WERNER HEISENBERG AND THE SEMANTICS OF QUANTUM MECHANICS

Semantical Revision and Heisenberg’s Doctrine of Closed-off Theories

          Heisenberg's response to the conflicting influences of Einstein and Bohr was his doctrine of closed-off theories.  An earlier and a later version of his semantical doctrine 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, 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.  His mature philosophy of science is not Positivist, but 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 classical 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.  The experiences that provide the basis of relativity theory have demonstrated that the simple concept of time in Newton's mechanics ceases to be of use, when dealing with bodies moving with a velocity approaching that of light.  Similarly in microphysics classical mechanics can predict the correct track of the electron in the Wilson cloud chamber.  But if without observation of its track the electron is reflected at a diffraction grating, the basis for an unam­biguous application of the space-velocity concept disap­pears, and classical laws cannot be applied to such a process.
          Having thus described how 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 the 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.  For example 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.
          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 sunlight [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 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 the earlier version meanings found in ordinary-language words, which are associated with variables in mathematically expressed axiomatic systems of physical theories, retain their vagueness in Newtonian physical theory.  In his latter version association of the vague meanings with the terms in the axiomatic system resolves the vagueness, because the axiomatic systems have a definitional function.  This development represents his transition to a context-determined semantics, where the relevant context is the axiomatic system of a physical theory.  Consider firstly Heisenberg’s earlier version of his semantical metatheory: 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.  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 misleads 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 physicists no longer say that Newton mechanics is false and must be replaced by quantum mechan­ics which is correct.  Instead it is said 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 are 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.  He says that 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 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.
          A comment may be interjected here about the later version of closed-off theories: Heisenberg’s purported historical and operational continuity between everyday and classical concepts seems motivated by his agenda of making classical physics a permanently valid observation language, and so explains why he does not distinguish everyday concepts from classical concepts in most other passages in his literary corpus.  But in his exposition of his later version of his doctrine of closed-off theories, he distinguishes the everyday and the classical types of concepts.  The classical concepts are those defined by the context of the classical axiomatic system, while the everyday concepts are not defined by this context, but instead have a vagueness and “lack of precision” that makes their semantics silent about other concepts to which they could be but are not related in an axiomatic system such as Newtonian or quantum physics, a vagueness that enables them to be “compliant toward nature”.  On the Pragmatist thesis of the contextual determination of meaning, both the everyday and classical concepts have both vagueness and defining contexts.  But these concepts differ in that the former’s context lacks the higher degree of clarity supplied by the context constituting the axiomatic deductive system of a physical theory that is had by the latter.  The continuity between classical and quantum concepts, such that on Heisenberg’s view the latter presuppose the former for observation, is more problematic since the two types of concepts are not in logically consistent axiomatic systems, but rather are on opposite sides of the schism in physics. But on the Pragmatist view the everyday, classical, and quantum concepts share component parts that make them relevant to the same subject.  The everyday concepts are simply those that are vague, because they do not contain any of the mutually exclusive and inconsistent parts not shared by the classical and quantum concepts in their respective axiomatic systems.
          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 uncertainty 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".  The historical processes that have given rise to the whole of modern physics since the conclusion of the Middle Ages, is a developmental process consisting of 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 role 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.  He does not admit a separate set of distinctively quantum concepts, because he maintains an instrumentalist interpretation of the quantum theory formalism.   In his view there are no quantum concepts defined by the equations of the quantum theory, but rather there are only classical concepts and the semantically uninterpreted mathematical formalism used for generating predictions expressed in classical terms.

Bohr's "Forms of Perception" and Neo-Kantianism

          Having based his doctrine of closed-off theories on Bohr's philosophy of observation, Heisenberg attempted to relate Bohr's philosophy to the history of philosophy, and specifically to that of Kant.  Heisenberg's statements are found in his "Recent Changes in the Foundations of Exact Science" (1934) in Philosophical Problems of Quantum Phys­ics, in his "The Development of Philosophical Ideas Since Descartes in Comparison with the New Situation in Quantum Theory" in Physics and Philosophy, in his "Quantum Physics and Kantian Philosophy (1930-1932)" in Physics and Beyond, and in his "Planck's Discovery and the Philosophical Prob­lems of Atomic Theory" in Across the Frontiers.  Like Ein­stein, Heisenberg rejects the Positivist phenomenalism and advocates realism; he was never a metaphysical Idealist.  In "Planck's Discovery" he states that quantum theory does not consider sense impressions to be the primary given, and that if anything is the primary given in quantum theory, it is the reality described with the concepts of classical physics.  And in "Development of Philosophical Ideas Since Descartes" he describes his realistic variation on Kant's views with the phrase "practical real­ism", since in Heisenberg's view things rather than percep­tions are the given for the human mind.
          But while Heisenberg is opposed to Positivism as much as Einstein, his referencing the philosophy of Kant is not motivated by his anti-Positivism.  Heisenberg is interested merely in relating Kantianism to the philosophy of observation he took from Bohr and incorporated in his doctrine of closed-off theories.  In "Recent Changes in the Foundations of Exact Science" he says that in the field of philosophy of perception, Kant's philosophy has been put into a new light as a result of the critique of absolute time and Euclidian space by relativity theory and by the critique of the law of causality by quantum theory, and that the question of the priority of the forms of perception and of the cate­gories of the understanding must be reconsidered.  He states that there are two apparently contradictory propositions that must be reconciled: On the one hand relativity theory and quantum theory have shown that our space-time forms of perception and the category of causality are not independent of all experience in the sense that they must for all time remain essential constituents of every physical theory.  On the other hand, as Bohr taught, the applicability of the classical (i.e. Kantian) forms of perception and the law of causality are the premises of every objective experience even for modern physics.  The physicist can only communicate the course of an experiment and the result of a measurement by describing the necessary manual operations and instrument readings as objective events taking place in the space and time known to our intuition.  And he could not infer the properties of the observed object from the result of measurement, unless the law of causality guaranteed an unambiguous connection between measurement and object.  Heisenberg resolves the contradiction between the two statements as follows: Physical theories can have a structure differing from classical physics, only when their aims are no longer those of immedi­ate sense perception; that is to say, only when they leave the field of common experience dominated by classical physics.   In "Quantum Physics and Kantian Philosophy" Heisenberg views Kant's philosophy of perception as a closed-off theory, as he elsewhere describes closed-off theories in physics.  He compares the validity of Kant's philosophy to the validity of Archimedes' theory of the lever, and he states that Kant's theory is eternally true, just as Archi­medes' theory is eternally true.   Kant's analysis of perception represents true knowledge that applies wherever thinking beings enter into the kind of contact with their environment called "experience".  Relativity theory and quantum theory have defined the limits of the a priori in the exact sciences in ways that could not have been known to Kant.  The a priori has not been eliminated from physics, and Kant's analysis of how we come by our experiences is essentially correct.  But the a priori has become "relativised" in the sense that classical concepts are a priori conditions for relativity and quantum theory, since clas­sical concepts are necessary for experiments.  Remarkably Heisenberg says that the progress of science has changed the structure of human thought, and has taught us the meaning of "understand­ing".  In the closing paragraph of his "Quantum Physics and Kantian Philosophy" Heisenberg states that he has described the relationship between Kant's philosophy and modern physics from the perspective of Bohr's teachings.
          The impor­tance of Heisenberg's discussion of Kant is that it treats the philosophy of perception.  And the philosophy of percep­tion in turn is important because it often serves as a phil­osophy of observation in philosophy of science and epistem­ology.  In the context of the philosophy of modern physics the central problem is the semantics of modern physical theory.  On the one hand where the semantics of the language of physics is said to be supplied by observation and percep­tion, the traditional assumption is that perception is a natural cognitive process that predetermines the semantical content of language in an invariant, objective, and atemporal manner.  On the other hand the history of science is a history of change of theory, which involves semantical change that is not easily reconciled with such a view of per­ception.  Traditional philosophy of perception suggests a naturalistic philosophy of the semantics of language, while history of science suggests an artifactual philosophy of semantics.  In anticipation of the discussions to follow about the views of other philosophers, it may be said that contempor­ary philosophers have addressed this semantical issue and specifically the topic of perception in a different manner than did Heisenberg or Bohr, or for that matter most earlier philosophers.  Unquestionably there are limitations to what can be perceived; there are objects that are too small to be seen with the human eye, there are sounds that are pitched too high to be heard by the human ear, etc.  Yet observation is permeated with learned ideas, permeated with interpreta­tion, such that it has variability, subjectivity, and historicity that are not invariably associated with the outcomes of the functioning of our natural faculties for per­ception.  The Pragmatist philosopher of science, Hanson, addressed this difficult mixture of nature and cul­ture in knowledge by reconsidering the concept of perception in observation.  Hanson's answer is the same as Einstein's admonition to Heisenberg, that theory decides what the phys­icist can observe.  But Hei­senberg does not consider this view in his discussion of his doctrine of closed-off theories or in his discussion of Kant, notwithstanding that he used it for his development of the indeterminacy relations.  On the other hand a theory of knowledge based on per­ception is sometimes called a "psychologistic" theory of knowledge, and some philosophers object to psychologism, even when the particular psychologistic position advocated does not assert that the laws of logic are "laws of thought" in the sense of psychological laws.  The notable contempor­ary example is the philosopher of science Karl Popper, who rejects psychologism, and separates observation from perception with his distinction between "world two", the domain of subjective psychology including perception, and "world three', the domain of objective knowledge including observation.  In this way Popper separates the roles of nature and culture, so that following Einstein, who said that theory decides what we can observe, Popper says that there is no observation without theory.  The contemporary philosophers of science agree that knowledge is not predetermined by nature.  Thus they depart not only from Kant and the Posi­tivists but also from Bohr, Heisenberg and the other Copenhagen physicists.

Pages [1] [2] [3] [4] [5] [6]
NOTE: Pages do not corresponds with the actual pages from the book