WERNER HEISENBERG AND THE SEMANTICS OF QUANTUM MECHANICS

Heisenberg's Discovery and Einstein's Ontological Criteria

          An ontology consists of those entities and aspects of the real world that are described by the semantics of a discourse, such as a scientific theory, which is believed to be true.  Unlike Bohr, who took an instrumentalist view of the equations of the quantum theory, Heisenberg believed that quantum theory has an ontology, that is, that the equations constituting the language of the theory describe aspects of the real world.  And he maintained that the ontology of quantum theory includes the Copenhagen duality thesis, the thesis that wave and particle are two aspects of the same physical entity, and are not two separate physical entities.  Initially, however, his ontological views were not based in the language of the mathematically expressed quantum theory, but were based in the ordinary everyday language that can be used to express experimental findings.  In the opening sentence of the “Introductory” chapter of his Physical Principles of the Quantum Theory (1930), a book based on lectures he gave at the University of Chicago in the Spring of 1929, Heisenberg says that the experiments of physics and their results can be described in the language of daily life.  He adds that if the physicist did not demand a theory to explain his results and could be content with a description of the lines appearing on photographic plates, then everything would be simple and there would be no need for an epistemological discussion.  He states that difficulties arise only in the attempt to classify and synthesize the results, to establish the relations of cause and effect between them - in short, to construct a theory.  The concept of everyday language appears again later in Heisenberg’s doctrine of closed-off theories. 
          No contemporary Pragmatist would accept the Positivist thesis that there is any completely nontheoretical or pretheoretical observation language.  With an adequate metatheory of semantical description the Pragmatist philosopher maintains that the everyday observational description, which is part of the test design language used in experiments, is sufficiently vague that it neither affirms nor denies any specific microphysical theory proposed for testing.  But in his Physical Principles Heisenberg is not thinking of the vagueness of everyday language.  Here he wishes to argue that the everyday description of certain experimental findings implies the Copenhagen ontology, and he proceeds to give a brief description of several experiments which show that both matter and radiation sometimes exhibit the properties of waves and at other times exhibit the properties of particles.  He notes that it might be postulated that two separate entities, one having all the properties of a particle and the other having all the properties of wave motion, are combined in some way to form light.  But he then adds that such a theory is unable to bring about the “intimate relation” between the two entities, which seems required by the experimental evidence.  He argues that both light and matter are single entities, and that the apparent duality, the properties of wave and particle, arises in the limitations of our language.  This thesis of the limitations of language reveals the influence of Bohr’s philosophy.            Other physicists such as de Broglie, Einstein, and Bohm did not agree with Heisenberg’s view that there is any such compelling experimental evidence for the Copenhagen ontology.  Both philosophers and scientists have had different ontological commitments, because they hold different criteria for determining which among alternative descriptive discourses is true, and more fundamentally because they maintain different philosophies of language. 
          It may be said that Einstein had two different onto­logical criteria for physics, one explicitly set forth by him, and another that he tacitly used and which therefore may be called his implicit criterion.  In Newtonian physics and in relativity theory these two different criteria are not easily distinguished, because in each case they yield similar ontologies, but in quantum theory they yield funda­mentally different ontologies.  Einstein's explicit ontological criterion for deciding what is physically real is set forth in his "Can Quantum Mechanical Description of Physical Reality be Considered Complete?" in Physical Review (1935), in his "Physics and Reality" in The Journal of the Franklin Institute (1936), and in his "Reply to Criticisms" in Albert Einstein (ed. Schilpp, 1949).  There are several statements.  One that he sets forth as his "programmatic aim of all physics" is his criterion of logical simplicity, which he sets forth as the aim of science: The aim of science in Einstein's view is a comprehension as complete as possible of the connec­tions among sense impressions in their totality, and the accomplishment of this aim by the use of a minimum of primary concepts and relations.  He goes on to say that the essential thing about the aim of science is to represent the multitude of concepts and theorems close to experience as theorems logically deduced from and belonging to a basis, as nar­row as possible, of axioms and fundamental concepts, which themselves can be chosen freely.  Thus the aim of science is the logical unity of the world picture.  Einstein interprets the history of physics as an evolution under the direction of this aim of science.  This criterion requires that microphysical and macrophysical theories affirm one single con­sistent ontology, and use the same basic concepts of what is physically real.  He also says that the conviction that field theory is unable to give a solution to the molecular structure of matter and to the quantum phenomenon, is a false prejudice.  He demands that the ontology of field theory supply the uniform fundamental ontology, and he uses this explicit ontological criterion to criticize the Copenhagen statistical interpre­tation of quantum physics.
          In a famous article titled "Can Quantum Mechanical Description of Physical Reality be Considered Complete?" in Physical Review co-authored with Podol­sky and Rosen, Einstein describes the Copenhagen interpretation as "incomplete".  By this he meant that further research is needed to make quantum theory consistent with the ontology of field physics, the ontology of deterministic causality and of the physical continuum in four dimensions.  The argu­ment in this paper, often called the "EPR argument" after the three co-authors, includes a thought experiment, which is based on explicit criteria for completeness and for physical reality.  The completeness criterion says that a physical theory is complete only if every element of the physical reality has a counterpart in the physical theory.  The criterion for physical reality is that if without in any way disturbing a system, one can predict with certainty the value of a physi­cal quantity, then there exists an element of physical real­ity corresponding to this physical quantity.  This criter­ion's reference to independence of any act of observation is repeated in a later statement of the programmatic aim of all physics in "Remarks" in Schilpp’s Albert Einstein.  The thought exper­iment in the EPR argument attempts to demonstrate that the quantum theory's satisfaction of the reality criterion does not result in satisfaction of the completeness criterion.
          The stated criteria for completeness and for physical reality are defined such that field theory satisfies both criteria while quantum theory does not.  The point of departure, the basic premises of the argument, is Einstein's ontological preferences.  In an article with the same title also appearing in Albert Einstein Bohr argued that the phrase "without in any way disturbing a system" in Einstein's criterion for physical reality is ambiguous, because its meaning in classical physics is not the same as that in quantum physics.  Bohr maintained that in quantum measurements the object measured and the observing apparatus form a single indivisible system that defies any further analysis at the quantum level.  A large literature developed around the technicalities of the physical thought experiment, but in practice the physicists chose their ontological premises according to their preferences about the ontological conclusions, depending on whether one agreed or disagreed about Einstein's view that quantum theory must have the same ontology as field physics.   And for most of the following half century the preferred conclusion was the Copenhagen interpretation of the quantum theory.
          On the other hand Einstein's implicit ontological criterion was operative in his development of the special theory of relativity.  This criterion (stated explicitly) is that the empirically adequate scientific theory must be interpreted realistically.  Unlike Einstein’s explicit criterion, which subordinates a scientific theory and its interpreta­tion to a preconceived ontology, the implicit criterion sub­ordinates ontological commitment to the outcome of empirical scientific criticism.  And Heisenberg applied this same ontological criterion to the mathematical expressions of the quantum theory to defend the Copenhagen dualistic ontology against Ein­stein's criticism based on the latter's explicit ontological criterion for physical reality.  In this defense based on the mathematical language of the quantum theory instead of the everyday language of the microphysical experiments, Heisenberg referenced Einstein's real­istic interpretation of the Lorentz transformation equation.  In his discussions about Einstein's special theory of rela­tivity in Physics and Philosophy and in Across the Frontiers Heisenberg describes as the "decisive" step in the develop­ment of special relativity, Einstein's rejection of Lor­entz's distinction between "apparent time" and "actual time" in the interpretation of the Lorentz transformation equa­tion, and Einstein's taking "apparent time" to be physically real time, while rejecting the Newtonian concept of absolute time as real time.  In other words this decisive step consisted of taking the Lorentz transformation equation realistically, and of letting it define the ontology of the physi­cally real due to its empirical adequacy.
          Nowhere does Heisenberg write that he was consciously imitating Einstein at the time Heisenberg devel­oped the uncertainty relations.  But in "History of Quan­tum Theory" in Physics and Philosophy he describes his use of the same strategy.  In this description of his thought processes Heisenberg does not refer to his conversation with Einstein in Berlin in 1926.  He states that his thinking in the discovery experience of the uncertainty principle consisted of turning around a question.  Instead of asking himself how one can express in the Newtonian mathematical scheme a given experimental situation, notably the Wilson cloud chamber experiment, he asked whether only such experimental situations can arise in nature as can be described in the formalism of the matrix mechanics.  The new question is a question about what can arise or exist in reality.  Later in "Remarks on the Origin of the Relations of Uncertainty” in The Uncertainty Principle and Foundations of Quantum Mechanics (p. 42.) he explicitly states that this meant that there was not a Newtonian path of the electron in the cloud cham­ber.  Heisenberg's strategic answer to the new question, the uncertainty relation, resulted from this realistic inter­pretation of the quantum theory.  Similar remarks are to be found in "The Development of the Interpretation of the Quantum Theory" in Pauli's Niels Bohr and the Development of Physics (1955, p. 15) where Heisenberg says that he inverted the question of how to pass from an experimentally given situation to its mathematical represen­tation, by using the hypothesis that only those states which can be represented as vectors in Hilbert space can occur in nature and be realized experimentally.  And he immediately adds that this method of solution had its prototype in Einstein's special theory of relativity, when Einstein had removed the difficulties of electrodynamics by saying that the apparent time of the Lorentz transformation was the real time, that similarly it is now assumed in quantum mechanics that real states can always be represented as vectors in Hilbert space (or as mixtures of such vectors), and that the uncertainty principle is the simple expression for this assumption.
          If at the time that he developed the uncertainty prin­ciple, Heisenberg was not consciously imitating the disco­very strategy that Einstein used for development of special relativity, it is nevertheless not difficult to imagine how Heisenberg hit upon it independently.  For the realist it is a small step from Einstein's semantical thesis that it is the theory that decides what can be observed, to the onto­logical thesis that it is the theory that decides what is physically real, where the theory in question is empirically warranted, as was his matrix mechanics.  This strategy in which the empirical adequacy of a scientific theory as revealed by scientific criticism decides the ontology to be accepted, is a reversal of the more traditional relation in which cur­rently accepted ontological and metaphysical views are included among the criteria for scientific criticism, and operate prior to empirical criticism.  Heisenberg's approach is similar to the contemporary Pragmatist thesis of scientific realism.  Heisenberg explicitly compares his realistic interpre­tation of the statistical quantum theory to Einstein's real­istic interpretation of the Lorentz transformation equation, when he defends the ontology of his Copenhagen interpreta­tion against Einstein's explicit ontological criterion for physical reality.  In his "Criticism and Counter-proposals to the Copenhagen Interpretation of Quantum Theory" in Physics and Philosophy he characterizes the ontology advanced explicitly by Einstein as the ontology of "materialism", which he says rests upon the “illusion” that the kind of existence familiar to us, the direct actuality of the world around us, can be extrapolated into the atomic order of magnitude.  In the closing paragraphs of this chapter of his book he states that all counterproposals offered in opposition to the Copenhagen interpretation must sacrifice what he calls the symmetry properties of the quan­tum theory, namely the wave-particle symmetry and the position-momentum symmetry.  He explicitly states that like Lorentz invariance in the theory of relativity, the Copen­hagen interpretation cannot be avoided, if these symmetries are held to be genuine features of nature.
          However, there is an ambiguity in Heisenberg’s practice of scientific realism.  The position-momentum symmetry that he construes realistically is clearly expressed by the indeterminacy relations.  But the wave-particle symmetry of the Copenhagen interpretation is that the wave and particle are dual alternative manifestations of the same entity.  This thesis cannot be affirmed on the basis of the mathematically expressed quantum theory, because descriptive language having mathematics for its grammar does not have the syntactical categories for expressing reference to entities. Statements referencing entities, such as Aristotelian or Russellian logic or ordinary thing-language (as Caranp would say) must be added to the mathematically expressed quantum theory in order for a realistic version of the Copenhagen duality thesis to be either affirmed or denied.  A better example of Heisenberg’s practice of scientific realism is his potentia ontology given in his summary of the Copenhagen interpretation of the statistical nature of the quantum theory in "The Copenhagen Interpretation of Quantum Theory" in his Physics and Philosophy (1958).   Heisenberg invokes Aristotle's idea of potentia to express thew thesis that wave and particle do not appear simultaneously, and are always wave or particle manifestations of the same entity.  His interpretation of the probability function is that it has both a subjective and an objective aspect.  The subjective aspect makes statements about the observer's incomplete knowledge, while the objec­tive aspect makes statements about what Heisenberg calls "tendencies" and "possibilities", and it is in this latter aspect he refers to the idea of potentia. The probability function in the quantum theory is subjective and represents incomplete knowledge, because the observer's measurements are always inaccurate.  The subjective reason that they are inaccurate is the ordinary errors of measurement that occur both in classical physics and in quantum physics.  But the objective reason is distinctive to quantum physics, and it is the inaccu­racy caused by a disturbance introduced by the meas­urement apparatus in the measurement process.  Heisenberg illustrates this by means of an ideal experiment involving a gamma-ray microscope used to observe an electron.  In the act of observation at least one light quantum of the gamma ray must have passed the microscope, and must first have been deflected by the electron.  Therefore the electron must have been impacted by the light quantum and must have changed its momentum.  The uncertainty rela­tions give the uncertainty of this change.  When the probability function is written down, it includes both these inaccuracies, and there must be at least two such disturbing observations in an atomic experiment. The probability function also contains an objective element, but it is not like the description of motion in classical physics.  The classical physicist would like to say that between the initial and the second observation the electron has described an unknown path in a cloud chamber.  But Heisenberg says that between the two observations the electron has not described any path in space and time, since the electron has not been anywhere.  The probability func­tion does not represent a course of events in the course of time, but rather represents statistical possibilities or tendencies, which are actualized by the second act of obser­vation.  The transition from the possible to the actual takes place with the act of observation involving the inter­action of the electron with the measuring device.  Heisen­berg notes that the transition applies to the physical and not to the psychological act of observation, and that certainly quantum theory does not contain "genu­ine subjective features" in the sense that it introduces the mind of the physicist as a part of the atomic event.
          The objective aspect of the statistical quantum theory is described in terms of the transition from the possible to the actual is due to the wave-particle duality, which Heisenberg illustrates by another experimental set up, the historic interference experiment firstly performed by Thomas Young in 1801.  It involves passing monochromatic light through a screen with two holes or slits in it, and then registering the light on a photo­graphic plate. Viewed as a wave phenomenon there are pri­mary waves entering the slits, and there are secondary spherical waves starting from the slits, that interfere with each other to produce a pattern on the photographic plate.  But the registration on the plate is a quantum process, a chemical reaction.  If the quantum passes through either slit, the other one is irrelevant.  But the existence of the other slit is in fact relevant, because the photographic plate registers an interference pattern.  Therefore the statement that any light quantum must have gone through either just one or just he other slit is problematic.  Heisenberg maintains that this problematic outcome shows that the con­cept of the probability function does not allow a descrip­tion in space and time of what happens between the two observations.  The description of what "happens" is restricted to the observation process in which there occurs the transition from the possible or potentia to the actual.  As it happens, the idea of construing the indeterminacy realistically as potentiality had been proposed several years earlier by David Bohm in his Quantum Theory (1951), written while he accepted the Copenhagen interpretation and before proposing his hidden-variables thesis.  But Heisenberg does not reference Bohm in his own thesis of potentia, and seems to have derived the idea independently from his knowledge of Aristotle’s philosophy.
          Contemporary philosophers and historians of science have learned to recognize in the history of science the occurrence of the scientific realism, the realistic interpretation of empirically successful theories.  As new and empirically superior the­ories are developed, their realistic interpretations produce new ontologies with new ideas and beliefs about what is real, including ideas of the nature of causality.  Hanson describes the scientists’ gradual acceptance of scientific realism with his metaphor of the black box, the gray box, and the glass box, where a new theory is seen to reveal reality as the transparent glass box reveals its contents.  As Feyerabend notes, when the new theory with its new ontology is attacked by the establishment, the so-called authorities of the particular scien­tific profession, it is invariably attacked with the ontological beliefs defined by a preceding and less empirically adequate theory.  Einstein seems not to have been unaware of this historical of phenomenon.  In his "Reply to Criticisms" he stated that the scientist cannot afford to carry his striving for epistemological systemic as far as will the philosopher, and that while the scientist gratefully accepts the epistemologist's analysis, nonetheless the facts of experience, by which he presumably means scientific evi­dence, do not let the scientist be too much restricted in the construction of his conceptual world by the adherence to an epistemological system.  Einstein was faithful to this insight to the extent that he rejected the Positivist philosophy, but he did not follow through with it, when he func­tioned as his own epistemologist and attempted to impose the deterministic ontology of field theory upon quantum theory.

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