WERNER HEISENBERG AND THE SEMANTICS OF QUANTUM MECHANICS
BOOK IV - Page 2
Bohr's Influence on Heisenberg and Issues with Einstein
Niels Bohr was one of the leading atomic physicists of the first half of the twentieth century. He had studied in England under J.J. Thompson and Lord Rutherford, and received the Nobel Memorial Prize for Physics in 1922 for his theory of the structure of the atom. He founded the Copenhagen Institute for Theoretical Physics in 1920, and as its director was actively recruiting talented staff members, when he accepted an invitation to deliver a series of lectures on atomic physics at the University of Göttingen in the summer of 1922.
In “Quantum Theory and its Interpretation” in Niels Bohr (1963) Heisenberg reports that he first met Bohr at these Göttingen lectures, which he attended with his teacher, Arnold Sommerfeld. At the time Heisenberg was a twenty-two year old student at the University of Munich. Heisenberg came to Bohr’s attention, because in the discussions following one of the lectures, he dissented from Bohr’s optimistic assessment of a theory developed by Kramers at Copenhagen. Heisenberg relates that Bohr was sufficiently worried about the objection, that after the discussion he asked Heisenberg to take a walk with him for a conversation. During the walk Bohr talked about the fundamental physical and philosophical problems of modern atomic theory.
The encounter resulted in an invitation for Heisenberg to visit the Institute at Copenhagen for a few weeks, and later to hold a position. Heisenberg describes Bohr as primarily a philosopher rather than a physicist, and he states that he found Bohr’s philosophy to be fascinating, although he also states that he and Bohr had different views on the rôle of mathematics in physics.
Bohr’s philosophy of atomic physics is set forth in his Atomic Physics and the Description of Nature (1934), “Discussions with Einstein” in Albert Einstein (ed. Schilpp, 1949), Atomic Physics and Human Knowledge (1958), and Essays 1958/1962 on Atomic Physics and Human Knowledge (1963). Bohr’s philosophical views may have been influenced by some casual reading of the philosophical literature, but he never references any philosopher in his writings. His views seem largely to be the product of his own reflections on his research in atomic physics and on the work of his staff at Copenhagen. In “Quantum Theory and Its Interpretation” Heisenberg states that Bohr had developed views on the semantics of language and scientific theory many years before he met Bohr and before he developed his matrix mechanics.
Bohr’s mature philosophy of science included two theses: Firstly that the mathematical formalisms of microphysics cannot describe the microphysical domain that lies beyond ordinary experience. Secondly that the only language that is capable of a descriptive semantics is the language of ordinary discourse and its refinement in classical Newtonian physics. Heisenberg did not accept the first thesis, because he had a different concept about the abstract nature of mathematics. But Bohr’s second thesis had a lifelong influence on him, an influence that had a retarding effect on his development of his own philosophy of microphysics.
Bohr gives various reasons why in his view the mathematical formalisms of microphysics have no descriptive semantics and are only symbolic instruments for making calculations and predictions. One reason given in “Discussions with Einstein” is the occurrence of a complex number in the formalism. Apparently he believed that reality could be described only by equations having variables and parameters that admit only real numbers. Another reason given in “The Solvay Meetings and the Development of Quantum Theory” (1962) in his Essays 1958/1962 is the interpretation of the statistical wave function in a configuration space of more than four dimensions. Like Einstein, Bohr believed that real physical space-time has no more than four dimensions.
But the basic reason why Bohr interpreted the mathematical formalism of quantum theory instrumentally is his belief that only the language of everyday discourse and its refinement in classical physics can have descriptive semantics. He maintained that ordinary language and classical physics must be used to describe any experimental set up in physics, while at the same time he believed that classical physics is too limited to describe the microphysical domain beyond ordinary experience. It is limited not only because Newtonian physics is inadequate as a microphysical theory, but also due to the inherent nature of human cognitive perception. This is a philosophy of the semantics of language that is a naturalistic thesis. Due to Bohr’s philosophy of perception, Einstein as well as many philosophers of science were led to conclude that Bohr’s philosophy of science is positivist.
If Bohr’s philosophy of science is a positivist philosophy, it is a peculiar one. His statements of his philosophy that are most often referenced in this connection by philosophers of science are those in Atomic Physics and the Description of Nature. In the opening “Introductory Survey (1929)” he states that both relativity theory and quantum theory are concerned with physical laws that lie beyond ordinary experience, and which therefore present difficulties to our “accustomed forms of perception”. In quantum theory the limitations of these forms of perception are revealed by the need for complementary, the inconsistent Newtonian description of the quantum phenomenon as both a wave and a particle. Both of these two forms based on classical physics are necessary for a complete description, even though they are inconsistent in classical physics. Yet these “customary” forms of perception cannot be dispensed with, since all human cognitive experience must be expressed in terms of them. The fundamental concepts of classical physics therefore will never become superfluous for the description of physical experience; they must be used to describe experiments and to relate the mathematical symbolisms to the perceptions in experience.
In Einstein’s attack on Bohr’s philosophy of quantum theory the central issue is the ontology of the Copenhagen interpretation, which Einstein critiqued with his programmatic aim of all physics. The explicit criterion set forth in the programmatic aim of science is the “complete” description of any individual situation, as it supposedly exists irrespective of any act of observation or substantiation. Accordingly he characterized the Copenhagen interpretation as a version of Bishop Berkeley’s idealist thesis “esse est percipi”, a characterization that is not accurate, because Bohr did not maintain that the atomic phenomenon is produced by a cognitive process but rather by the physical processes of measurement in the experimental set up. In this matter Einstein seems to have confused an epistemological issue with a physical one.
But Bohr is not blameless for the confusion. For example in “Introductory Survey (1929)” he opens with statements emphasizing the subjectivity of all experience and the difficulties in distinguishing between phenomena and their observation; and he concludes the chapter with the statement that “to be” and “to know” lose their unambiguous meanings. From an epistemological viewpoint some of Bohr’s statements are ambiguous as to whether he is advancing a realist or an idealist philosophy. Some of Heisenberg’s earlier statements are also suggestive of an idealist position. For example he writes in the opening chapter of The Physicist’s Conception of Nature, that since we can no longer speak of the behavior of the particle independently of the process of observation, the natural laws formulated in the quantum theory no longer deal with the elementary particles themselves, but only with our knowledge of them. But later Heisenberg is very clear about avoiding any metaphysical idealism. In “The Copenhagen Interpretation of Quantum Theory” in Physics and Philosophy he states explicitly that quantum theory does not contain genuinely subjective features, since it does not introduce the mind of the physicist as part of the atomic event, and that the transition from possible to actual in the act of observation is in the physical and not the psychical act of observation.
Any metaphysical idealist/realist ambiguity notwithstanding, however, Einstein’s central ontological thesis is that the statistical quantum theory is incomplete in the sense that further theoretical research is necessary, in order to develop a complete theory that would give Heisenberg’s indeterminacy relations a status in future physics, which he thought should be analogous to the status had by statistical mechanics. It is noteworthy that Einstein admits the indeterminacy principle is not empirically incorrect, even as he rejects the Copenhagen nondeterministic ontology, because it does not conform to his explicit ontological criterion. In the 1949 “Reply to Criticisms” Einstein conceded that his incompleteness thesis is the minority view among physicists; many contemporary philosophers as well as physicists have accepted the indeterminacy thesis of the Copenhagen interpretation of the statistical quantum theory, and have rejected the deterministic ontology advocated by Einstein. When confronted with the dilemma of having to choose between an established ontological criterion and a new but empirically adequate quantum theory, both the contemporary physicists and the contemporary pragmatist philosophers of science opt for the latter, contrary to Einstein’s arguments for the former.
In addition to the ontological issue between Bohr and Einstein about what is physically real, there is also a related epistemological issue about the relation between sense perception and intellectual concepts. Einstein had portrayed Bohr as a positivist due to Bohr’s views about perception and the semantics of language. This portrayal is debatable, because positivists do not usually speak of what Bohr called “forms of perception”, and particularly about the limitations of such forms of perception for physics. But in his 1934 book Bohr writes of the necessity of these forms of perception for science to reduce our “sense impressions” to order. Even though Einstein himself uses the phrase “sense impressions” in his statement of the aim of science in “Physics and Reality” in 1936, he seems to have taken Bohr’s discussion referencing sense impressions to mean that there are no concepts or categories in perception.
Einstein opposed this view, and stated in 1949 in his “Reply to Criticisms” that thinking without positing categories and concepts is as impossible as breathing in a vacuum. He furthermore states that his philosophy differs from Kant’s since he does not view categories as unalterable and as predetermined by the faculty of understanding, but rather views them as “free conventions”. The philosopher of science may ask whether Einstein’s neo-Kantian views without Kant’s idealism and a priorism is still recognizably Kantian. But the point to be emphasized is that Einstein’s thesis that concepts are necessary for perception and that they are free conventions amounts to a restatement of what he told Heisenberg in 1926, when he said that theory decides what the physicist can observe. In this earlier statement Einstein might consistently have told Heisenberg that observation without theory is as impossible as breathing in a vacuum. Perhaps it was in response to Einstein’s criticisms in these matters that Bohr refrains in his later writings from using the phrase “sense impressions”. Instead Bohr merely describes the concepts of classical physics as a refinement of the concepts of ordinary discourse, so he is no longer misunderstood as saying that perception occurs without any concepts.
Nonetheless there is still a fundamental difference between the semantical views of Bohr and Einstein. Einstein’s thesis that concepts are free conventions is intended to mean that there are none of the inherent limitations in observation or in language that Bohr had maintained. In Bohr’s phrase “customary forms of perception”, the term “customary” does not mean the same thing as the term “convention” in Einstein’s phrase “free conventions”. The limitations that Bohr said these customary forms of perception impose on descriptive language are not temporary limitations, which will be removed with the change in language customs resulting from the further development of theory. Rather these limitations are inherent in the nature of the human cognitive processes of perception and consequently in the semantics of descriptive language. They are therefore permanent. There is no such permanence according to Einstein’s view; the free conventions of human thought, in the concepts and categories in language and scientific theory, are not only conventions that are free to change, but are destined to change with the advancement and further development of scientific theory. The difference between Bohr’s and Einstein’s semantical views is the difference between the naturalistic and the artifactual philosophies of the semantics of language.
Semantical Revision and Heisenberg’s Doctrine of Closed-off Theories
Heisenberg called quantum theory “closed”, while Einstein in contrast said it is “incomplete”. An earlier and a later version of Heisenberg’s semantical doctrine of “closed-off theories” may be distinguished. The earlier version is given in his “Questions of Principle in Modern Physics” originally given as a lecture at the University of Vienna in 1935 and since published in his Philosophical Problems of Quantum Physics, where he sets forth the central questions that are addressed by his philosophy of physics. He firstly asks how it is possible for there to have occurred the strange revision of the fundamental concepts of physics during the preceding thirty years. Then secondly he asks what is the truth content of classical physics and of modern physics in view of this conceptual revision. He notes that these are also the questions that were posed and discussed by Bohr, who approached them from the fundamental premises of quantum theory. It is noteworthy that Heisenberg’s philosophy of science addresses questions formulated by Bohr. The formulation of the questions in terms of how a conceptual revision is possible suggests a naturalistic philosophy of the semantics of language as a point of departure, since on the artifactual thesis the possibility of a fundamental semantical revision is not problematic. When concepts and meanings are understood to be cultural artifacts, then semantical change may be expected as a matter of course.
As it happens, in his doctrine of closed-off theories Heisenberg did not depart very far from the naturalistic thesis. He developed a theory of semantical revision, but it is also a theory of semantical permanence. Heisenberg has an earlier and a later version of his doctrine of closed-off theories. In the earlier 1935 version he maintains that classical physics is permanently valid, and that its concepts are necessary for experimentation in physics. He states that classical physics is based on a system of mathematically concise axioms, whose physical content is fixed by the choice of words used in them. These words determine unequivocally the application of the system of axioms to nature. Wherever concepts like mass, velocity and force can be applied, there Newton’s law, F=ma, will be true. The validity of the claim of this law is comparable to Archimedes law of the simple lever, which today forms the theoretical basis for all load-raising machines, and which will be true for all time. Therefore in spite of the fact that there has been a revision of mechanics, the axiomatic system developed by Newton is still valid. The revision pertains to the limits encountered in the application of the axiomatized system of concepts of classical physics; it is not the validity but only the applicability of classical laws that has come to be restricted by relativity theory and quantum theory.
Having thus described how he believes that the axiomatized mathematical system of classical physics is permanently valid, Heisenberg then describes how revision is possible. The revision of classical physics is possible due to a “lack of precision” in the concepts used in the system. While the quantitative variables x, t, and m used in the Newtonian system are linked without ambiguity by the system of equations, which contain no degree of freedom apart from initial conditions, the words “space”, “time”, and “mass”, which are attributed to those quantities are tainted with all the lack of precision that may be found in their everyday use. The validity of classical physics is limited by the lack of precision of the concepts contained in its axioms. As a result of this lack of precision science may be forced into a revision of its concepts as soon as it leaves the field of common experience; the concepts currently used may lose their value for the orderly presentation of new experience. But this revision cannot be known in advance.
He notes for example that before the experiences of quantum theory the results of the Wilson cloud chamber experiments could unhesitatingly be expressed as “we see in the cloud chamber that the electron has described such and such a path”, and this simple description could be accepted as an experimental fact. It was only later that physicists came to know from other experiments the problematic nature of the phrase “path of an electron”. Scientific progress consists initially in the unhesitating use of existing terms for the description of experience, and then subsequently in the revision of those terms as demanded by new experience. The lack of precision contained in the systems of concepts of classical physics is necessary, and therefore even the mathematically exact sections of physics represent only tentative efforts to find our way among a wealth of phenomena.
Central to the doctrine of closed-off theories is the thesis that classical concepts must be retained for experimentation in physics. So far as the concepts of space, velocity and mass can be applied unhesitatingly, as in everyday experiences, Newtonian principles still apply. The Newtonian laws represent an “idealization” achieved by taking into account only those parts of experience that can be ordered by the concepts of space, time and mass on the assumption of objective events in time and space. Therefore they always remain the basis for any exact and objective science. Since we demand of the results of science that they can be objectively demonstrated, we are forced to express these results in the language of classical physics. For example for an understanding of relativity theory, it is necessary to stress that the validity of Euclidian geometry is presupposed in the instruments that are used to show the deviation from Euclidian geometry, i.e., the measure of the deviation of light (an apparent reference to Eddington’s 1919-eclipse experiment to test relativity theory). Furthermore the very methods used for the manufacture of these instruments enforce the validity of Euclid’s geometry for these instruments within the range of their accuracy. Similarly we must be able to speak without hesitation of objective events in time and space in any discussion of experiments in atomic physics. Heisenberg concludes that while the laws of classical physics seen in the light of modern physics appear only as limiting cases of more general and abstract connections, the concepts associated with these laws remain an indispensable part of the language of science, without which it is not possible even to speak of scientific results. Therefore, while mathematically exact sections of classical physics are tentative, the classical concepts must nevertheless be used for the description of experiments.
Heisenberg offers a later version of his doctrine of closed-off theories in several later articles and chapters in his books. In his earlier version meanings found in everyday words, which are associated with variables in mathematically expressed axiomatic systems of physical theories, retain their vagueness in Newtonian physical theory. In his later version association of the vague everyday meanings with the terms in the axiomatic system resolves their vagueness, because the axiomatic systems have a definitional function. This development represents his transition to context-determined relativized semantics, where the relevant context is the axiomatic system of a physical theory.
In “The Notion of a ‘Closed Theory’ in Modern Science” in Across the Frontiers he discusses the criteria for scientific criticism and the evolution of the aim of science. He writes that when Einstein developed his special theory of relativity, it was evident that Maxwell’s theory of electromagnetic phenomena could not be traced back to mechanical processes that obey Newton’s laws, and the inference seemed unavoidable that either Newtonian mechanics or Maxwell’s theory must be false. Physicists concluded that Newton’s theory is strictly speaking false. This mislead many scientists into unwittingly attempting to describe the phenomena of the world exclusively by means of the concepts of field theory. This represented an aim of science that is commonly accepted from Newton’s theory that science should proceed by means of a unitary conceptual scheme, except that now the concepts should be those of field theory instead of classical mechanics.
But in both cases the concepts supplied an objective and causal description of the process involved, and were therefore thought to be universal. These common concepts were rejected by quantum theory for the description of the atom, although they must still be used to describe the results of an observation while standing in a complementary relation to one another. Thus Heisenberg concludes that physicists no longer say that Newton mechanics is false and must be replaced by quantum mechanics which is correct. Instead they say that classical mechanics is a consistent self enclosed scientific theory, and that it is a strictly true and correct description of nature, whenever its concepts can be applied. Quantum theory has only restricted the applicability of Newtonian mechanics, and has made classical physics a “closed-off” theory. Heisenberg says that in contemporary physics there are four great disciplines that have closed-off theories. They are firstly Newtonian mechanics, secondly Maxwell’s theory and special relativity, thirdly the theory of heat and statistical mechanics, and fourthly nonrelativistic quantum mechanics, atomic physics and chemistry. General relativity is not yet closed off.
Heisenberg then turns to a discussion of the properties of a closed-off theory and of its truth content. A closed-off theory is consistent as an axiomatized mathematical system. The most celebrated example is Newton’s Principia Mathematica. And the concepts of the theory must be directly anchored in experience. Before the axiomatic system is developed, concepts describing everyday life remain firmly linked to the phenomena and change with them; they are compliant toward nature. But when they are axiomatized, they become rigid, and they “detach” themselves from experience. This is the distinctive aspect of his later version of the doctrine of closed-off theories. The system of concepts rendered precise by axioms is still very well adapted to a wide range of experiences, but axiomitization of concepts sets a decisive limit to their field of application. The discovery of these limits is part of the development of physics. Yet even when the boundaries of the closed theory have been encountered and overstepped, and when new areas of experience are ordered by means of new concepts, the conceptual scheme of the closed theory still forms an indispensable part of the language in which the physicist speaks of nature. The closed theory is among the presuppositions of the wider inquiry; we can express the result of an experiment only in the concepts of earlier closed theories. Heisenberg summarizes the properties of closed-off theories as follows: Firstly the closed-off theory holds true for all time. Whenever experience can be described by the concepts of the closed-off theory, even in the most distant future, the laws of this theory will always be correct. Secondly the closed-off theory contains no perfectly certain statements about the world of experiences; its successes are contingent. Thirdly even with the indeterminacy of its contingency, the closed-off theory remains a part of scientific language, and therefore is an integrating constituent of our current understanding of the world.
Heisenberg sees the evolution of modern science differently than Einstein’s description in “Physics and Reality”. Heisenberg says the historical process that gave rise to the whole of modern physics since the conclusion of the Middle Ages, consists in a succession of intellectual constructs, which take shape as if from a “crystal nucleus”, out of individual queries raised out of experience, and which eventually once the complete crystal has developed, again detach themselves from experience as purely intellectual structures that forever illuminate the world for us as closed-off theories. Thus the history of science is like the history of art, where the goal is to illuminate the world by means of intellectual constructs. In his “The End of Physics” in Across the Frontiers he adds that while physics consist of many closed-off systems, it is not possible to close off physics as a whole. Today it is necessary to seek out new and still more comprehensive closed-off theories or “idealizations” as he also calls them, which will include both relativity theory and quantum theory as limiting cases.
Closely related to his thesis of closed-off theories is Heisenberg’s theory of abstraction. In “Abstraction in Modern Science” in Across the Frontiers he defines abstraction as the consideration of an object or a group of objects under one viewpoint while disregarding all other properties of the object. All concept formation depends on abstraction, since it presupposes the ability to recognize similarities. Primitive mathematics developed from abstraction, e.g., the concept of the number three. Mathematics has formed new and more comprehensive concepts, and thereby ascended to ever higher levels of abstraction. The realm of numbers was extended to include the irrational and complex numbers. This view is quite different from Bohr’s, who believed that the mathematical formalisms used in physics have no descriptive semantical value but are merely symbolic, i.e., semantically vacuous, instruments for calculation and prediction, particularly if they contain complex numbers or represent more than four dimensions as in quantum theory. In Heisenberg’s philosophy abstraction, the consideration of the real from a selective viewpoint, produces idealizations of reality which are axiomatic mathematical structures that become closed-off, as the historical development of science reveals the limitations of their applicability and occasions the creation of new theories.
In expounding his semantical doctrine of closed-off theories Heisenberg departed from Bohr. Comparison of their views reveals essential similarities, but it also reveals differences. Bohr’s semantical views are stated in “Discussions with Einstein” where he says that Planck’s discovery of the quantum of action makes classical physics an “idealization” that can be unambiguously applied only in the limit, where all actions involved are large in comparison with the quantum. A more elaborate statement is given in “The Solvay Meetings” in Essays 1958/1962. There he firstly says that unambiguous communication of physical evidence demands that the experimental arrangement and the reading of observations be expressed in common language suitably refined by the vocabulary of classical physics. Then secondly he states that in all experimentation this demand is fulfilled by using as measuring instruments bodies like diaphragms, lenses, and photographic plates, which are so large and heavy that notwithstanding the decisive rôle of the quantum for stability and properties of such bodies, all quantum effects can be disregarded in the account of their position and motion. Finally and thirdly he says that in classical physics we are dealing with an idealization according to which all phenomena can be arbitrarily subdivided, and all interaction between measuring instruments and the object under investigation can be neglected or compensated for. Bohr seems to be using the term “idealization” as Heisenberg does, but he reserves it for the classical physics. Bohr does not admit a separate set of distinctively quantum concepts, because he maintains an instrumentalist interpretation of the quantum theory mathematical formalism. In his view there are no quantum concepts defined by the equations of the quantum theory, but rather there are only classical concepts, while the semantically uninterpreted mathematical formalism generates predictions expressed in classical terms.