development of Physics, Pergamon Press, London, 1955, section III.

**) “We can say that the state of a closed system, represented by a Hilbert vector, is in fact objective, but not real, and that the classical idea of ‘objectively real things’ must here be abandoned.” Ibid.

through the slits of the diaphragm manifested itself discretely also when it fell upon the scintillating screen after passing through the diaphragm—then why is it not possible to determine through which of the two slits of the diaphragm it passed? And why does the presence of the second slit influence the character of the electron’s motion? Does this not indicate that the electron also possesses wave properties? Can one ascribe to the electron a simultaneously discrete-and-wave nature, and how is this to be imagined?

All these are physical questions about the structure and relations of the electron, understood as a certain objective entity. But physical questions are inseparable from philosophical ones. The question inevitably arises: what is an object, and what paths lead to it? The attempt to create an image of the micro-object on the basis of the “visual representations” of classical physics (a solid particle with fixed momentum and coordinates, etc.) proves impossible. The investigator was confronted with the complex task of reconstructing the image of the micro-object on the basis of the experimental results of quantum physics. But here a new difficulty arose: its experimental results, concerning a stream of the same particles, sometimes appear to physicists as mutually exclusive. Thus arose the problem known as the “duality of waves and corpuscles.”

Positivism suggests a “convenient” solution to this difficulty: by recognizing that physical reality is only a situation in an experimental apparatus, it removes the very task of reconstructing the image of the micro-object. As soon as a physicist adopts this position, the task of his investigations is simplified in a certain respect: now it consists in establishing the presence of definite experimental situations; practical requirements compel him also to learn to predict new situations, but it seems to him that this problem, too, is fully resolved within the limits of the same mode of thought—namely, by introducing the concept of the probability of an event, which is convenient because it appears to free one from knowing the necessary connection of different situations.

If a physicist does not proceed from the existence of the object on which experiments are performed, if he assumes that physical reality is only a situation in an experimental apparatus, then the formulation of the concrete physical problem is radically changed as well. The question of the passage of “this electron” through one slit or another is dismissed not because it is physically illegitimate owing to the specific character of the electron’s connection with the field of the grating, but because the very formulation of the question about the behavior of the object is recognized as meaningless. In exactly the same way, the need to synthesize the results of experiments by thereby creating an image of the object disappears: the discrete and wave pictures appear before us as two different “physical realities,” two “experimental situations,” arising in instruments of two mutually exclusive and mutually complementary classes. This philosophy of reality was indeed expressed in the conception of complementarity. Let us recall how P. Jordan assessed the role of the idea of complementarity: “The enlightening power of this idea consists in resolving the seemingly insoluble riddle and contradiction vividly demonstrated in the well-known problem of the dualistic nature of light. The properties connected with the wave nature of light, on the one hand, and the properties connected with its corpuscular nature, on the other hand, ‘complement’ one another in the sense that they can never appear in one and the same experiment (and, consequently, come into real direct collision). Experiments that make it possible clearly to reveal the wave aspect of light compel (owing to the intervention connected—

...with each experiment) the corpuscular nature of light retreats into the indefinite and unobservable; other experiments, which make prominent the corpuscular aspect of light, leave indefinite and indistinguishable all the properties that previously revealed to us the wave nature of light. By means of this astonishing mechanism of complementarity, nature combines in one and the same physical object properties and regularities that contradict one another in such a way that they could never exist directly at one and the same time” *).

We see that P. Jordan perceives the possibility of a real, direct collision between corpuscular and wave properties in an object as a difficulty incomprehensible to thought and one that must be avoided; in experimental situations this is always achieved by virtue of the action of the “astonishing mechanism of complementarity”: in any experiment the opposite side “retreats into the indefinite and unobservable.” For this reason we limit ourselves only to stating that in the “indefinite and unobservable” both sides somehow combine, but our thinking is freed from the necessity of synthesizing in a single image of the object both sides (which exist in it simultaneously as an objective possibility), since it confines itself only to the realm of what is observed in instruments.

Here the same understanding is expressed as in W. Heisenberg: physical reality is a “situation in an experiment”; everything that lies beyond this situation, i.e. the material formation, the object that produces a definite action in the experimental setup, is, according to P. Jordan, “indefinite and unobservable,” to which there is no transition from the “experimental situation.” And W. Heisenberg expresses the same idea. In his recent article mentioned above, the terms “real” and “objective” occur, but from the real, i.e. from the “situation in the experimental setup,” there is no transition to the “objective.” The “objective” exists as an abstract possibility, ultimately as a convenient term for designating certain mathematical representations.

The matter is presented as though modern physics had proved these ideas by compulsion, having discovered the fundamental statistical character of elementary atomic processes, the uncertainty relation, the uncontrollability of interactions, and the principle of complementarity. It not only has not disclosed any paths of transition from the “real” to the “objective,” but, on the contrary, has allegedly proved that such paths cannot exist.

However, as we shall see below, this point of view is not shared by all representatives of the Copenhagen school.

In this respect the position of Max Born is of interest.

1. Max Born belongs to that leading group of theorists which actively developed the Copenhagen interpretation of quantum theory. He is the founder of the statistical treatment of wave functions; this treatment he opposes to determinism, which, moreover, is interpreted by him as Laplacean unambiguous determinacy excluding chance. His statements about the “idea of complementarity” are imbued with the same sympathy as P. Jordan’s statements: he sees in it a new, science-transforming method of thought, having universal significance for all sciences. He accepts all the formulations characteristic of the “Copenhagen interpretation” concerning the presence of an element of uncontrollability in the interaction between an apparatus and a microparticle, concerning

) Pascual Jordan, Die Physik des 20. Jahrhunderts*, 1936, p. 110.

...that the boundary between object and subject in contemporary physics is becoming less definite.

M. Born likewise highly values the role of positivist philosophy in science. He believes that it was precisely positivism that refuted Kantian apriorism, which had barred the way to genuine knowledge, and greatly raised the significance of experience in natural science. The positivists’ point of view, according to Born, “pushed physicists toward taking a critical position with respect to traditional views, and helped them in creating the theory of relativity and quantum theory”*). M. Born is fully aware that many physicists who actively developed quantum theory in the spirit of the “Copenhagen interpretation” are under the direct influence of this philosophy. As long as twenty years ago, in the lecture “Some philosophical Aspects of modern Physics,” delivered in Edinburgh, M. Born said: “From the works of the latter (the reference is to Ernst Mach.—S. S.) there arose a new philosophical system, the logical positivism of which is in great favor in our day. Its influence can be traced in Heisenberg’s fundamental works on quantum theory; true, it also met with energetic opposition, for example, from Planck. In any case, positivism is an operative force in science”**). In this same lecture M. Born sets forth P. Jordan’s positivist views and characterizes his book Anschauliche Quantentheorie (J. Springer, Berlin, 1936) as “a brilliant exposition of the positivist point of view”***).

And yet, despite his high appraisal of positivism, M. Born as early as twenty years ago expressed his own special attitude toward the basic position of positivism: he did not agree with the positivist view of the objective world. In the lecture mentioned, Born posed the question: “Observation itself changes the order of events. How, in that case, can we speak of an objective world?” According to him, certain theoretical physicists, such as Dirac, state that they do not know what the objective world is, and this does not trouble them; all they need is a mathematically consistent theory with the help of which one can predict unobserved phenomena. “Only the positivists, who claim to possess an exclusively scientific philosophy, answered our question,” Born said. “Their point of view (Jordan, 1936)****) is even more radical than the above-mentioned point of view of Dirac. Whereas the latter states that he is satisfied with formulae and is not interested in the question of the objective world, the positivists declare this question meaningless.”

While holding that the classification of questions into meaningful and meaningless is a great merit of positivism, M. Born, however, did not agree that the question of the objective world belongs among the meaningless. “Positivism,” Born maintained, “holds that the only initial assertions that are immediately evident are assertions describing immediate sensory perceptions. All other assertions are indirect, theoretical constructions whose aim is to describe, in concise terms, the connections and relations of primary perceptions.

*) M. Born, Physics in my Generation, Pergamon Press, London — New York, 1956, p. 49.

**) First published in Proc. Roy. Soc. Edinburgh, vol. LVII, Part I, pp. 1—18, 1936—1937. This article remained unknown to broad circles of Soviet scholars. Recently it was published in the book: M. Born, Physics in my Generation, Pergamon Press, London — New York, 1956, pp. 37—54.

***) It must be thought that M. Born’s testimony may be fully relied upon, for no one will suspect him of a biased attitude toward the Copenhagen school.

****) The above-mentioned book is meant: P. Jordan, Anschauliche Quantentheorie, J. Springer, Berlin, 1936.

Only the latter have the character of reality. Secondary assertions (i.e., concepts, theories, and, in general, conclusions based on perceptions.—S. S.) do not correspond to anything real and have nothing in common with the existence of the external world; they are agreements, artificially invented in order to arrange and “economically” simplify the flow of sensory perceptions. This point of view, M. Born concludes, has no foundation in science itself; no one can prove by scientific methods that it is correct.

It seems that the positivist point of view on reality is presented here objectively, as is the attitude toward it of genuine science.

Further, M. Born presented his arguments against these positivist views on reality. He pointed out that already in the simplest acts of perception we have not a set of uncoordinated sensations, but an image (Gestalt) of an integral object, which is created by our subconscious. “When these images are considered by consciousness, they become concepts and are supplied with words. The unsophisticated mind is convinced that they are not arbitrary products of thought, but impressions that are produced in thought by the external world. I cannot see any argument for refuting this conviction in the scientific field.” And further: “The positivists say that this concept of the external world is a step into metaphysics; it is meaningless, since we shall never know anything about it except through the perceptions of our senses. This is obvious. Kant expressed the same point of view, distinguishing the empirical thing and the ‘thing in itself’ that lies behind it. If the positivists continue to say that all our assertions taking the external world into account are only symbolic, that their meaning is conditional, then I object. For then every single proposition would be symbolic, conditional, even if I say only: ‘I am sitting here in an armchair’... The question of reality is therefore not meaningless, and the application of this concept is not only symbolic or conditional.”*.

Almost twenty years later M. Born again returned to the question of physical reality, devoting to it a special article, the translation of which is published in this issue.

In this article M. Born speaks out unreservedly against those philosophical currents which “teach that only the spiritual world is real and that the physical world is only an appearance, a shadow without substance.” M. Born calls these currents “physical solipsism,” which does not solve the problem of cognition but evades it. One cannot but agree with his assertion that only those people can renounce the concept of reality “who live in isolated ivory towers, far from all experience and from all actual affairs and observations.” M. Born again criticizes the logical positivists, who regard concepts as “purely mental tools” by means of which sensory perceptions are surveyed and ordered; he rejects the interpretation of sensory perceptions as primary data, “behind which alone they (the positivists.—S. S.) recognize the character of reality.”

Max Born presents arguments in favor of why a physicist cannot regard molecules merely as “counters” in the game of our thought. In fact, says M. Born, in his investigations the physicist proceeds along many different paths, but always discovers the same molecular constants. “A small number of molecular constants determines, on the basis of the molecular hypothesis, an unlimited number of phenomenological properties. Therefore every new property that is predicted is

* M. Born, Physics in My Generation, 1956, p. 50.

confirmation of the molecular hypothesis.” These arguments remind us of Jean Perrin’s arguments in favor of the reality of molecules*), as well as of Max Planck, who for many years fought against Mach’s subjectivist views in physics.

M. Born’s conclusion is natural: science cannot merely externally correlate two concomitant phenomena, for between them there exists a real connection, the disclosure of which constitutes the task of science. Thus, between the firing of a rifle and the bullet extracted from a person’s wound there undoubtedly exists a physical connection, although under ordinary conditions it is not detected. M. Born believes that this connection exists; that our conception of the bullet flying from the rifle is not “a play of theoretical fantasy”; that in the interval between the shot and the wound the real bullet described a quite definite trajectory between the rifle and the target.

Assertions that “belief in the existence of the external world is devoid of meaning and for the progress of science is simply an obstacle,” that “everything with which the physicist is concerned can be attained satisfactorily only in terms of ‘experience,’ and not of the external world,” meet with protest on M. Born’s part. “In reality the matter stands quite otherwise,” he declares, and one cannot but agree with this.

It is true that in this article Born’s criticism of the positivists is combined with the acceptance of a number of propositions which have led others to positivism. For example, he indicates that in atomic physics every measurement includes a “factor of unreliability,” which excludes deterministic prediction, owing to the fact that in atomic interactions one must take into account the reaction of the instruments, which obeys the same laws as the observed particle. In view of this, according to Born, “it would obviously be an idle matter to discuss the situation that would have arisen without the intervention of the observer or independently of him.”**)

However, if W. Heisenberg, P. Jordan, and others believe that modern physics excludes the transition from the “situation in the experimental arrangement” to the object, then M. Born, on the contrary, tries to indicate these paths. Whatever the results of this attempt may be, in itself it already represents a progressive step away from the positivism of certain representatives of the Copenhagen school and from the hopeless character of their conclusions about the fundamental incompleteness of our knowledge.

In refuting “physical solipsism,” M. Born creates his own conceptions of “physical reality,” and they differ substantially from the positivist identification of reality with the “situation in the experimental arrangement.”

Of course, M. Born also considers that the physicist is concerned above all with the “situation in the experimental arrangement.” But, in contrast to W. Heisenberg, P. Jordan, and others, M. Born sees in it not physical reality, but only its “projection onto the instrument.” The character of the projection also depends on the instrument; with different instruments there will be different projections of one and the same reality.

It is already clear from this that M. Born assigns to the instrument a different role than is done in positivist conceptions: the instrument does not create reality, but is only a means to its cognition. Such an understanding of the mediating role of the instrument compels one to go further. Indeed, having admitted that

*) J. Perrin, Les atomes, 1913.

**) Stating the oft-repeated assertion that quantum mechanics destroyed the distinction between object and subject, for it can describe the situation in nature not as such, but only as a situation created by a human experiment, M. Born immediately afterward writes: “This is perfectly correct.”

he is dealing only with projections onto an apparatus, the researcher can no longer confine himself to observing only these projections; he will seek that which is projected and which, consequently, does not depend on the apparatuses. And physics, according to Born, has indeed indicated the ways of finding that which is projected: in the totality of projections that vary in each apparatus, it finds something unchanging, constant; it finds invariants.

The idea of invariants, according to Born, is the “key to the rational concept of reality.”

Max Born points out that such is the characteristic path of cognition in all modern physics: everywhere in it projections are perceived and analyzed, and from them a transition is made to invariants. The chief progress in the structure of concepts in physics M. Born sees in the discovery that a certain quantity which had been regarded as a property of an object is in fact a property only of its projection. He shows how this feature of cognition is realized in various modern physical theories—in the theory of relativity, in quantum mechanics.

Thus, the theory of relativity considers projections of the properties of bodies onto reference frames moving relative to one another, and then seeks invariants in these projections. Masses increasing with the motion of bodies, shortened lengths and times—these are not real masses, not real lengths and times, but their projections onto the given reference frame; real masses, lengths, and times are masses, lengths, and times considered in their own reference frame. M. Born regrets that, owing to the conservatism of thought in natural science, the same names have been retained for the projections of real quantities as for the real quantities themselves.

In exactly the same way, quantum mechanics also deals above all with projections, and this fact, according to Born, is reflected in the conception of complementarity. N. Bohr introduced the concept of complementarity precisely “to express the fact that maximal knowledge of a physical entity cannot be obtained from a single observation or from a single experimental arrangement, but that different experimental devices are necessary, mutually excluding one another yet complementary.” M. Born translates this idea into the language of invariants as follows: “Maximal knowledge can be obtained only through a sufficient number of independent projections of the physical entity itself.” In other words, mutually exclusive and mutually complementary aspects in apparatuses of complementary classes are not yet physical reality, but only its projections onto apparatuses; the physicist must make the transition from them to the invariants, which are what constitute physical reality.

It is not difficult to see that, in accepting the principle of complementarity, M. Born gives it an interpretation substantially different from that of W. Heisenberg or P. Jordan. For the latter, the principle of complementarity is a component part of a conception in which only the “situation in the experimental arrangement” is recognized as “physical reality”; in this conception it plays the role of an “astonishing mechanism” which excludes the possibility of a clash between the opposite sides of “physical reality” (wave and corpuscular properties, causal interconnection and the spatio-temporal form of existence, etc.) and automatically removes a number of difficulties of cognition by renouncing cognition of the objective world.

For M. Born, the principle of complementarity is a way of reflecting the quantum object in apparatuses through a set of corresponding projections; in this interpretation, the principle of complementarity does not remove the necessity of synthesizing the opposite sides in the reality which the researcher must discover on the basis of knowledge of its projections.

It is also easy to see that Bohr’s principle of complementarity is a special case of a more general principle, which, apparently, could be formulated as follows: the cognition of any physical objects is accomplished through the perception of the complete set of its independent projections onto coordinate systems (instruments), and the discovery in these projections of invariant properties. A “complete set of independent projections” is a set not of arbitrary projections, but of “mutually complementary” ones; for example, the complete set of projections of the geometrical form of a body consists of its projections onto three non-coplanar planes; this complete set of projections could be called the dimensionality of the object’s spatial form.

Thus M. Born, in essence, reduced the principle of complementarity to the role of a special case, where the matter concerns the representation of quantum objects. What is essentially new in Born’s generalized principle consists in the requirement that, in the projections, invariant properties independent of coordinate systems be found, i.e. in the requirement of a transition from projections to physical reality itself and its properties.

This requirement compels him to seek new formulations of the problem of the interrelation of object and subject. We have seen above that M. Born also agrees with the subjectivist formulation of this relation defended by W. Heisenberg, P. Jordan, and others; this formulation was presented as an immutable conclusion from physical facts, and this, apparently, influenced many physicists. However, on this question too M. Born takes, though a timid, yet natural step forward from subjectivism. While acknowledging that “the boundary between the action of the subject and the reaction of the object is in any case inexact,” he nevertheless believes that “this does not prevent us from applying these concepts in a reasonable way.” The role of the instrument cannot be ignored, but it does not prevent us from knowing reality. “The process by means of which we acquire this knowledge is undoubtedly conditioned also by the observing subject, but this, however, does not mean that there is no reality in the results.” The path to reality lies through the discovery of invariants. M. Born holds that, by applying this method, we can always obtain information “independent of the observer and his instrument, namely, invariant features of a certain number of suitably projected experiments.”

Thus, in any experiment we are dealing not with physical reality, but with its “projections,” from which we must pass to invariants. Only those concepts have the character of real things, M. Born asserts, which are invariants with respect to the transformations that take place. “Invariants are concepts about which natural science speaks in the same way as ordinary language speaks about ‘things’.” In asserting this, M. Born adds the reservation that they are not “things” in the generally accepted sense, for an electron, for example, is not the same as a grain of sand, although it does have certain properties in common with an ordinary particle; this reservation is not essential for understanding the role that M. Born assigns to the invariant; what he means is that the “mathematical concept of an invariant with respect to transformations” corresponds to the concept of reality.

Such is Born’s conception of physical reality. In it the idea of invariance acquires a special, gnoseological meaning: the presence, in different experimental projections, of invariant quantities discovered by mathematical methods is regarded as the criterion of the existence of “physical reality” as a reality independent of projections and, consequently, of the form of perception.

1. The ideas expressed by M. Born did not arise in a vacuum; they have a rational basis.

It has long been proved that the path to the cognition of reality is in fact not direct: we cognize first of all phenomena, and through them—the essence, the inner nature of things, the law-governed regularity specific to them. Phenomena, i.e., the forms in which essence manifests itself in interaction with other things, are inseparably connected with essence, but they do not immediately coincide with it. K. Marx said that if phenomenon and essence coincided, there would be no need for sciences. Philosophical thought for more than a century—and long before the emergence of the theory of relativity and quantum theory—has dealt with the problem of the transition of knowledge from phenomenon to essence. This is a most important epistemological problem, because the way philosophers answer the question of the relation between essence and phenomenon reveals their belonging to one or another trend in philosophy. Subjective-idealist philosophy, for example, identifies phenomenon with essence and, by virtue of this, denies the necessity of passing from phenomenon to essence. In asserting that physical reality is only a “situation in an experimental setup,” W. Heisenberg and others take precisely such a position.

In modern physics the fact is revealed with particular clarity that the image of a micro-object is synthesized on the basis of cognition of its individual aspects, of its essential manifestations. These individual manifestations of the micro-object may, if one wishes, be called its “projections.” Then it becomes clear that M. Born’s ideas—that cognition deals above all with “projections” of reality (phenomena), from which it is then necessary to pass to reality itself (to essence)—do indeed have a very broad foundation; at the same time, we see that they are not a discovery of modern physics or its specific attribute.

On the other hand, invariants play an essential role in physics. The property of invariance of physical quantities with respect to transformations recognized as valid (for example, Lorentz transformations) serves for the physicist as a criterion of the legitimacy of introducing these quantities into theory. In a number of cases the invariance of physical quantities receives a clear interpretation—for example, the independence of the length of a segment from its projections in three-dimensional space, the invariance of the interval in passing from one system to another in the four-dimensional continuum, and so on. In all cases invariance emphasizes the independence of certain properties of an object from particular aspects (frames of reference, instruments), from “situations in an experimental setup.” It is therefore understandable that, trying to break out of the closed circle of “situations in an experimental setup” and seeing no other paths, M. Born turned to the idea of invariants.

However, being only a physical theory, the theory of invariants cannot be a “key to the rational concept of reality,” cannot replace epistemology—the science of the process of cognition; for this it lacks—and this is natural—a number of necessary elements: a clear criterion of the essence of reality, a clarification of the relation of thought to it, and a criterion of the truth of knowledge.

The theory of invariance does not answer (and is not in a position to answer) the fundamental epistemological question: what, then, should be understood by “reality”? Reading M. Born’s article, we see how indeterminate his conception of reality is. Let us trace the course of his thought.

Discussing at the very beginning the question of reality in general, M. Born declares it open because of its particular difficulty; he depicts this difficulty

in the following words: “The ‘realities’ of the peasant or the artisan, the merchant or the banker, the statesman or the soldier, obviously have little in common. For each of them the real things are those that stand at the center of his spiritual activity, while the word ‘real’ is used almost as a synonym for the word ‘important’.”

But what M. Born calls the “reality” of the banker or the peasant is not reality, but only its subjective perception, or, to use the author’s terminology, only a “projection of reality.” Reality, however, is characterized by an objective law-governed regularity, independent of any perception. Indeed, however differently the banker and the peasant may relate to the reality in which they act, i.e., to capitalist society, the latter is characterized not by the perceptions of the banker or the peasant, nor even by their totality, but by the objective economic laws inherent in this society, the inevitable product of which are the banker and the peasant themselves, with their capitalist relations.

Having established the ambiguity of the general concept of “reality,” M. Born then turns to the question of reality in natural science; as was said above, here he speaks out against the positivist denial of the external world, in favor of recognizing a “physical reality” independent of the “situation in the instruments,” the existence of which is substantiated by the presence of invariant quantities in projections.

But the nature of an object is characterized not so much by a set of constants (invariant quantities) as by the law-governed regularity inherent in the object, by its connections with other objects, from which its constants must be explained. Modern materialism, which has generalized the development of science in all fields of knowledge, recognizes that to know an object means to disclose the specific objective law-governed regularity proper to it. This also means finding the conditions under which an object of a given type arises, is stable, and then turns into an object of another type, with another regularity. The disclosure of the specific regularity of an object has epistemological significance, for outside the specific law of motion of an object of a given type, it does not exist. This has been proved by the rich experience of cognition accumulated by humanity, and not only in the field of physics, but also in all other fields—in biology, political economy, and so on. Society exists as a whole, as an object, only because laws independent of human consciousness operate in it and determine its development. Whatever external criteria physicists may use to establish the presence of a new type of objects, in the final analysis the criterion for the presence of a new type of object comes down to what has been said. Cautious researchers resort to this criterion even without entering into a discussion of epistemological problems. Let us give two examples.

As is known, the new particles discovered in the experiments of O. Chamberlain, E. Segrè, and others were identified with antiprotons mainly on the grounds that the mass of the new negatively charged particles coincides, to an accuracy of 5%, with the mass of protons. So the researchers themselves assert.* However, these external features (negative charge, definite mass) would by themselves be insufficient if there were no specific regularities present, which are discussed by the authors in the section “Possible Sources of Error.” On the basis of the indicated features, negative

* See O. Chamberlain, E. Segrè, et al., “Observation of Antiprotons,” UFN, vol. LVIII, no. 4, 1956.

hydrogen ions. The authors exclude the latter, in view of the fact that it is “extremely improbable that such an ion would pass through all the counters without losing its electron.” Observation of the magnitude of the pulses in the counters showed that the new particles were singly charged. These remarks by the authors amount to an actual taking into account of the presence of specific regularities of the new particles. It should also be borne in mind that the authors’ experiments on the bevatron were preceded by the development of the theory of charge symmetry, which had received a number of experimental confirmations, and on the basis of which conceptions of the antiproton were created that led to the prediction of the decay \(\pi_0 \longrightarrow 2\gamma\). Antiprotons, with the regularity specific to them, even before the direct experimental confirmation of their existence, became a necessary element in the explanation of the general picture of physical processes.

The experimental discovery of the antineutron was pending. How could it be identified? On this matter, even before its discovery, Ya. B. Zel’dovich wrote: “To the question ‘what is an antineutron?’ it is often answered that it is a neutral particle with a mass equal to the mass of the neutron, but with the opposite sign of the magnetic moment, just as \(\bar p\) differs from \(p\) by the negative sign of the electric charge. Such a definition cannot be called erroneous, but it is very incomplete; it speaks of a certain partial property and does not mention the main, the most essential one. In reality, the most important common property of antinucleons—\(\bar n\) and \(\bar p\)—is their ability to annihilate with nucleons” *). Therefore the author concluded that “the antineutron will have to be identified by its nuclear interactions.” In fact, the method of identification by nuclear interactions was used in the subsequent discovery of the antineutron.

As we see, the establishment of specific regularities for the identification of new objects comes to the fore.

The search for certain invariant quantities with respect to this more general task is only a particular task, revealing only certain properties, certain interrelations in material objects.

At the same time, it is very essential that these interrelations prove to be valid under definite conditions. Indeed, invariants are always sought relative to definite transformations, taken to be valid. Classical physics, in studying the laws of motion of bodies in various systems, regarded the Galilean transformations as valid. For centuries there was not even the thought of the possibility of another type of transformation. But in studying the laws of motion of rapidly moving bodies it was discovered that the Galilean transformations are limited and are a special case of more general transformations—the Lorentz transformations **). The old theory did not withstand the test of broader experience, and it had to be generalized in order to include the new experience as well.

But what, then, is the source of new experience? Whence arises the compelling necessity of a transition to new theories?

These questions inevitably arise in the analysis of the development of any theory; they have a very general character; the answer to them we can obtain not in the theory of invariants, but in the sphere of gnoseology.

If sensations are not the primary elements of the world, as M. Born justly concluded, joining on this point all

) Ya. B. Zel’dovich, “The Development of the Theory of Antiparticles and the Properties of Heavy Mesons,” UFN*, Vol. LIX, issue 3, 1956.

**) M. Born, of course, also says this, but he does not draw the necessary conclusions from it.

materialists of the world, then physical theories are not such. The primary thing is the external world and the laws inherent in it, while theories are nothing other than continually improving images of the external world. The correspondence of our theories to the external world is confirmed by the results of our practical activity.

Thus, the question of the type of transformations with respect to which invariants should be sought is resolved by us through investigation of the external world and practical verification of the results of this investigation. It follows from this that, in proceeding in this way, we inevitably proceed from physical reality before we seek an invariant—unless, of course, we stubbornly take the position that M. Born characterized as “physical solipsism.” The existence of “physical reality,” more precisely, of the objective world, is the initial premise of physical investigations, and by no means a logical conclusion from an invariant that has been found.

Consequently, epistemologically the problem is posed not as follows: since we discover invariant quantities in the totality of projections, we thereby break out of the closed circle of “situations in the experimental setup” and become convinced that there exists in nature a physical reality independent of instruments. This problem is posed otherwise: practice convinces us that everywhere we are compelled to take account of an objective law-governed order independent of us; therefore, even long before the development of the theory of invariants, humanity became convinced of the existence of an external world, of a reality independent of man; we reflect this reality in our theories, and practice again shows us whether we have reflected it correctly, or whether theory has helped us to expand our connections with it and to apply the laws discovered in the required way. Broader practice leads to the conclusion that our theory is relative, to the necessity of generalizing it. The process of cognition continues uninterruptedly, the image of reality becomes ever deeper, and the use of the laws of nature ever more effective.

This is the materialist theory of knowledge. There are no other paths to a rational conception of reality that exclude the path just indicated. The theory of knowledge cannot be replaced by a mathematical operation.

In this light, an invariant may be regarded not as a justification for the existence of reality in the materialist sense, but as one of the elements of the image of reality. The identification of the invariant with reality by no means arms the physicist against a positivist attitude toward reality.

In fact, M. Born uses the fact that the invariant is independent of the projections that we perceive. However, the invariant is unchanged only with respect to various projections. But in the process of cognizing an object it turns out that quantities invariant in one aspect cease to be such in another. M. Born himself quite rightly notes: “It is natural that quantities which in the old theories were regarded as invariants—for example, distance in stationary systems, time intervals marked by clocks located in different places, masses of bodies—are now regarded as projections, as components of invariant quantities that are not directly accessible.”

The invariance of certain quantities, like the validity of a certain group of transformations, is relative. If one considers that the concept of an invariant corresponds to the concept of reality, then the latter becomes something indeterminate, dependent on the level of knowledge, i.e., on subjective factors. Today the length of a segment is regarded as invariant, since the Galilean system of transformations is applied, and, consequently—

Consequently, today the length of a segment is regarded as real; tomorrow it is no longer reality, for the system of Lorentz transformations is being applied. In such a case the concept of reality ceases to correspond to the concept of objectivity. The variability of invariants in the historical process of cognition, or, to use M. Born’s language, the transformation of invariants in new theories into “projections,” positivists can use for a critique of the objective meaning of reality. There will be no grounds for this if invariants are considered not as a criterion and not as a sign of reality, but as what they in fact are—namely, as one of the elements of the image of objective reality, whose correctness must be proved by practice. The image of objective reality really does not remain unchanged; it is deepened as our knowledge develops, and this is what happens with invariants.

However, the image of objective reality is created not only from invariant quantities; along with invariants, noninvariant quantities also play their role in its creation—Born’s projections—those regarding which M. Born expresses regret that conservative thinking has left them their former name; they cannot be declared unreal merely because they are not invariant. The increasing mass of a proton in an accelerator is just as real as the rest mass; for it was precisely taking into account the real increase of this mass that compelled the construction of the synchrophasotron, in which it proved possible to obtain particles with energies one or two orders of magnitude higher than had been obtained before. When the mass of a fast-moving particle increases above a certain limit, the initial particle, under known conditions, may disintegrate and give rise to new particles (an avalanche process). These are entirely real processes, the regularity of which is expressed by the image of objective reality no less than by invariant quantities.

All this shows that the theory of invariants cannot serve as the foundation for an antipositivist interpretation of “physical reality.” The criterion for the existence of reality lies not in the sphere of mathematical formulas. In resolving the philosophical question, it is not formulas that will help, but an integral world-view that generalizes the results of the development of all fields of knowledge. This integral world-view is modern scientific materialism, which proceeds from the existence of the objective world. Consequently, positivist notions that reduce atoms and other physical objects to auxiliary concepts supposedly introduced by us for the purpose of ordering our perceptions can be criticized only from the standpoint of this integral world-view. This means that critics of positivism, if they wish to be consistent, must accept materialism’s understanding of objectivity, its interpretation of the relation between being and thought, its understanding of the process of cognition as a process in which the image of the object is formed in human consciousness, and must recognize practice as the criterion of the correctness of the images of reality we create.

But M. Born, apparently not by chance, seeks support against positivism in mathematical theories. He rejects not only the positivist interpretation of reality, which reduces the latter solely to our perceptions, to the situation in the apparatus; he also rejects materialism. As early as the aforementioned article of 1936, while criticizing positivism, M. Born at the same time wrote that “the time of materialism has passed.” He drew this conclusion on the grounds that modern science had proved the irreducibility of the regularities of the biological cell to the sum of the regularities of the atoms composing it. Thereby M. Born showed that he knows modern materialism no better than do W. Heisenberg, P. Jordan, and other critics of materialism. For only mechanistic materialism, long since superseded by life, stood on the position of “reduction”; dialectical materialism decisively rejects the reduction of the regularities of higher forms of the motion of matter to the regularities of the lower forms.

mechanistic materialism of the eighteenth century; already in the nineteenth century it degenerated into the current that K. Marx and F. Engels called “vulgar materialism.” As for modern, scientific materialism, it has never taken the position of ignoring the specific regularities inherent in complex formations. It is enough to recall the struggle of Marx and Engels against the epigones in political economy—Proudhon, Dühring, and others—against the notorious Dühringian “Robinsonade,” which sought to find the roots of the economic relations of capitalist society in the nature of individual people, in the relations between Robinson and Friday, in order to understand that the merit of scientific materialism lies in the profound disclosure of the fact that every complex formation possesses its own specific regularity. Marx and Engels substantiated historical materialism not by reference to the fact that society consists of material units—people—but by proving that in society there operate objective economic laws, specific to the given society and independent of people’s consciousness. The time of materialism has not passed, but has arrived; materialism, as a scientifically grounded worldview, was established more than a hundred years ago.

Already after the publication of the article “Physical Reality,” M. Born attempted to interpret the conception of reality he had presented there as directed against materialism. Thus, examining the reasons why A. Einstein diverged from the Copenhagen school in his assessment of the paths of development of physics, M. Born writes: “A. Einstein’s rejection of modern quantum physics is due not so much to the question of determinism as to his belief in the objective reality of physical being independently of the observer. Elsewhere I have shown that Einstein’s objections can be answered if one analyzes the concept of the reality of physical objects and at the same time makes appropriate use of the mathematical concept of invariance with respect to transformations” *).

It follows that modern quantum physics, which M. Born fully supports, is incompatible with belief in “the objective reality of physical being independently of the observer”; it follows that what brought A. Einstein into contradiction with modern physics was precisely his belief in objective reality. But what is the recognition of the objective reality of physical being, independently of the observer, if not materialism? M. Born wants to suggest to the reader that his interpretation of “physical reality,” in which he used “the mathematical concept of invariance,” differs from the objective reality of physical being independently of the observer (although, as we have seen, he proved the possibility of obtaining information “independent of the observer and his instrument”). It is difficult to escape the impression that, by this argument against Einstein, M. Born devalues his own critique of positivism.

We have seen that, in objecting to the subjectivist interpretation of reality, M. Born advanced many correct propositions. But, in developing his own interpretation of physical reality, he wants to rely on a formal criterion—the mathematical apparatus—and to set his position in opposition to materialist philosophy. This opposition, generally speaking, may be the result of a consciously pursued philosophical line; in that case we could recall the historical experience which shows that attempts to pursue a “third line” between materialism and idealism have never led to success. But it may also be the result of ignorance of modern scientific

) See Max Born, “Albert Einstein and Light Quanta,” lecture at the Berlin Physical Society, March 18, 1955, Uspekhi fizicheskikh nauk*, vol. LIX, no. 1, 1956, p. 131.

materialism, for which there is considerable evidence; in that case we could only regret the widespread misconceptions and the weakness of the propaganda of materialism in connection with the analysis of the results of contemporary physics.

Be that as it may, it seems to us that M. Born’s statements on the philosophical questions of physics show that not all representatives of the Copenhagen school are united in the desire to link the ideas of contemporary physics with positivism. And however imperfect M. Born’s attempt may be, it reveals to everyone what has long been obvious to materialists—namely, that it is possible and necessary, while preserving all the achievements of physical theory, to give the latter an anti-positivist interpretation.

In this lies the objective value of M. Born’s articles.