Abstract
An integrated view concerning the probabilistic organization of quantum mechanics is obtained by systematic confrontation of the Kolmogorov formulation of the abstract theory of probabilities, with the quantum mechanical representationand its factual counterparts. Because these factual counterparts possess a peculiar spacetime structure stemming from the operations by which the observer produces the studied states (operations of state preparation) and the qualifications of these (operations of measurement), the approach brings forth “probability trees,” complex constructs with treelike spacetime support.
Though it is strictly entailed by confrontation with the abstract theory of probabilities as it now stands, the construct of a quantum mechanical probability treetransgresses this theory. It indicates the possibility of an extended abstract theory of probabilities including explicit representations of the cognitive operations involved in the probabilistic descriptions. So quantum mechanics appears to be neither a “normal” probabilistic theory nor an “abnormal” one, but a pioneering particular realization of afuture extended abstract theory of probabilities.
The consequences of the integrated perception of the probabilistic organization of quantum mechanics are developed constructively. The current identifications of spectral decompositions, with superpositions of states, are removed. Then: (a) Inside the frontiers of the purely operational-observational orthodox formalism, operators of state preparation and the calculus with these are defined consistently with the definition and the calculus of quantum mechanical operators representing measurable dynamical quantities. This permits to grasp the physical meaning of superselection rules. Furthermore, a complement to the quantum theory of measurements is obtained. These prolongations of the orthodox formalism bring forth a “probabilistic incompleteness” of the quantum theory. (b) Beyond quantum mechanics as it now stands, a model is outlined that removes this probabilistic incompleteness, “the [particle + medium] individual model,”microscopic by certain aspects andcosmic by others.
Globally, the approach draws attention upon the possibility and the interest of a general representation of the descriptions of any kind founded upon the explicit specification of the epistemic operations—with their spacetime features—by which the observer, who always is involved, produces the objects to be qualified and the qualifications of these.
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References
M. Mugur-Schächter, “Elucidation of the probabilistic structure of quantum mechanics,”Found. Phys. 13, 419–465 (1983).
M. Mugur-Schächter, “Esquisse d'une représentation générale et formalisée des descriptions et le statut descriptionnel de la mécanique quantique,”Epist. Lett. 1–67 (1984).
M. Mugur-Schächter, “Mécanique quantique, probabilités, relativités descriptionnelles et propensions popperiennes,” in R. Bouveresse and H. Barreau, eds.,Karl Popper Science et Philosophie (Vrin, Paris, 1991).
M. Mugur-Schächter, “Operations, classifications, forms, probabilities, strategies, Shannon information,”Analyse de Systèmes XI(4) 40–82 (1985).
M. Mugur-Schächter, “The probability trees of quantum mechanics: Probabilistic metadependence and meta-metadependence,” in M. Carvallo, ed.,Nature, Cognition and Systems (II) (Kluwer, Dordrecht, to be published).
K. R. Popper,The Logic of Scientific Discovery (Hutchinson, London, 1959).
K. R. Popper, “Quantum mechanics without The Observer,” inQuantum Theory and Reality, Mario Bunge, ed. (Springer, 7–44. New York, 1967).
G. Mackey,Mathematical Foundations of Quantum Mechanics (Benjamin, New York, 1963).
S. Gudder, “A generalized measure and probability theory,” inFoundations of Probability Theory, Statistical Inference, and Statistical Theories of Science (Reidel, Dordrecht, 1976), pp. 120–139.
P. Suppes, “The probabilistic argument for a nonclassical logic of quantum mechanics,”Philos. Sci. 33, 14–21 (1966).
P. Mittelstaedt, “On the applicability of the probability concept to quantum theory,” inFoundations of Probability Theory, Statistical Inference, and Statistical Theories of Science (Reidel, Dordrecht 1976), pp. 155–165.
B. C. Van Fraassen and C. A. Hooker, “A semantic analysis of Nields Bohr's philosophy of quantum mechanics,” inFoundations of Probability Theory, Statistical Inference, and Statistical Theories of Science (Reidel, Dordrecht, 1976), pp. 221–241.
L. Cohen, “Rules of probability in quantum mechanics,”Found. Phys. 18, 983–998 (1988).
D. Bohm,Quantum Theory (Prentice-Hall, Englewood Cliffs, New Jersey, 1951).
L. de Broglie, “Une tentative d'interprétation causale et non-linéaire de la mécanique ondulatoire (Gauthier Villars, Paris, 1956).
H. Primas, “Realistic interpretation of the quantum theory for individual objects,”Nuova Critica I–II, 13–14, 41–72 (1990).
E. Lubkin, (1976) “Quantum logic, convexity, and a Necker-cube experiment,” inFoundations of Probability Theory, Statistical Inference, and Statistical Theories of Science (Reidel, Dordrecht, 1976), pp. 143–153.
L. Cohen, “Momentum spread: Amplitude and current contributions,”Found. Phys. 20, 1455–1473 (1990).
J. L. Park, and H. Margenau, “Simultaneous measurability in quantum theory,”Int. J. Theor. Phys. 1, 211–283 (1968).
M. Mugur-Schächter, “Quantum mechanics and relativity: Attempt at a new start,”Found. Phys. Lett. 2, 261–286 (1989).
E. P. Wigner,Am. J. Phys. 31, (1963).
M. Mugur-Schächter, “Spacetime quantum probabilities, relativized descriptions, and popperian propensities. Part II: Relativized descriptions and popperian propensities,”Found. Phys., forthcoming.
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Mugur-Schächter, M. Spacetime quantum probabilities, relativized descriptions, and popperian propensities. Part I: Spacetime quantum probabilities. Found Phys 21, 1387–1449 (1991). https://doi.org/10.1007/BF01889651
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DOI: https://doi.org/10.1007/BF01889651