Lande 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), Lande 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 Lande'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 Lande’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.
          Lande 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 diffraction 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.  Lande references the Stern-Gerlach experi­ment, 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.  Lande 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.  Lande 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 Lande'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 criteria 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 containing periodi­cies in time and space.  Lande 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, Lande adds Duane's quantum rule for linear impulse changes as the third postulate for quantum physics.  Lande 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 matters is the conservation of charge and of total momentum in the reaction between elec­tron and diffractor.
          For these reasons Lande 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 uncertainty 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, Lande 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, which occasionally give the appearance of wave action, and the real constituent of light is a continuous electro­magnetic field, which 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.  Lande 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 Lande, 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 Lande 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 Lande, 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 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 which was formerly regarded as the property of a thing, is in fact only the property of a projection.  The 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.  Using 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 Lande 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.  Lande 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 together with Bohr's instrumentalist interpretation, and Lande's own 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.

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, Heisenberg's 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.  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 an indeterministic 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 the objective interpreta­tion.  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.  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 he 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 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; and 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 Lande's description of the experiment with the ivory balls and steel blade, which Lande 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(a,ß) is the proportion of equally possible cases compa­tible with the event ß, that are also favorable to the event a.  The frequency interpretation is that P(a,ß) is the relative frequency of the events a among the events ß.  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, where the weights are experimentally determined measures of the propensity or tendency of a pos­sibility to realize itself upon repetition.  Thus in the propensity interpretation the measure P(a,ß) is the propen­sity of a given experimental conditions ß.  It is the sum of the weights of the possible cases that satisfy the condition ß which are also favorable to a, divided by the sum of the weights of the possible cases that satisfy ß.  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.

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