Abstract
What is the structure of reality? Physics is supposed to answer this question, but a purely empiristic view is not sufficient to explain its ability to do so. Quantum mechanics has forced us to think more deeply about what a physical theory is. There are preconditions every physical theory must fulfill. It has to contain, e.g., rules for empirically testable predictions. Those preconditions give physics a structure that is “a priori” in the Kantian sense. An example is given how the lattice structure of quantum mechanics can be understood along these lines.
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References
Aerts, D., and Daubechies, I. (1978). Physical justification for using the tensor product to describe two quantum systems as one joint system.Helvetica Physica Acta,51, 661.
Birkhoff, G., and von Neumann, J. (1936). The logic of quantum mechanics.Annals of Mathematics,37, 823.
Drieschner, M. (1979).Voraussage, Wahrscheinlichkeit, Objekt. Über die Grundlagen der Quantenmechanik, Springer, Heidelberg.
Drieschner, M. (1992). The subject matter of quantum mechanics,International Journal of Theoretical Physics,31, 1615–1625.
Fölsing, A. (1983).Galileo Galilei—Prozess ohne Ende, Piper, Munich.
Hume, D. (1963).An Enquiry Concerning Human Understanding, E. C. Mossner, ed., New York.
Kant, I. (1955).Prolegomena to Any Future Metaphysics, P. Carus, transl., La Salle, Illinois.
Matolcsi, T. (1975). Tensor product of Hilbert lattices and free orthodistributive product of orthomodular lattices.Actes de L'académie des Sciences de Szeged, Classe de Sciences Mathématiques,37, 263.
Piron, C. (1993).International Journal of Theoretical Physics, this issue.
Pulmannová, S. (1985). Tensor product of quantum logics.Journal of Mathematical Physics,26, 1.
Scheibe, E., Süssmann, G., and von Weizsäcker, C. F. (1958). Komplementarität und Logik III: Mehrfache Quantelung.Zeitschrift für Naturforschung,13a, 705.
Zecca, A. (1981). The superposition of the states and the logic approach to quantum mechanics.International Journal of Theoretical Physics,20, 191.
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Drieschner, M. Lattice of quantum predictions. Int J Theor Phys 32, 1853–1861 (1993). https://doi.org/10.1007/BF00979506
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DOI: https://doi.org/10.1007/BF00979506