Abstract
It is a curious fact that our popular text books and most discussions of conceptual and philosophical problems of quantum mechanics are still based on the very first attempts to formalize this theory which have been worked out more than 50 years ago. These formulations of nonrelativistic quantum theory do, however, not represent the state of the art.
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References
C. Agnes and M. Rasetti: Word problem, undecidability and chaos. In: Advances in Nonlinear Dynamics and Stochastic Processes II. Ed. by G. Paladin and A. Vulpiani. Singapore. World Scientific. 1987. Pp. 1–24.
F. Bacon: De Dignitate et Auzumentis Scientarum. 1623. English translation: Of the Advancement and Proficience of Learning. Oxford. 1640.
N. Bohr: Quantum physics and philosophy, causality and complementarity. In: Philosophy in the Mid-Century. A Survey. Ed. by R. Klibansy. Florence. La Nuova Italia Editrice. 1958. Pp. 308–314.
O. Bratteli and D. W. Robinson: Operator Algebras and Quantum Statistical Mechanics. C*- and W*-Algebras, Symmetry Groups, Decomposition of States. Vol. 1. New York. Springer. 1979.
O. Bratteli and D. W. Robinson: Operator Algebras and Quantum Statistical Mechanics. Equilibrium States. Models in Quantum Statistical Mechanics. Vol. 2. New York. Springer. 1981.
M. L. d. Chiara: Logical self reference, set theoretical paradoxes and the measurement problem in quantum mechanics. J. Philosophical Logic 6, 331–347 (1977).
P. Curie: Sur la symétrie dans les phénomènes physiques. Journal de Physique 3, 393 (1894).
P. Curie: Reprinted m: Oeuvres de Pierre Curie. Paris. Gauthier-Villars. 1908. Pp. 118–141.
P. A. M. Dirac: The Principles of Quantum Mechanics. London. Oxford University Press. 1930.
J. Dixmier: C*-Algebras. Amsterdam. North-Holland. 1977.
D. A. Dubin: Solvable Models in Algebraic Statistical Mechanics. Oxford. Oxford University Press. 1974.
A. Einstein: Einleitende Bemerkung über Grundbegriffe. In: Louis de Broglie. Physicien et Penseur. Paris. Editions Albin Michel. 1953.
B. d’Espagnat: Conceptual Foundations of Quantum Mechanics. Second ed. London. Benjamin. 1976.
B. d’Espagnat: Physics and reality. In: Atti del Congresso Logica e Filosofia della Scienza, oggi. Vol. II Epistemologia e logica induttiva. Bologna. CLUEB. 1986. Pp. 73–78.
D. Finkelstein: Finite physics. In: The Universal Turing Machine. A Half-Century Survey. Ed. by R. Herken. Hamburg. Kammerer & Unverzagt. 1988. Pp. 349–376.
D. Finkelstein and S. R. Finkelstein: Computational complementarity. Int. J. Theor. Phys. 22, 753–779 (1983).
K. Gödel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik 38, 173–198 (1931).
A. S. Holevo: Probabilistic and Statistical Aspects of Quantum Theory. Amsterdam. North-Holland. 1982.
R. V. Kadison and J. R. Ringrose: Fundamentals of the Theory of Operator Algebras. I. Elementary Theory. New York. Academic Press. 1983.
R. V. Kadison and J. R. Ringrose: Fundamentals of the Theory of Operator Algebras. II. Advanced Theory. Orlando. Academic Press. 1986.
A. N. Kolmogorov: Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin. Springer. 1933.
A. Komar: Undecidability of macroscopically distinguishable states in quantum fieldtheory. Phys. Rev. 133, B542–B544 (1964).
B. O. Koopman: Hamiltonian systems and transformations in Hilbert space. Proc. Nat. Acad. Sci. U.S. 17, 315–318 (1931).
W. Kuyk: Complementarity in Mathematics. Dordrecht. Reidel. 1977.
W. E. Lamb: Schrödinger’s cat. In: Reminiscences About a Great Physicist: Paul Adrien Maurice Dirac. Ed. by B. N. Kursunoglu and E. P. Wigner. Cambridge. Cambridge University Press. 1987. Pp. 249–261.
L. H. Loomis: Note on a theorem by Mackey. Duke Math. J. 19, 641–645 (1952).
G. W. Mackey: A theorem of Stone and von Neumann. Duke Math. J. 16, 313–326 (1949).
J. v. Neumann: Die Eindeutigkeit der Schrödingerschen Operatoren. Mathematische Annalen 104, 570–578 (1931).
J. v. Neumann: Mathematische Grundlagen der Quantenmechanik. Berlin. Springer. 1932.
J. v. Neumann: Zur Operatorenmethode in der klassischen Mechanik. Annals of Mathematics 33, 587–642, (1932).
J. v. Neumann: Zur Operatorenmethode in der klassischen Mechanik. Annals of Mathematics 33, 789–791 (1932).
W. Pauli: Naturwissenschaftliche und erkenntnistheoretische Aspekte der Ideen vom Unbewussten. Dialectica 8, 283–301 (1954).
G. K. Pedersen: C*-Algebras and their Automorphism Groups. London. Academic Press. 1979.
A. Peres and W. H. Zurek: Is quantum theory universally valid? Amer. J. Phys. 50, 807–810 (1982).
C. Piron: Quantum mechanics: fifty years later. In: Symposium on the Foundations of Modern Physics. 50 Years of the Einstein-Podolsky-Rosen Gedankenexperiment. Ed. by P. Lahti and P. Mittelstaedt. Singapore. World Scientific. 1985. Pp. 207–211.
M. Polanyi: Personal Knowledge. London. Routledge and Kegan Paul. 1958.
H. Primas: Theory reduction and non-Boolean theories. J. Math. Biology 4, 281–301 (1977).
H. Primas: Foundations of theoretical chemistry. In: The New Experimental Challenge to Theorists. Ed. by R. G. Woolley. New York. Plenum Press. 1980.
H. Primas: Chemistry, Quantum Mechanics and Reductionism. Berlin. Springer, second edition 1983. 1981.
H. Primas: Objekte in der Quantenmechanik. In: Grazer Gespräche 1986.Ganzheitsphysik. Ed. by M. Heindler and F. Moser. Graz. Technische Universität Graz. 1987. Pp. S. 163–201.
H. Primas: Contextual quantum objects and their ontic interpretation. In: Symposium on the Foundations of Modern Physics, 1987. The Copenhagen Interpretation 60 Years after the Como Lecture. Ed. by P. Lahti and P. Mittelstaedt. Singapore. World Scientific. 1987. Pp. 251–275.
H. Primas: Induced nonlinear time evolution of open quantum objects. In: Sixty-two Years of Uncertainty: Historical, Philosophical and Physics Inquiries into the Foundations of Quantum Mechanics. Ed. by A. I. Miller. New York. Plenum. 1990.
H. Primas: Time-asymmetric phenomena in biology. Complementary exophysical descriptions arising from deterministic quantum endophysics. In: Proceedings of the International Workshop “Information Biothermodynamics”. Torun. In press.
G. A. Raggio: States and Composite Systems in W*-algebraic Quantum Mechanics. Thesis ETH Zürich, No. 6824, ADAG Administration & Druck AG, Zürich. 1981.
F. Rapp: Kausale und teleologische Erklärungen. In: Formen teleologischen Denkens. Ed. by H. Poser. Berlin. TUB-Dokumentation, Heft 11, Technische Universität Berlin. 1981. Pp. 1–15.
A. Rosenberg: The number of irreducible representations of simple rings with no minimal ideals. Amer. J. Math. 75, 523–530 (1953).
O. E. Rössler: Endophysics. In: Real Brains, Artificial Minds. Ed. by J. L. Casti and A. Karlqvist. New York. North-Holland. 1987. Pp. 25–46.
J. Rothstein: Thermodynamics and some undecidable physical questions. Philosophy of Science 31, 40–48 (1964).
S. Sakai: C*-Algebras and W*-Algebras. Berlin. Springer. 1971.
G. L. Sewell: Quantum Theory of Collective Phenomena. Oxford. Oxford University Press. 1986.
A. Shimony: The Quantum World. Manuscript for a yet unpublished book, distributed at a seminar at the ETH Zürich, Nov. 1984.
A. Shimony: Events and processes in the quantum world. In: Quantum Concepts in Space and Time. Ed. by R. Penrose and C. J. Isnam. Oxford. Clarendon Press. 1986. Pp. 182–203.
G. Spencer Brown: Laws of Form. London. Allen and Unwin. 1969.
M. H. Stone: Linear transformations in Hilbert space. III. Operational methods and group theory. Proc. Nat. Acad. U.S. 16, 172–175 (1930).
F. Strocchi: Elements of Quantum Mechanics of Infinite Systems. Singapore. World Scientific. 1985.
A. Tarski: Logic, Semantics, Metamathematics. Oxford. Clarendon Press. 1956.
A. Tarski: Truth and proof. Scientific American 220, 63–77 (1969).
M. Zwick: Quantum measurement and Gödel’s proof. Speculations in Science and Technology 1, 135–145, (1978).
M. Zwick: Quantum measurement and Gödel’s proof. Speculations in Science and Technology 1, 422–423 (1978).
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Primas, H. (1990). Mathematical and Philosophical Questions in the Theory of Open and Macroscopic Quantum Systems. In: Miller, A.I. (eds) Sixty-Two Years of Uncertainty. NATO ASI Series, vol 226. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8771-8_14
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DOI: https://doi.org/10.1007/978-1-4684-8771-8_14
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