BOOK IV - Page 1

     This book examines Werner Heisenberg’s interpretation of quantum theory and the influence of Albert Einstein.  Heisenberg’s semantical view is the chrysalis of the contemporary pragmatist philosophy of language.

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 Göttingen 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 indeterminacy 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 Göttingen, 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 academic 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 in BOOK II in the discussion of Mach’s philosophy about the influence of Einstein’s aphorism 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 deserves close examination. 

He had initially believed 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 version of quantum theory.

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 Einstein 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.  Einstein 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 upon 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.  Einstein objected that Heisenberg was 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 wave-particle “complementarity” description.  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 replied that Mach thought a theory combines complex sense impressions just as the word “ball” does for a child.  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 his Physics and Beyond 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 the chapter titled “Fresh Fields (1926-1927)” Heisenberg offers a description of his own mental processes in his development of the indeterminacy relations.  To the contempor­ary reader this description has value apart from his systematic and explicit 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 with 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 (1926-1927)” in Physics and Beyond 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 they are valuable as an historical document.  As it happens, in the contemporary pragmatist philosophical perspective these recollections are far more valuable than Heisenberg’s explicit attempt to philosophize on the nature of language and perception.

These writings reveal that his development of the indeterminacy relations 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 wave equation gives the probability of finding an electron at the 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 both of ordinary discourse and of classical physics these two concepts are mutually exclusive.  A wave is spread out in space, while a particle is concentrated nearly at a point.  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 logically derivable from the matrix mechanics.  Heisenberg reports that this objective was one of the reasons that led him to derive the indeterminacy relations.

A second reason leading him to the indeterminacy relations was the fact that neither the wave mechanics nor the matrix mechanics seemed capable of explaining the observed track of the electron in the Wilson cloud chamber. The cloud chamber developed by C.T.R. Wilson in 1912 consists of a chamber containing a saturated vapor under pressure.  When the pressure is rapidly reduced, the vapor cools and becomes supersaturated, as the temperature drops below the dew point.  The passage of a charged particle, i.e., an electron, through the vapor causes ion pairs to form droplets.  A string of these droplets mark the track of the passage of the charged particle.  But such ideas as tracks 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 is spread over volumes that are much larger than the dimensions of an electron.  This problem of the observed track 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 track 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 earlier 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 the theory decides what the physicist can observe.  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 track.  The idea of a track is a concept in Newtonian physics.  Therefore, when he thought that he was observing the track 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 very 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 the physicist can observe, Heisenberg concluded that the processes involved in any experiment or observation in microphysics must satisfy the laws of quantum mechanics.  The magnitude of the observed water droplets suggested room for approximation for the minute electron, and Heisenberg asked whether it is possible to imagine these approximations so close that they do not cause experimental difficulties.  He then derived the indeterminacy relations in which the approximations are limited by Plank’s constant.

Heisenberg had formulated his indeterminacy 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 indeterminacy 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 everyday language, which is suitable only to describe phenomena at the macrophysical level.  What is expressed consistently with the mathematical formalism of the indeterminacy 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 limits of 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 tried to reconcile the dilemma, but never did.

Heisenberg’s description, which is based on his own experience of the interpretative character of all perception and observa­tion and of the rôle 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 with his two-tier semantics, but also because Heisenberg’s description of his experiences is given in the context of his development of the indeterminacy principle, one of the most noteworthy achievements of twentieth-century physics.

As it happens, Heisenberg did not like the pragmatism he encountered at the University of Chicago 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 still influenced by Bohr in ways that impeded his developing a philosophy of language that is consistent with Einstein’s thesis that theory decides what the physicist can observe.  This influence places Heisenberg’s explicit philosophy of science closer to the positivist philosophy than either Einstein’s or the pragmatists’ views.  This influence originated in Bohr’s naïve naturalistic philosophy of the semantics of language.  And the result was Bohr’s thesis of “forms of perception” and Heisenberg’s consequent neo-Kantian rendering of Bohr’s philosophy of perception.

Heisenberg’s Discovery and Einstein’s Ontological Criteria

An ontology consists of the entities and aspects of the real world that are described by the semantics of a discourse, such as a scientific theory that is believed to be true.  Unlike Bohr, who took an instrumentalist view of the equations of the quantum theory, Heisenberg maintained that quantum theory describes ontology, that is, that the equations constituting the language of the theory describe aspects of the real world.  Thus he maintained that the quantum theory describes nondeterministic microphysical reality and the Copenhagen wave-particle duality, the thesis that wave and particle manifest two aspects of the same physical entity and do not represent two separate physical entities. 

Initially, however, Heisenberg’s ontological views were not based in the language of the mathematically expressed quantum theory, but were based in the everyday language that can be used to express experimental findings.  In the opening sentence of the “Introduction” 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.

Heisenberg maintained that the everyday description of certain experimental findings implies the Copenhagen ontology, and he proceeds to give a brief description of several experiments including Young’s two-slit experiment, 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.  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 wave and particle are a single entity, and that the apparent duality, the properties described in Newtonian mechanics as “wave” and “particle”, is due to the limitations of language.  Such recourse to the limitations of language reveals the influence of Bohr’s philosophy.  For Heisenberg both quantum experiments and quantum mechanics redefines the meaning of the word “entity”.  Other physicists such as Einstein, de Broglie, and Bohm did not agree with Heisenberg’s view that there is any such compelling experimental evidence for the Copenhagen duality ontology.  Both philosophers and scientists have had different ontological commitments, often because they maintain different philosophies of language. 

Einstein’s ontological view influenced Heisenberg’s ontological ideas.  Therefore briefly consider Einstein’s views.  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 states 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 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 that are close to experience, as theorems logically deduced from and belonging to a basis as nar­row as possible, of axioms and fundamental concepts that themselves can be chosen freely.  This is a coherence concept of the aim of science as the logical unity of the world picture, and it might be described as an aspiration to what today is called a “theory of everything”.  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.  Einstein thus maintains that the conviction that deterministic 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 this uniform fundamental ontology, and he uses this explicit ontological criterion to criticize the nondeterministic Copenhagen interpretation.

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 space-time 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 in turn 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: Philosopher-Scientist.  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 Schilpp’s 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 even today many 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.

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.  This is the contemporary pragmatist view, which Quine calls “ontological relativity”.  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 Lor­entz’s “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 describe 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 indeterminacy relations.  But in his “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 indeterminacy principle consisted of his 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 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 indeterminacy relations, 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 (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 that can be represented as vectors in Hilbert space can occur in nature and be realized experimentally.  And he immediately adds that this method 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 is real time.  He similarly assumed in quantum mechanics that real states can be represented as vectors in Hilbert space (or as mixtures of such vectors), and that the indeterminacy principle is the simple expression for this assumption.

If at the time he developed the indeterminacy 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 theory decides what can be observed, to the onto­logical thesis that theory decides what is physically real, where the theory in question is empirically warranted, as was Heisenberg’s 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 or even in disregard of the outcome of empirical criticism.  Heisenberg explicitly compares his realistic interpretation of 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 Heisenberg 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 position-momentum symmetry properties of the quan­tum theory.  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.

Another example of Heisenberg’s practice of scientific realism is his potentia ontology given in his summary of the Copenhagen interpretation of the quantum theory in “The Copenhagen Interpretation of Quantum Theory” in his Physics and Philosophy.  This might be taken as his redefinition of the meaning of “entity”. Heisenberg invokes Aristotle’s idea of potentia to express the thesis that wave and particle do not appear simultaneously, and are 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 that he refers to the idea of potentia. The probability function in the quantum theory is subjective and represents incomplete knowledge, because observers’ measurements are always inaccurate.  The subjective reason that they are inaccurate is the ordinary errors of measurement, the empirical underdetermination that occurs both in both classical physics and quantum physics.  But the objective reason is distinctive to quantum physics, and it is the inaccu­racy caused by a disturbance introduced by the apparatus in the measurement process. 

Heisenberg illustrates this objective aspect by means of an ideal experiment involving a gamma-ray microscope used to observe an electron.  In the act of observation at least one 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 quantum and must have changed its momentum.  The indeterminacy relations give the indeterminacy of this momentum change.  When the probability function is written down, it includes both the objective and subjective inaccuracies, and there must be at least two such disturbing observations in an atomic experiment. The objective element in the probability function 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.  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 also 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.

Heisenberg attributes the objective aspect of the quantum theory to duality, which he construes as a transition from possible to actual.  In his Physics and Philosophy Heisenberg illustrates duality by the two-slit experiment, 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 then there are secondary spherical waves starting from the two slits, which interfere with each other to produce an interference pattern on the photographic plate.  But the registration on the plate is a quantum process, a chemical reaction.  If the quantum particle passes through either slit, the other one would normally be viewed as irrelevant.  But the existence of the other slit is in fact relevant, because the photographic plate registers the 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 measurement observation process in which there occurs the transition from the possible or potentia to the actual.  David Bohm had also proposed construing indeterminacy realistically as potentiality in his Quantum Theory (1951), written while he accepted the Copenhagen interpretation and before proposing his alternative hidden-variables thesis.  But Heisenberg does not reference Bohm for his own thesis of potentia, and he seems to have derived the idea independently, probably from his reading of Aristotle’s philosophy.

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