BOOK V - Page 3

Popper's Particle-Propensity Interpretation of Quantum Theory

Popper explains the basis for the schism in physics as follows: On the one hand Einstein was a determinist, who believed that the statistical nature of quantum theory is due to the physicist’s ignorance of the underlying deterministic laws, which have not yet been discovered.  Therefore Einstein chose a subjective interpretation of probability based on the scientist’s ignorance.  On the other hand Hei­senberg was an indeterminist, but because the only objective interpretation of probability available at the time was the frequency inter­pretation.  His introduction of the observer’s disturbance of the quantum phenomenon by the measurement apparatus resulted in the combination of both the objective and subjective interpretations of the probability function in the Copenhagen interpretation of the quantum theory.  But the frequency interpretation is applicable only to mass phenomena, while the quantum theory pertains to singular events.  Therefore in order to describe the single quantum event, it seemed necessary to view probability as describing the scientist’s ignorance resulting from the disturbance.  For this reason according to Popper the Copenhagen interpretation also relies on the subjective interpretation of probability.  Popper’s propensity hypothesis advances an objective interpretation of the probability calculus and of probabilistic theories in physics, and it is an objective interpretation that is applicable to singular events.  Popper has arguments for probability interpretations that are exclusively objec­tive, but any objective interpretation requires a realistic philosophy with a nondeterministic ontology.  Therefore he also advances arguments for realism and indeterminacy as well as for objectivism.

Popper has several arguments against the subjective inter­pretation of probability and for an objective interpreta­tion.  Firstly some quantum theorists such as Pauli introduce the idea of induction into discussions about the statistical nature of quantum theory.  Popper rejects this application of inductivism for the same reasons that he rejects all applications of the idea of induction; induction is psycho­logistic and confuses world 2 with world 3.  Secondly he also argues that the idea of explaining the statistical outcomes of experiments and predictions in terms of the ignorance of the physicist is absurd.  Empirical science absolutely never explains anything in terms of the researcher’s ignorance; it always explains phenomena in terms of other phenomena.  While this argument of Popper’s is true and may apply to some subjective interpretations of the quantum theory, it does not apply to interpretations such as Heisenberg’s, which invoke the subjective interpretation of probability only to address the problem of measurement errors, thus giving the subjective interpretation a metalanguage status instead of the object-language status of an explanation in physics.

Popper’s argument for realism is based on his falsificationist thesis of scientific criticism.  Simply stated, he argues that the possibility of falsification is evidence of the existence of the real world that is independent of human knowledge.  He furthermore argues that the fact that theo­ries are conjectures does not imply that they do not des­cribe the real world.  Rational criticism results in better theories that have greater verisimilitude.  Popper argues against instrumentalism, which he associates with both Bohr and Heisenberg.  In “Three Views Concerning Human Understan­ding” in Conjectures and Refutations Popper references Heisen­berg’s thesis that physical theories such as Newton’s are not falsified, but rather have had their applicability restricted by later theories such as relativity and quantum mechanics. 

This view is an aspect of Heisenberg’s doctrine of closed-off theories, although Heisenberg did not set forth his doctrine of closed-off theories as an instrumen­talist thesis.  In a footnote in this paper Popper states that Heisenberg’s instrumentalism is far from consistent, and that he has many anti-instrumentalist remarks to his credit, but that Heisenberg’s view of quantum theory necessarily leads to an instrumentalist philosophy by neglecting falsification and stressing application.  A mere instrument cannot be fal­sified, and the instrumentalist view may be used ad hoc to rescue a theory threatened by falsifications.  Popper main­tains that such an evasion was the reason that Bohr advanced his prin­ciple of complementarity, the renunciation of the attempt to interpret atomic theory as a description of anything; the self-consistent formalism need not be reconciled with its inconsistent applications, if it is left uninterpreted.  On Popper’s view the unfalsifiability thesis of the instrumen­talist view makes instrumentalism incapable of explaining scientific criticism and scientific progress.  Only by reaching for refutations can science hope to learn and to advance.

Popper argues against determinism, and in this respect he takes exception to Einstein, although he says that he may have changed Einstein’s mind about determinism in a conver­sation at Princeton in 1950.  Popper distinguishes between metaphysical determinism, which is a thesis about the whole world, and scientific determinism, which is a thesis about the part of the world described by a scientific theory.  He classifies Einstein as a metaphysical determinist, and reports that in his discussions with Einstein he referred to him by the name Parmenidies, because like the ancient philosopher Parmenidies, Einstein’s metaphysical determinism implies that the future is entirely contained in the past, and that change is not real but is merely an appearance. 

Popper also argues against scientific determinism, and specifically he denies that Newtonian mechanics implies a deterministic ontology.  He describes the theories of clas­sical physics as prima facie deterministic, by which he means that the deterministic character is a property of the theory and not of the real world.  He maintains that clas­sical physics does not imply real determinism any more than quan­tum physics does, because there is always an irreducible and stable statistical element in any predictions made with a prima facie deterministic theory.  It is always necessary to add to the deterministic theory a probability assumption to explain the statistical component in the prediction, because statistical conclusions require statistical premises.  Popper quotes at length Landé’s description of the experiment with the ivory balls and steel blade, which Landé uses to argue that statistical results require statistical assumptions about the initial conditions.  Therefore Popper rejects attempts to explain the statistical outcomes subjec­tively by reference to lack of knowledge of the experimenter for the reasons given above, and he maintains that the law-like behavior of statistical sequences is for the deter­minist ultimately inexplicable.

Popper developed his propensity interpretation of prob­ability in 1950 specifically to address the interpretation problem arising from statistical quantum theory, but it is also intended to be applicable to all physics.  While it is but one of many interpretations for the probability calcu­lus, it is the best for physics in Popper’s view.  Popper distinguishes three objective interpretations of the proba­bility calculus: the classical interpretation, the frequency interpretation, and his propensity interpretation.  The classical interpretation is that the probability measure P(α, β) is the proportion of equally possible cases compa­tible with the event β that are also favorable to the event α.  The frequency interpretation is that P(α, β) is the relative frequency of the events α among the events β.  The propensity interpretation is a refinement of the classical interpretation.  In the classical interpretation experimen­tation is not needed, because it deals with equally possible cases, such as the two sides of a coin or the six faces of a die.

The propensity interpretation substitutes weights for equally possible cases in the classical interpretation, where the weights are experimentally determined measures of the propensity or tendency of a possibility to realize itself upon repetition.  In the propensity interpretation the measure P(α, β) is the propen­sity of α given experimental conditions β.  It is the sum of the weights of the possible cases that satisfy the condition β which are also favorable to α, divided by the sum of the weights of the possible cases that satisfy β.  The propen­sity interpretation is closely related to the frequency interpretation; the latter is about frequencies in actual finite sequences of experiments, while the former is about virtual finite sequences.  In the propensity interpretation probability statements are about some measure of a physical property of the whole repeatable experimental arrangement, a measure of a virtual frequency, and the probability distribution is taken to be a property of the single experiment.  The fact that the probability distribution in the propensity interpretation is a property of a single experiment is the strategic characteristic of this interpretation for quantum theory.  Previously in Logic of Scientific Discovery Popper had attempted to modify the frequency interpretation so that it could address single events by means of what he called “formally singular statements.”  He abandoned this idea, when he developed the propensity interpretation.  Now he says that the frequency measurements function to test the conjectured virtual frequency, which is a conjecture like any other scientific hypothesis.

The propensity interpretation is consistent with Popper’s particle interpretation of the quantum theory that he had advanced years before in Logic of Scientific Disco­very.  According to Popper`s particle interpretation the Heisenberg indeterminacy relations are statistical scatter relations that describe the lower limits of the dispersion of particles; they are not the upper limits of the accuracy of measurements, as Popper construes Heisenberg’s view.  The indeterminacy relations apply only to the magnitudes that belong to the particle after the disturbing measurement has been made.  The particle always has position and momentum, and has both these properties up to the instant of measurement, which can be ascertained in principle with unlimited accuracy.  It is not the impossibility of precise measurement, but the statistical scatter that makes it impossible to predict the path of the particle after the disturbing measurement oper­ation.  The scatter relations are statistical predictions about paths, and the paths must be measurable in order to test the statistical theory.  For these reasons Popper rejects the view he incorrectly attributes to Heisenberg’s view that the uncertainty relations express limits to our subjective know­ledge instead of expressing objective statistical scatter relations, and that measurements are impossible due to the nonexistence of the entities measured.  What is impos­sible is producing dispersion-free quantum states.  The statistical laws add to our knowledge.  They do not set limits to our knowledge; they set limits to the scatter relations and tell us that the scatter is an objec­tive reality that cannot be suppressed.

The propensity interpretation purports to solve the problem of the relationship between particles and their statistics, and between particles and waves.  Popper calls the Copenhagen wave-particle dualistic interpretation the “great quantum muddle.”  The great quantum muddle results from the mistake of taking the probability distribution function as a physi­cal property of the elements of the population.  Popper believes that this mistake is historically due to the fact that the works of de Broglie and Schrödinger led physicists to view the wave as the structure of the particle, and thus to view the particle as a “wave packet” or a “wavicle”.  Popper maintains that the statistical wave function is a property characterizing a sample space and not a property of the elements of the sample space.  The elements have the proper­ties of a particle.  The propensity interpretation achieves the application of probability theory to single cases, but it does not do this by speaking about single electrons or protons; it speaks about propensities, which are properties of each instance of the whole repeatable experimental situa­tion involving a single particle.

Propensity statements in physics describe properties of the situation, and are testable if the situation is typical.  Popper accepts Landé’s explanation of the two-slit experi­ment, and he references what he calls the Duane-Landé space periodicity formula.  The two-slit experiment is a space periodicity experiment, in which the particle interacts with the whole experimental situation including the crystal.  More specifically from the viewpoint of the propensity interpretation, it is the whole experimental arrangement that determines the propensities.  The possible results of any one experiment are different in the case of both slits being open from the case where only one is open; propensi­ties are dependent on possibilities, such that the results will differ with different experimental arrangements, one slit or two.  Thus in the two-slit arrangement the particle will pass through only one of the slits and in a sense will remain unaffected by the other slit.  What the other slit influences are the propensities of the particle relative to the entire experimental arrangement and not relative to the particle itself: the propensities for reaching the one point or the other point on the screen with the two slits.  The Schrödinger wave equation enables the physicist to determine the propensities, and it entails the Heisenberg scatter relations, which limit the possible predictions.

Popper states that Schrödinger had anticipated one of the most important aspects of the propensity interpretation, namely the objectivity and reality of the waves in configu­ration space.  One of the features of Popper’s propensity interpretation is his thesis that the propensities are real, just as forces are real, and he speaks of propensity fields, just as contemporary physicists are accustomed to speak of force fields.  The propensities are dispositional relational properties of the experimental set up.  The waves are pro­pensities of the particles to take up certain states under the conditions of the experimental set up, and the propen­sity waves are therefore no less real than electromagnetic waves.  Landé believes that if he admitted to the reality of the Schrödinger wave, then like Born he would have to make what he called “concessions” to the Copenhagen dualistic thesis.  Therefore Landé maintains that the Schrödinger wave function interpreted as a probability wave is merely a statistical function that is no more real than a mortality table, which Landé did not view as real.  But Popper uses Landé’s criterion of interaction, and argues that because the proba­bility waves can interact to produce interference, they must be real, and are not merely mathematical tables.  Popper sup­ports Landé’s rejection of the Copenhagen dualism, but contrary to Landé, Popper says that he prefers to speak of the particle and its associated propensity fields, instead of speaking of the particle and its associated mathematical probability function.

On Crucial Experiments and Scientific Revolutions

Unlike the positivist philosophy of science, which has been interred to its resting place in the history of philosophy, Popper’s philosophy of science is still a living philosophy in the sense that it is still accepted and debated in the professional literature.  Popper has addressed more than one generation of philosophers during his lifetime.  Initially his philo­sophy was a critique of the positivists, who viewed his philosophy as an unconventional novation, while today his philosophy is criticized by the contemporary pragmatists, who view his philosophy as the conventional wisdom.  The central contemporary issue in which Popper represents the conservative position is the problem of the decidability of scientific criticism including most notably the decidability of crucial experiments.  The origin of the problem is the thesis shared by both Popper and the wholistic pragmatists, and also enunciated by Einstein, that theory decides what the physicist can observe.  To these pragmatists this thesis implies that the description of the observed results from an experimental test cannot be under­stood in the same way by different scientists who maintain alternative theories in an experimental test, which is crucial in the sense that it purportedly decides between the alternative theories.  If theory determines what is observed, then scientists maintaining different theories do not observe the same thing, and the observed outcome from the crucial experiment cannot decide between the alternative theories.  To Popper on the other hand, Eddington’s 1919-eclipse experiment, which is widely regarded as the historic crucial experiment deciding on behalf of Einstein’s theory of relativity, demonstrates conclusively that crucial experiments are decisive.

It should be noted at the outset that even in his earliest writings Popper maintained that falsification is never finally and permanently conclusive, because the singular basic statements that are potential falsifiers may be revised, thus occasioning the revision of a falsifying test outcome.  The empirical test may be said to be conclu­sive only to the extent that interested scientists agree to accept certain basic statements.  Popper states that in some cases it has taken scientists a long time before a falsifi­cation is accepted, and that it was often not accepted until a falsified theory had been replaced by the proposal of a new and more adequate theory.  But Popper does not find this historical fact to be problematic, even though in his view it is responsible for having led the pragmatists to accept irrationalism and relativism in philosophy of science.  In his introduction to Realism and the Aim of Science he gives several examples of successful falsifications that furthermore have led to important scientific revolutions. 

Just as the development of Einstein’s relativity theory can be said to be the formative influence in Popper’s philosophy of science, the development of the quantum theory can be said to be the formative influence in the contemporary pragmatist phil­osophy of science.   The topic of crucial experiments has assumed its controversial status in the professional litera­ture due to the Copenhagen interpretation of quantum theory.  The Copenhagen interpretation denies that a crucial experiment can decide between the wave and particle interpretations of microphysics, because the electron has the properties of both wave and particle.  Quine invoked Duhem’s philosophy of physical theory not only due to Duhem’s rejection of the decidability of crucial experiments for establishing a theory, but also more fundamentally due to Duhem’s thesis of the organic character of the semantics of theory language in physics.  In his “Two Dogmas of Empiricism” Quine extended Duhem’s thesis of the organic or wholistic character of the seman­tics of physical theory, to make it a general theory of the semantics of language as such, including the language used by physicists to describe observed experimental test outcomes. 

As a result of this extended thesis, which is now conventionally called the Duhem-Quine thesis, the wholistic character of the semantics of language explains why crucial experiments are undecidable not only in the wave-particle issue in quantum theory, but also more generally for all scientific criticism.  Even where one of the alternatives is the Copenhagen dualistic interpretation, as in Landé’s list of seven interpretations, the crucial experiment cannot effectively decide among them, according to the wholistic version of the contemporary pragmatist philosophy.  The issue of crucial experiments has become a focal point in philosophy of science for the larger issues of the decidability of scientific criticism and of the nature of the semantics of language in general.

The historic transition from the positivists’ naturalistic phil­osophy of the semantics of language to the contemporary artifactual philosophy of the semantics of language has thus resulted in two alternative artifactual philosophies of the semantics of language: The one is the organic or wholistic thesis advocated by some pragmatists, which they use to attack the decidability of crucial experiments and of scien­tific criticism in general.  The other is the mechanistic or logical thesis advocated by Popper, which he uses to defend the decidability of crucial experiments for eliminating theories and for defending the rationality of scientific criticism in general.

In his “Three Views Concerning Human Knowledge” (1956) reprinted in his Conjectures and Refutations Popper discus­ses Duhem’s views on crucial experiments.  He notes that Duhem shows that crucial experiments cannot establish a the­ory simply by refuting its alternatives, and emphasizes that Duhem does not say that theories cannot be refuted in crucial experiments.  Popper maintains that crucial experiments can be used to decide between alternative theories, as occurs when a new theory is proposed as a superior alternative to an older theory.  The new theory is tested by applying it to cases for which it yields results that are different from what is expected from the older theory.  He says that such cases are “crucial” in the Baconian sense that they indicate the crossroads between two or more theories, but not in the Baconian sense that any theory can be conclusively established.

Popper then turns to Duhem’s thesis that in every test it is not only the theory under investigation that is tested, but also the whole system of assumptions made by the theory, such that it is never possible to be certain which of the assump­tions is refuted by the test.  Popper states that if the scientists consider each of the two theories in the crucial test together with all the background knowledge assumed by both theories, then the scientists decide between the two systems, which differ only over the two alternative theories in the test.  Popper adds that scientists do not assert the refutation only of one of the theories by the test, but rather the theory together with the background assumptions.  By this he does not mean that every statement in the theory and its assumed background is refuted, but only that there is at least one statement that is erroneous, and that it may be in either the theory or the assumed common background.  Thus he also says that in future tests parts of the background knowledge may be rejected as responsible for the falsification of the theory in the current crucial test.

Popper then proposes to “characterize the theory under investigation” in the crucial test precisely as that part of the vast system of knowledge for which the scientist has an alternative in mind, and for which he has therefore designed the crucial test.  This may be taken as Popper’s basis for individuating theories: theory α is distinguished from the­ory β, because α makes a claim or statement than is an alternative to that made by β, and because α consists in the language that makes it an alternative to β.  Thus it may be said that Popper individuates theories by reference to the theories’ semantical properties as manifested in the crucial-test situation. 

However, Popper does not define theory lan­guage by reference to the crucial test situation as such; he often states that the background knowledge includes theories other than the tested one.  In his philosophy, therefore, theory language is any testable general statement regardless of whether or not it is being tested, which is to say that he defines theory by reference to its syntactical property of universal quantification and not by reference to its semantics or its pragmatics.  Further­more Popper’s concept of theory language may be contrasted with that of the positivists, who believed that it is possible to define theory in terms of its semantical properties by means of their distinction between theoretical and obser­vation terms; Popper rejects this basis for their distinction.

In his “Truth, Rationality, and the Growth of Know­ledge” (1961) reprinted in Conjectures and Refutations Popper turns to Quine’s use of Duhem’s philosophy.  Quine maintains a wholistic view of empirical testing, and in his “Two Dogmas of Empiricism” in From A Logical Point of View he states that our statements about the external world face the tribunal of experience not individually but as a corporate body.  Popper replies that this wholistic view of tests, even if it were true, would not create a serious problem for the falsificationist philosopher of science.  He repeats his thesis that to say scientists take a vast amount of background knowledge for granted, is not to say the scientist must uncritically accept it, because the background knowledge too may be challenged and tested.  Even though all of the back­ground assumptions may be challenged, it is quite impossible to challenge all of the assumptions at the same time.  All criticism must be “piecemeal”, which Popper says is only another way of saying that the fundamental maxim of every critical discussion is that one should “stick to the problem”, because the misguided attempt to question all background assumptions merely leads to a breakdown of critical debate.  Critics such as Feyerabend will view this thesis as the parallel postulate of Popper’s philosophy of science to be replaced with a pragmatist philosophy of language.

Furthermore even though the falsification of a theory does not reveal where the error is, it is still possible to find the hypothesis that is responsible for the refutation, i.e., to find which hypothesis is responsible for the falsified prediction.  The fact that such logical depen­dencies may be discovered is established by the existence of independence proofs for axiomatized systems; these are proofs that show that certain axioms of a system cannot be derived from the others in the axiomatic system.  Popper argues that the existence of such proofs shows that Quine’s wholistic view of the global character of all empirical tests is untenable, and that it explains why even without axiomatized physical theories, the scientist may still have an inkling of what has gone wrong with the theory.  In Realism and the Aim of Science Popper affirms as historical fact, that scientists are sometimes highly successful in attributing to a single hypothesis the responsibil­ity for the falsification of a complex theory or of a system of theories, and he argues that this success remains to be explained if one adopts the wholistic view of empirical testing.

In 1962 Thomas Kuhn wrote Structure of Scientific Revolutions in which he used the wholistic thesis to inter­pret the history of science.  And in 1970 Kuhn defended his whol­istic interpretation against critics in Criticism and the Growth of Knowledge.  The leading critic in this later book was Popper, who contributed “Normal Science and its Dangers.”  In his earlier statements in defense of the decidability of crucial tests Popper did not explicitly address the basis of the wholistic view of testing, namely the thesis that the semantics of language is wholistic.  The wholistic thesis of the semantics of language means that the meanings of terms are mutually determined in the context of the discourse in which they occur, such that alternative contexts consisting of alternative theories produce a semantic ambiguity or equivocation that is propagated through all of the related language. In other words when considering the alternative theo­ries investigated in a crucial test, all that constitutes the background assumptions is ambiguous. 

Therefore there is really no common background, because one semantical interpretation is given to the language expressing the background assumptions by one of the theories in the test and another interpretation is given by the other theory in the same test.  However, Quine also says that the propagation of change is damped by vagueness in language.  Often the two alternative semantical interpretations are spoken of as two different languages, and there is said to arise a problem of translation from one to the other.  This thesis is strategic to Kuhn’s critique of the positivists, because the lack of any common semantics for alterna­tive theories that makes impossible a common background for crucial tests, also makes impossible a common observation language for decidable testing.

Kuhn maintains that the kind of scientific progress that Popper describes with its crucial experiments and fal­sifications can occur only within a linguistic framework, and he calls this type of scientific progress “normal sci­ence”, which Kuhn opposes to another type which he calls “extraordinary science” or “revolutionary science”.  Revolu­tionary science is a transition from one language framework to another, where the term “framework” in the discussion refers to discourse having a univocal semantical interpreta­tion and associated ontology.  Popper rejects this theory of scientific revolution as irrational, when he criticizes Kuhn in Criticism and the Growth of Knowledge.  While admitting that “normal science” as a behavior in Kuhn’s sense does exist, Popper argues that such normal science is dogmatic.  He says that science is essentially critical, that it consists of bold conjectures controlled by criticism, and that it may be called revolutionary in this rational sense.  He rejects Kuhn’s relativism, the thesis that the linguistic framework cannot be critically discussed, and he calls this “the myth of the framework.”  Comparison of different frameworks is always possible on Popper’s view, and so is critical discus­sion therefore.  Even totally different languages are not untranslatable. 

Thus Popper argues that it is simply false to say that the transition from Newton’s theory of gravitation to Ein­stein’s theory is an irrational leap, and that the two are not rationally comparable; the transition to Einstein’s theory was genuine progress in comparison with Newton’s.  Popper concludes that the myth of the framework is in our time the central bulwark of irrationalism, and that it exaggerates a difficulty with communication and criticism into an impossibility.  In place of criticism as is found in Popper’s falsification thesis, Kuhn proposes turning for enlightenment concerning the aim of science to psychology and sociology.  But Popper rejects this proposal, and states that compared with physics, sociology and psychology are riddled with fashion and with uncontrolled dogmatism.  He believes that such a proposal is a backward regression that cannot solve the difficulty.

In his “The Rationality of Scientific Revolutions” in Problems of Scientific Revolution Popper distinguishes between the sociological and the logical or rational dimen­sions in the history of science, when he distinguishes ideological from scientific revolutions.  By an ideology he means any nonscientific theory, creed, or view of the world that is attractive or interesting to people including scientists.  He cites the Copernican and Darwinian revolu­tions as examples of scientific revolutions that gave rise to ideological revolutions, because each changed man’s view of his place in the universe.  But these were also scienti­fic revolutions in so far as each overthrew a dominant scientific theory, the one a dominant astronomical theory, the other a dominant biological theory.  He also cites Einstein’s relativity theory as a revolution, a truly scientific revolution that gave rise to operationalism and supported positivism, even though Einstein later rejected these ideologies.  And Popper also refers to the subjecti­vist interpretation of quantum theory as an ideology.

The wholistic thesis of the semantics of language is used by many pragmatists to explain events that have been obser­ved in the history of science: the impediment that language creates both to the development of new theories and to the communication of new theories within a profession.  However, Popper relegates all semantical analysis to the status of a variation on the essentialist metaphysical thesis; in his autobiography in Philosophy of Karl Popper he admonishes the reader never to let himself be “goaded” into taking seri­ously problems about words and their meanings.  He maintains that words “merely” play a technical or “pragmatic” rôle in the formulation of theories, just as the letters in written words play such a rôle in the formation of the words.  Contrary to Popper contemporary pragmatists do not believe that language has such a passive rôle in concept formation and in human cognitive processes.  And it may be noted that contemporary pragmatists are as anti-essentialist as Popper; one need only recall Quine’s rhetor­ical ridicule that an essence is merely a “meaning wedded to a word”.  Regrettably Popper’s philosophy does not offer a theory of semantical description to reconcile the phenomenon of semantical change with his views on the decidability of criticism.

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