WERNER HEISENBERG AND THE SEMANTICS OF QUANTUM MECHANICS

            Werner Heisenberg (1901-1976) was born in Wurzburg, Germany, and studied physics at the University of Munich, where he wrote his doctoral dissertation under Arnold Sommerfeld in 1923 on a topic in hydrodynamics.  He became interested in Niels Bohr's atomic theory and went to the University of Gottingen to study under Max Born.  In 1924 he went to Bohr's Institute for Theoretical Physics in Copen­hagen, where he developed the quantum matrix mechanics in 1925, and then developed the uncertainty principle in 1927.  From 1927 to 1941 he was a professor of physics at the University of Leipzig.  In 1932 he was awarded the Nobel Memorial Prize for Physics.  In the Second World War, he was the director of the Kaiser Wilhelm Institute for Physics in Berlin.  After the war he established and became director of the Max Planck Institute of Physics initially at Gottingen, and then after 1958 at Munich.  His principal publications in which he set forth his philosophy of physics consist of the "Chicago Lectures of 1930" published as The Physical Princi­ples of the Quantum Theory (1950, [1930]), Philosophical Problems of Nuclear Science (1952) currently published under the title of Philosophical Problems of Quantum Theory (1971), The Physicist's Conception of Nature (1955), an interpretative history of physics, Physics and Philosophy: The Revolution in Modern Science (1958), his intellectual autobiography published as Physics and Beyond (1971), and Across the Frontiers (1974).
          Heisenberg's philosophy of science was not significantly influenced by the doctrines of professional philosophers, although he was a Positivist early in his career and later rendered Bohr's view of observation in neo-Kantian terms, even though neither he nor Bohr were metaphysical ide­alists.  The formative intellectual influences on his philosophy were Einstein and Bohr.  These two philosophical influences were contrary to each other, and each pulled Heisenberg's thinking in opposite directions.  Therefore, consider firstly the philosophical views of Einstein and Bohr.

Heisenberg's Discovery and Einstein's Semantical Views

          Reference was made above in the discussion of the phil­osophy of Mach, about the influence of Einstein's admonition on Heisenberg's development of the indeterminacy relations.  This episode in the history of science, which Heisenberg re­lates in "Quantum Mechanics and a Talk with Einstein (1925­-1926)" in Physics and Beyond, is a watershed event for the contemporary Pragmatist philosophy of science.  His description of his personal experience and thought processes deserve close examination.  Firstly he discusses why he had been led to believe that he could develop a quan­tum theory exclusively on the basis of observed magnitudes.  He writes that in the summer of 1924 he had attempted to guess the formula that might successfully describe the line intensities of the hydrogen spectrum using methods involving the idea of electron orbits, which he thought would be succes­sful in view of the previous work of Kramers in Copenhagen.  When use of these methods hit a dead end, he became convinced that he should ignore the idea of electron orbits.  He decided instead that he should treat the frequencies and amplitudes associated with the spectral line intensities as substi­tutes, because the line intensities are observable directly, while the electron orbits are not.  He was led to this approach because he recalled a conversation years earlier in which a friend told him that Einstein had emphasized the importance of observability in relativity theory.  In May of 1925 Heisenberg suffered a severe hay fever attack and had to absent himself from his academic duties.  While recuperating on the island of Heligoland he continued to work on the problem by considering nothing but observable magni­tudes, and during this period of isolation he developed his matrix mechanics.
          About a year later he was invited to give a lecture at the University of Berlin physics colloquium to present his matrix mechanics.  Einstein was in the assembly, and after the lecture he asked Heisenberg to discuss his views with him in his home that evening.  In that discussion Einstein argued that it is in principle impossible to base any theory on observable magnitudes alone, because in fact the very opposite occurs: it is the theory that decides what the physicist can observe.  He argued that when the physicist claims to have observed something new, he is actually saying that while he is about to formulate a new theory that does not agree with the old one, he nevertheless must assume that the new theory covers the path from the phenomenon to his consciousness and functions in a sufficiently adequate way, that he can rely on it and can speak of observations.  The claim to have intro­duced nothing but observable magnitudes is actually to have made an assumption about a property of the theory that the physicist is trying to formulate.  Heisenberg was thus using his idea of observation as if the old descriptive language could be left as it is.  Heisenberg replied that Einstein was using language a little too strictly, and that until there is a link between the mathematical quantum theory and the traditional language, physicists must speak of the path of an electron by asserting a contradiction, notably Bohr's complementarity.  Heisenberg also replied by referencing Mach's view that a good theory is no more than a condensation of observations in accordance with the principle of thought economy.  Ein­stein explained that Mach thought a theory combines complex sense impressions just as the word "ball” does for a child.  But he also stated that the combination is not merely a psychological simplification but is also an asser­tion that the ball really exists, because it makes asser­tions about possible sense impressions that may occur in the future.  Einstein thus affirmed a realistic philosophy, and criticized Mach for neglecting the fact that the real world exists, that our sense impressions are based on something objective, and that observation cannot be just a subjective experience.  Heisenberg accepted Einstein's realism on these grounds, and admitted that theory reveals genuine features of nature and not just of our knowledge.
          In the preface to Physics and Beyond Heisenberg states that conversations cannot be reconstructed literally after several decades, and that the book is not intended as a collection of memoirs.  But he notes that careful attention has been paid to the precise "atmosphere" in which the conversations took place, because in that conversational atmosphere the creative process of science is made manifest.  His book contributes to explaining how the cooperation of different people may culminate in scientific results of the utmost importance.  Heisenberg stated that his purpose is to convey even to readers who are remote from atomic physics, some idea of the mental processes that have gone into the genesis and devel­opment of science.  In a chapter titled "Fresh Fields (1926-1927)" Heisen­berg offers a description of his own mental processes in his development of the uncertainty relations.  To the contempor­ary reader this description has value apart from his philosophy.  Just as Newton attempted to philosophize about his work with his denial that he created hypotheses, so too did Heisenberg attempt to philosophize about his work in his own systematic and explicit philosophy of language, his doctrines of closed-off theories and of perception.  But the recollections of his cognitive experiences in "Fresh Fields" are not an attempt at a systematic philosophy; they are more simply his recollection of his own cognitive experien­ces as a central participant in the development of the quantum theory, and are valuable as a historical document.  As it happens, in the contemporary philosophical perspective these recollections are more valuable than his explicit attempt to philosophize on the nature of language and perception.
          These writings reveal that his development of the uncertainty relation was occasioned by several historical circumstances.   One of these that he discusses in "Fresh Fields" was the development of the wave mechanics by Schrödinger and its disturbing effects on the thinking of the physicists at Copenhagen.  The wave equation did not contain Planck's constant as did Heisenberg's matrix mechanics, while Planck's constant was thought by Bohr and the Copenhagen physicists to be central and necessary for any modern microphysical theory.  Then Max Born, formerly a teacher of Heisenberg, proposed a probability interpretation of the wave equation, such that for each point in space and instant in time the equation gives the probability of find­ing an electron at a given point and instant.  The upshot was that while neither the matrix mechanics nor the wave mechanics could be rejected for empirical reasons, they nevertheless seemed to be logically incompatible.  In addressing this problem Bohr and Heisenberg took different approaches.  Bohr attempted to admit simultaneously to the validity of both theories by maintaining that both the classical wave and the classical particle concepts used to describe the experimental observations are necessary for characterizing atomic processes, even though in the language of ordinary discourse and of classical physics, these two concepts are mutually exclusive.  This semantic inconsistency became Bohr's complementarity principle.  But Heisenberg relates that he did not like this approach, and that he wanted a “unique”, that is, a consistent and unequivocal physical interpretation of the magnitudes in the mathematical formal­ism, one that is derivable from the matrix mechanics by strict logic.  Heisenberg reports that this objective was one of the reasons that led him to derive the uncertainty relation.
          A second reason leading him to the uncertainty prin­ciple was the fact that neither the wave mechanics nor the matrix mechanics seemed capable of explaining the observed phenomenon of the trajectory of the electron in the Wilson cloud chamber.  Such ideas as trajectories and orbits do not figure in the mathematical formulations of the matrix mechanics, and the wave mechanics could only be reconciled with the existence of a densely packed beam of matter, if the beam spread over volumes that are much larger than the dimensions of an electron.  This problem of the observed phenomenon in the cloud chamber led Heisenberg to reform­ulate the questions he was asking himself in his statement of the problem; he attempted to relate the observed path of the electron in the cloud chamber to the mathematics of the matrix mechanics.  In February and March of 1927 Bohr was vacationing in Norway and Heisenberg was again alone with his thoughts, as he had been when he had first devel­oped the matrix mechanics.  At this time his attempt to relate the cloud chamber observations to the matrix mechanics bought to mind his discussion with Einstein the prior year in Berlin, and specifically Einstein's statement that it is the theory that decides what can be observed.  In "Fresh Fields" he describes his thinking processes when he attempted to employ Einstein's advice: Firstly he reconsidered the idea that what is observed in the cloud chamber is a trajectory.  The idea of a trajectory is a concept in Newtonian physics.  Therefore, when he thought that he was observing the trajectory of an election in the cloud chamber, the theory that was deciding what was being observed was the Newtonian theory, not his quantum theory.  Then secondly after reconsidering the Newtonian observations and recognizing that it is not necessary to think in Newton­ian terms, he viewed the phenomenon as merely a series of ill defined and discrete spots through which the electron had passed, somewhat like the water droplets which of course are much larger than the dimensions of the electron.  Then thirdly he reformulated his problem, and asked how quantum theory instead of Newtonian theory can represent the fact that an electron finds itself approximately in a given place and that it moves approximately with a given velocity.  Using Einstein's thesis that the theory decides what can be observed, Heisenberg concluded that the processes involved in any experiment or observation in microphysics must satisfy the laws of quantum theory.  The magnitude of the observed water droplets suggested room for approximation for the minute electron, and Heisenberg asked whether it is possible to make these approximations so close that they do not cause experimental difficulties.  He then derived the mathematics of the uncertainty principle in which the approximations are governed by a limit that is a function of Plank's constant.
          It may be noted parenthetically that Heisenberg's use of Einstein's thesis may be contrasted with Duhem's Positivist view.  Unlike earlier Positivists, Duhem admitted that theory has a valid place in science, but he did not view the concepts used for observation as dependent upon theory, as did Einstein.  Instead, Duhem maintained that while theory provides an interpretation for observation, observation without theory is not only possible but furthermore offers a certitude that theory cannot offer, because he viewed theoretical interpreta­tion as something added to fundamental and uninterpreted observation.  Thus, the characterization of the tracks in the cloud chamber as a series of water droplets would on Duhem's thesis be an example of an atheoretical and uninter­preted observation.  On Einstein's thesis, however, there is no observation without theory, and the characterization of the condensed track in the Wilson cloud chamber as a series of water droplets is no less interpreted than the characterization of the phenomenon by means of Newtonian or quantum theoretical concepts.  Even though the interpretation in terms of water droplets does not employ a mathematically expressed theory, the concepts of water droplet, of the cloud chamber, and even of the reflected light needed to view the water drop­lets in the cloud chamber, have built into them many hypo­theses, or as Einstein says "expectations", that are tacitly assumed in order to make the observations.
          Heisenberg had formulated his uncertainty principle by the time Bohr had returned to Copenhagen from his vacation in Norway.  Initially Bohr objected to the idea, while at the same time Heisenberg disliked the complementarity idea that Bohr had developed.  After several weeks of argument they finally agreed that the two approaches are related.  The uncertainty principle reconciles at the micro­physical level and in the mathematical formalism of quantum mechanics, what cannot be avoided yet what cannot be stated consistently in the language supplied by classical physics and ordinary language, which is suitable only to describe phenomena at the macrophysical level.  What is expressed consistently with the mathematical formalism of the uncertainty principle is the impossibility of measuring simultaneously both the position and the impulse of the electron with a degree of accuracy greater than the limit imposed by Planck's constant, a limit that is imposed by virtue of the nature of the microphysical phenomenon itself and not merely by the measurement technique.  What are des­cribed inconsistently at the macrophysical level and in the language of classical physics by means of complementarity, are the observable wave and particle manifestations of the unitary phenomenon.  This concession to Bohr was at variance to Heisenberg’s acceptance of Einstein’s semantical thesis that the theory decides what the physicist can observe.
          Heisenberg's description based on his own experience of the interpretative character of all perception and observa­tion and of the role of scientific theory in determining the interpretation, articulates one of the most characteristic features of the contemporary Pragmatist philosophy of sci­ence.  It is more valuable than Duhem's exemplification of the theoretical interpretation of the laboratory apparatus in the opening passages of the chapter titled "Experiment in Physics" in Aim and Structure of Physical Theory, not only because Duhem's explanation is Positivist, but also because Heisenberg's description of his experiences is given in the context of his development of the uncertainty principle, one of the most noteworthy achievements of twentieth-century theoretical physics.  As it happens, Heisenberg did not like Pragmatism, or at least the Pragmatism he encountered during his visit to the United States and described in "Atomic Physics and Pragmatism (1929)" in Physics and Beyond.  Even though his description of the interpretative character of perception and observation actually contributed to the con­temporary Pragmatism, Heisenberg himself was influenced by Bohr in ways that impeded his developing a philosophy of science that is consistent with Einstein's thesis that theory determines what is observed.  And this influence places Heisenberg's explicit philosophy of science closer to the Positivist philosophy than either Einstein's or the Pragmatists' views.  This influence of Bohr consisted of a naturalistic philosophy of the semantics of language, and the result is Heisenberg's neo-Kantian philosophy of perception and his doctrine of closed-off theories.

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