KARL POPPER AND FALSIFICATIONIST CRITICISM
BOOK V - Page 3
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
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
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
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
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
Popper has arguments for probability
interpretations that are exclusively objective,
but any objective interpretation requires a
realistic philosophy with an indeterministic
Therefore he also advances arguments for
realism and indeterminacy, as well as for
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.