BOOK V - Page 2

On Computers, Induction Machines, and Scientific Discovery 

In his Logical Foundations of Probability and elsewhere Carnap proposed using a computer to make empirical general­izations with inductive logic.  Throughout his career Popper has rejected the idea of inductive logic, but in Realism and the Aim of Science (1982) he admits to induction machines of a certain type.  For such a machine he postulates a simple universe containing individuals and a limited number of pro­perties that the individuals can have.  This universe fur­thermore operates with a number of so-called “natural laws.”  Popper says that for this universe a machine can be created, such that in some reasonable period of time it will discover the laws that are valid in the postulated universe during the time period.  If the laws of its universe are modified, the machine will show its capacity for finding a new set of laws.  It would be capable of drawing up statistics about various distinguishable occurrences and of calculating aver­ages.  If the postulated universe is complicated further to include among its natural laws, the laws of succession, the general or conditional frequencies having a certain degree of stability, etc., then the machine can be enhanced to be able to formulate hypotheses, to test the hypotheses, and to eliminate those that should be eliminated.  Such a machine can learn from experience.

But Popper emphasizes that this inductive machine is limited to the universe that its architect has created for it.  The architect of the universe decides what are to be individual events, and what constitutes a property or a relation.  In general it is the architect of the machine who decides what the machine can recognize as a repetition.  And even more fundamentally it is the architect of the machine who decides what kinds of questions the machine is to answer.  All these considerations mean that the more important and difficult problems are already solved by the human designer, when he constructs the machine and the universe it can recognize.  Things that positivists such as Carnap had thought simply to be given by nature, the meanings that according to the naturalistic theory of the semantics of language are delivered by the natural operation of human perception, are in Popper’s view the product of the creative and imaginative powers of the human designer.  These powers enjoy a freedom that is permitted by the artifactual character of objective knowledge, and that is necessary for the creation of the hypotheses and theories that have characterized the growth of knowledge by science. 

The basis of this freedom is the nondeterministic relation between world 3 on the one hand and worlds 1 and 2 on the other.  Carnap had admitted that an induction machine cannot create hypotheses, and that theories are inventions created by the human mind.  But Popper does not admit to the positivists’ separation between empirical generalizations on the one hand and theories on the other; he maintains that there is no observation without theory.  He also argues that no human or computer can pre­dict the future growth of scientific knowledge without committing the fallacy of historicism. In his Poverty of Historicism (1975) as well as in Realism and the Aim of Science he maintains that historicism involves unconditional predictions, and he says that such predictions are impossible, because prediction in science requires universal laws, which are always condi­tional.

As it happens, the computerized development of hypo­theses and conjectures is precisely what information scien­tists attempt to accomplish by their “artificial-intelligence” computer systems, which Herbert Simon calls “discovery systems”.  These computer systems are instrumental to the scientist’s development of hypotheses.  They are not historicist, but are conditioned upon inputs that require preparation or initial conditions like those Popper says are needed for what he calls an “induction machine.” But Popper rejects the related theses of induction as the logic for making generalizations and hypotheses, of psychologism which proposes perception as the empirical basis of observation in science, and of the naturalistic theory of the semantics of language.  This places him in opposition to the cognitive psychologists including Simon, Thagard, Langley and their ilk.  Like Popper, Hickey accepts the artifactual view of semantics, and he is thus sympathetic to Popper’s views of knowledge.  Hickey therefore locates computational philosophy of science and its discovery systems more closely to computational linguistics than to cognitive psychology, and he views discovery systems as generative grammars.

The Schism in Physics and Metaphysical Research Programmes

The term “schism” in the context of the philosophical discussions of the quantum theory did not originate with Popper; Heisenberg introduced it.  In his “Recent Changes in the Foundations of Exact Sciences” (1934) in Philosophical Problems of Quantum Mechanics Heisenberg notes a “peculiar schism”, that he says is inescapable in the investigation of atomic processes.  He is not referring to a sociological phenomenon in the physics profession or to an issue that must be resolved; he views the schism positively as a development in physics.  As Heisenberg uses the term “schism”, it refers to the different concepts used by clas­sical physics and quantum physics and to the different ontolo­gies they describe.  On the one hand he has said as part of his doctrine of closed-off theories that there is a need for macrophysical classical concepts of space and time in quantum physics for the description of experiments and of the appa­ratus of measurement in experiments.  On the other hand he says that there is the mathematical expression suitable for the representation of microphysical reality, the wave function in multidimensional configuration spaces that allow of no easily comprehensible interpretation.  Heisenberg says that the dividing line between the classical and the quantum physics is the statistical relation.

Popper’s earlier views on quantum theory are set forth in his Logic of Scientific Discovery (1959 [1934]) and his more mature statement is set forth in his Postscript to the Logic of Scientific Discovery (1982).  The latter work is a collection of three volumes: Realism and the Aim of Science, The Open Universe: An Argument for Indeterminism, and Quantum Theory and the Schism in Physics.  Popper brings to statistical quantum theory a prior ontological commitment, which he calls “com­monsense realism”.  In Popper’s view physics has historic­ally developed out of one or another metaphysical view which he calls a “metaphysical research programme.”  A metaphysi­cal research programme is a set of ideas that are currently untestable, and that he therefore calls “metaphysical.”  In Pop­per’s philosophy the demarcation between science and meta­physics is testability thus giving metaphysics a residual status relative to science. 

The metaphysical research programme supplies the physicist both with a metaphysical view or ontology about the general structure of the world and with a metascientific view about such things as the criteria for a satisfactory scientific explanation based on the ontology contained in the metaphysical research programme.  Science needs metaphysical research programmes, because they largely determine its problem situations.  Popper cites Einstein’s way of looking at the Lorentz transformation as an example of how a metaphysical research programme can sup­ply a new way of looking at things that may change science completely.  Metaphysical research programmes change and are replaced as some parts become testable and are incorporated into science.  The relation between the testable theory and the metaphysical research programme is part of the history of problem situations of the science, along with the problems arising from inconsistency among theories and empirical falsifica­tions of theories.

Unlike Heisenberg, Popper views the schism in physics in more sociological terms and in terms of the issues that have given rise to the schism.  And unlike Heisenberg, he does not view the current schism in physics favorably.  In his opinion the acceptance of the Copenhagen interpretation and the rejection of what he calls the Faraday-Einstein- Schrödinger metaphysical research programme have left physics without any unifying picture of the world, without any theory of change, and without any general cosmology.  The current schism in physics is a clash between two meta­physical research programmes, neither of which in his view seems to be doing its job.  In Quantum Theory and the Schism in Physics he summarizes the current schism in terms of three issues: (1) indeterminism vs. determinism, (2) realism vs. instrumentalism, and (3) objectivism vs. subjectivism.  All three issues are closely related to one another and to the interpretation of the probability function in the sta­tistical quantum theory.

The schism has its orthodox group, and it has a variety of dissenters.  On the dissenting side of the schism he locates the views of Einstein, de Broglie, Schrödinger and Bohm, which he characterizes together as determinist, realist and subjectivist.  On the orthodox side of the schism he locates the Copenhagen school including Bohr, Heisenberg, Pauli and Born, which he characterizes together as indeterminist, instrumentalist and objectivist.  He does not consider Heisenberg’s views to be realist, and he effectively lumps Heisenberg together with Bohr, who was explicitly instrumentalist in his view of the formalism of quantum theory.  This amounts to a misrepresentation of Heisenberg. 

Popper proposes a new and unifying metaphy­sical research programme that he says offers a consis­tent ontology for both macrophysics and microphysics.  Such an ontology has been the Holy Grail of nearly every critic of the Copenhagen school.  In his autobiography he states that his views on quantum theory were greatly influenced by those of the physicist Alfred Landé, and he states in the Postscript that Landé antici­pated his own interpretation of the quantum theory.  There­fore, a brief examination of Landé’s interpretation of the statistical quantum theory is in order before proceeding further in the discussion of Popper’s particle-propensity interpretation.

Landé’s New Foundations of Quantum Physics

A brief biography of Alfred Landé (1888-1975) can be found in an obituary published in Physics Today (May 1976).  Landé was a German-born American physicist, who received a doctorate in physics in 1914 from the University of Munich, where he studied under Sommerfeld.  In 1918 he co-authored a paper with Born that refuted Bohr’s model of coplanar electronic orbits.  In 1931 he migrated to the United States, where he taught theoretical physics at Ohio State University until his retirement in 1960. Landé originally advocated the Copenhagen interpretation of quantum theory, but pub­licly disassociated himself from it with the publication of his Foundations of Quantum Theory (1955).  His most mature statement of his views is his New Foundations of Quantum Mechanics (1965), which includes ideas published in his previous papers.

As a physicist Landé had his own agenda: the solution of what he calls “The Quantum Riddle”, which is the deriva­tion of the laws of quantum mechanics from a nonquantal and nondeterministic basis without the ad hoc assumptions that he finds in the Copenhagen interpretation.  In his deductive explanation of quantum laws from three nonquantal postulates, he maintains that uncertainty is a physical principle for both classical and quantum physics, and he advances and defends a particle interpreta­tion of both Heisenberg’s indeterminacy relations and Schrödinger’s wave function.  Both of these views were central to Popper’s philosophy of science twenty years before Landé rejected the Copenhagen interpretation of quantum theory, and Landé references Popper’s views in his own literary corpus.  However, Landé maintains a contrary ontology with respect to the reality of the waves associated with the Schrödinger wave function.

In “Probability in Classical and Quantum Theory” in Scientific Papers Presented to Max Born (1953) Landé argues that classical thermodyna­mics cannot be reduced to deterministic mechanics, and that it is futile to search for hidden causes behind any distribution that satisfies the rules of probability either in classical or quantum physics.  To illustrate his thesis he describes an experiment in which ivory balls are dropped through a tube onto the center of a steel blade, resulting in an observed 50:50 average ratio of balls falling to the left or right.  On the determinist view the 50:50 ratio is possible only if it is already contained in the initial conditions, which in turn either implies an infinite regress to still prior conditions; otherwise the ratio is left unexplained. Landé rejects both these options.  Instead he concludes that random distribution is a physical reality, and that determinism is a purely academic construction, because a program of giving a deterministic theory of statistically distributed events leads nowhere.  Statistical theory can only reduce one prob­ability distribution to another, and when there are ensembles of events conforming to error theory, these events are not reducible to deterministic mechanics.

In New Foundations he states that the belief in deter­minism is as much beyond the domain of physics as the belief in indeterminism, because both ideas are metaphysical theses.  Observation only shows that equal preparation, as far as equality can be achieved, always leads to unpredictably different results.  Landé elevates this general insight to the physical prin­ciple of uncertainty.  In contrast to ordinary experience, classical mechanics was deterministic, while on the other hand ordinary experience and quantum mechanics agree.  Unpredictabil­ity understood as the acausality of individual events must be seen as an irreducible feature of natural science.  Sta­tistical mechanics can describe predictable averages for unpredictable individual events.  In quantum mechanics it is Heisenberg’s great merit that he established quantitative limits for the uncertainty of prediction, but Landé also states that unpredictability of future events does not pre­clude the reconstruction of past individual cases using a deterministic theory.

Landé rejects Heisenberg’s thesis that between two observations in atomic physics the electron is nowhere.  In his discussions of uncertainty and measurement in New Foun­dations he admits that while in classical physics a measure­ment value can be attributed to the object immediately before, during, and after the measurement, in quantum phys­ics there is an active, unpredictable, and unavoidable par­ticipation of the instrument or “meter” in producing the result, in which the microphysical object is thrown from its previous state into a new state.  Therefore in quantum phys­ics the measured value can be ascribed to the atomic object only immediately after the measurement is completed, and any subsequent measurement erases all traces of the first state and produces an entirely new situation.  Nevertheless Landé maintains that it is always possible to reconstruct one and only one path between the two space-time positions according to the laws of classical mechanics post factum, even though the path cannot be predicted.  He distinguishes between direct and indirect measurements; the former are coinciden­ces in space and time, and are the basis for all other measurements, which are indirect measurements.  Energy, momen­tum, and velocity are relevant examples of indirect measure­ments; velocity by definition requires measuring two adja­cent positions at two adjacent times.

Landé rejects the Copenhagen thesis that effectively equates “indirectly observed” with “not observed”, and then with “not observable”, and finally with “nonexistent” and “meaningless”.  The Copenhagen school wrongly maintains that only direct measures count as observation.  To say as they do, that position and momentum cannot be measured simultane­ously is only a half-truth.  If one includes “directly”, then it is trivial because momentum can never be measured directly.  And without the word “directly” the statement is wrong, because the momentum value acquired within a given position increment can be determined by reconstruction of space-time data with the help of theory.  The root of the difficulty with reconstructing values of indirect observ­ables is the ambiguity of their definition, which always requires theory. Landé maintains that classical theory can be used to make the indirect measurements needed to describe the path of an electron.  The controversy about the meaning of an atomic measurement is due to an erroneous connecting of the first measurement with a set of possible future measurements.  When the wave function is used as a mathe­matical representation of just one physical state, there is no confusion.  But when it is used to connect one measurement with a set of future possible measurements, misunderstanding occurs, which results in different interpretations of the wave function including the Copenhagen dualistic thesis that the wave function describes a physical state of matter, which is spread out in space and time, and which suddenly contracts to one point when the particle is measured.

Landé rejects subjective interpretations, and states that quantum physics deals with records of instruments rather than any observer’s consciousness, with physical objects rather than mental pictures, and with statistical distributions rather than lack of knowledge by human obser­vers.  Knowledge and conscious reading by observers are as irrelevant in atomic physics as they are in any other branch of physical science.  Echoing Einstein’s programmatic aim of all physics (but without referencing Einstein), Landé says that the object of natural science is to suppose that the real world exists without human advice and consent, and then to search for general regularities which may help to manipu­late things and events.  The significance of all that quan­tum theory stands for, is to provide formulas, tables, and other rules of correlation between events, and in particular between probabilities of transition.  To speak of the con­traction of the wave packet upon an observation is as sense­less in Landé’s opinion as to speak of a sudden contraction of a statistical mortality table upon an individual fatality.  A probability wave does not guide actual events any more than a mortality table guides actual mortalities, and it shrinks no more than a mortality table shrinks when an actual death occurs.  In Landé’s view the subjectivist confusion begins when the material body used as a measuring instrument is regarded as a subject, and when it is then said that quantum theory has changed the relation between subject and object.  This makes a great impression on those who mistakenly identify statistical distributions recorded by instruments with knowledge or lack of knowledge of observing subjects.

Landé advances a particle interpretation of the Heisenberg uncertainty relations and the Schrödinger wave function, and he criticizes the Copenhagen dualistic inter­pretation.  A central part of his criticism is his alterna­tive interpretation of the two-slit experiment, in which the diffraction pattern is construed by the Copen­hagen school as an interference pattern, that must be taken as evidence for the wave nature of the electron, which in turn must also be construed as a particle before its entry into the slit and then again upon its impact on the photo­graphic plate.  Landé references the Stern-Gerlach experi­ment (1922), the theory of William Duane (1923), and the work of Paul Ehrenfest and Paul S. Epstein (1924). He explains that Duane’s quantum theory was not immediately recognized as a way out of the Copenhagen duality paradox, because Duane’s pro­posed statistical particle theory of diffraction pertains to X-rays in support of the photon theory of light, and also because in 1923 diffraction of electrons was not yet discovered.  Landé references a letter written to him by Born stating that Duane’s 1923 paper on the particle theory of X-ray diffraction was well appreciated at the time of its publication, and stating that it is a riddle as to why its significance was overlooked when the diffraction of matter was discovered a few years later.  Landé remarks that he could not find any hint of recognition in any of the works of Bohr, Born, de Broglie, Dirac, Einstein, Heisenberg, Pauli, or Schrödinger, that Duane’s quantum rule is rele­vant to the alleged dilemma of matter diffraction and duality.

According to Duane’s quantum rule for linear momentum, the incident matter particles do not spread out as contin­uous matter waves or manifest themselves as though they do.  It is the crystal slit with its parallel lattice planes, which is already spread out in space, and which reacts as one rigid mechanical body to the incident particles, that produces the diffraction pattern.  Duane’s rule yields the same observed diffraction directly without appealing to any wave inter­lude.  Therefore, the idea of a dualistic change from matter particles to waves and then back to particles is a quite unnecessary and fantastic invention in Landé’s opinion.  According to his criteria for scientific criticism the scientific value of a theory is measured not only by its power to account for observed data, but also by the criterion of simplicity, freedom from ad hoc assumptions, and reducibil­ity to more general postulates. 

As a result of Duane’s theory, quantum physics has discovered that even such wave-like phenomena as matter diffraction through crystals can be understood in a consistent unitary way as produced exclusively by matter particles obeying the conservation laws of mechanics under special restrictions known as quantum rules, matter particles which react to bodies such as crystals containing periodi­cies in time and space.  Landé thus states that electrons always behave as particles, and never misbehave as waves; he calls Duane’s quantum rule the “missing link” between wave-like appearances and particle reality.  To the two recog­nized general quantum postulates, Planck’s rule for energy exchange and Sommerfeld-Wilson’s rule for angular momentum exchange, Landé adds Duane’s quantum rule for linear impulse changes as the third postulate for quantum physics. Landé thus answers the problem of the two-slit diffraction experiment, the problem of which of the two slits did the particle pass through.  He states that for its contribution to the diffraction pattern, it does not make any difference where exactly the diffraction takes place.  The electron changes its momentum in reaction to the harmonic components of the matter distribution of the crystal screen with two slits as a whole.  All that is important is the conservation of charge and of total momentum in the reaction between elec­tron and diffractor.

For these reasons Landé maintains that the Copenhagen school starts from “wrong physics”, when they maintain that wave-like appearances of matter diffraction are due to the periodic wave action of the electron.  The correct view is that the appearances are due to the periodic structure of the bodies in space (the crystal) and in time (the oscilla­tors) via the three corresponding quantum rules for the momentum and energy activity of the periodic bodies.  He calls his particle interpretation “practical realism”, and offers reinterpretations of Heisenberg’s and Schrödinger’s equations.  The Heisenberg indeterminacy relations describe objective statistical dispersion.  Heisenberg’s claim that simultaneous exact position and momentum measurement pairs, is meaningless and nonexistent, is incorrect because it confuses lack of predictability (which is true) with lack of measurability (which is false).  Unpredictable data including position and momentum measurement pairs can be reconstructed which are more accurate than Planck’s constant.  And what can be measured exists.  The doctrine of the indeterminacy of existence is a “semantic artifice” rather than legitimate physics.  Nor is denying that a particle always is somewhere, warranted by diffraction experiments, because each particle reacts to a space-extended periodic component in the matter distribution of the diffractor.  To say that the particle is nowhere is a “linguistic extravaganza” and not a philosophical innovation.

As for Schrödinger’s equation, Landé says that it does not deal with matter waves, but with probability amplitudes; it is a prob­ability table not essentially different from any mortality table.  The real constituents of matter are discrete parti­cles that occasionally give the appearance of wave action, and that the real constituent of light is a continuous electro­magnetic field that sometimes gives the appearance of photonic particles.  The Schrödinger wave function is a proba­bility curve describing betting odds for future events; it is not a real thing even when the curve looks wave-like.

Landé uses the phraseology of Dr. Samuel Johnson (a critic of Bishop Berkeley’s esse est percipi philosophy, who kicked a great stone and exclaimed “I refute him thus”) saying that you can kick a stone, and you can kick an electron and even a water wave and an electromagnetic wave, and be hurt by them, thus proving their reality.  But you cannot kick or be hurt by a wave-like curve representing probabilities of events.  For Landé, physical interaction is the only correct ontological criterion for physical reality.  He also takes exception to Born, his former colleague, who had initially developed the statistical interpretation of the Schrödinger wave function as a probability amplitude for particles, but who later made what Landé calls “belated concessions” to the Copenhagen dualistic interpretation.  He references Born’s “Physical Reality” appearing in Philosophical Quarterly (1953) in which Born sets forth his own ontological criterion, the criterion of invariance.  In this article Born is not expli­citly opposing Landé, but rather is opposing the idealist metaphysics and the logical positivist philosophy of pheno­menalism.

Born explains his criterion of invariance as follows: Most measurements in physics are not concerned with things that ordinarily interest us, but are concerned with some kind of projection which is defined in relation to a system of reference.  In every physical theory there is a rule which connects the projections of the same object on different reference systems.  The rule is called a law of transforma­tion, and all transformations have the property of forming a “group”, where the sequence of two consecutive transfor­mations is a transformation of the same kind.  Invariants are quantities having the same value for any system of reference, and therefore are independent of the transforma­tions.  The main advances in the conceptual structure of physics consist in the discovery that some quantity formerly regarded as the property of a thing, is in fact only the property of a projection. 

The long historical develop­ment of the theory of gravitation from pre-Newtonian physics to relativity theory is one example.  Another example is the development of quantum physics.  An observation or measure­ment in quantum physics does not refer to a natural pheno­menon as such, but to its projection on a system of refer­ence which is the whole apparatus used in the experiment. By use of instruments the physicist can obtain certain restricted but well described information, which is independent of the observer and of his apparatus, namely the invar­iant features of a number of properly devised experiments. Bohr’s complementarity principle means that the maximum knowledge of the quantum can only be obtained by a suffi­cient number of independent projections of the same physical entity.  The final result of complementary experiments is a set of invariants characteristic of the entity, and these invariants are called “charge”, “rest mass”, “spin”, etc.  In every instance, when we are able to determine these quan­tities, we decide we are dealing with a definite particle.  The words “photon”, “electron”, etc. signify definite invar­iants that can be constructed by combining a number of observations.

Born maintains that the idea of invariance is the clue to a rational concept of reality, not only in physics but also in every aspect of the world.  The power of the mind to neglect the differences of sense impressions and to be aware only of their invariant features is the most impressive fact of man’s mental structure.  He proposes translating the term “gestalt” not as “shape” or “form” but as “invariant”. And he proposes speaking of invariants of perception instead of sense impressions as the elements of our mental world.  In the closing paragraph of his article Born considers the reality of waves according to his ontological criterion of invari­ance.  He says that we regard waves on a lake as real, though they are nothing material but are only a certain shape of the surface of the water.  The justification for this view is that they can be characterized by certain invariant quantities like frequency and wavelength, or as a spectrum of these.  Born says that the same thing holds for light waves, and he asks rhetorically why the physicist should withhold the epithet “real” even if the waves repre­sent in quantum theory only a distribution of probability.

In his New Foundations Landé replies to Born’s rhetorical question from the viewpoint of his own criterion of interaction: Particles are real while Schrödinger waves are not real, for the same reason that sick people are real things while the wave-like curve which symbolizes the probability distribution during a fluctuating epidemic is not a real thing.  Landé says that a given formalism can always be interpreted in a variety of ways.  At the conclu­sion of his New Foundations he gives seven alternative interpretations of the Schrödinger wave function including Schrödinger’s, de Broglie’s, Bohm’s, Heisenberg’s subjec­tive interpretation, Heisenberg’s objective interpretation, Bohr’s instrumentalist interpretation, and Landé’s own particle interpretation.  He does not include Popper’s propensity interpretation.  He states that this list is indicative of the present confusion regarding the wave function, and paraphrases Mao Tse Tung saying that while it may be good politics to let a hundred flowers bloom and let a hundred schools contend, it is not good enough for sci­ence.  He asserts that only his interpretation stands up to realistic criticism in accordance with “monolithic” quantum mechanics, i.e., quantum theory with an ontology that is consistent with the rest of physics.  However, unlike Landé and Popper’s criterion of interaction for physical reality, Born’s criterion of invariants is consistent with the contemporary pragmatist thesis of ontological relativity, because Born’s subordinates ontology to the empirically adequate theory describing the invariants.

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