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Attempt of an axiomatic foundation of quantum mechanics and more general theories. III

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Abstract

Starting from axioms as physical as possible [1, 2, 3] about “effects” and “ensembles”, we shall investigate further consequences.

Concerning part I and II [4, 5] the axioms can be so formulated as to be surveyed more easily.

Besides, it is possible to prove some important theorems more simply.

New structures of the lattice of decision effects are pointed out, leading in two subsequent papers at last to the final aim, the structure of Hilbert-space.

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References

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    Ludwig, G.: Hauptsätze über das Messen als Grundlage der Hilbert-Raumstruktur der Quantenmechanik. Z. Naturforsch.22a, 1303–1323 (1967).

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    —— Ein weiterer Hauptsatz über das Messen als Grundlage der Hilbert-Raumstruktur der Quantenmechanik. Z. Naturforsch.22a, 1324–1327 (1967).

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    -- English preprint combining [1] and [2].

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    —— Versuch einer axiomatischen Grundlegung der Quantenmechanik und all-gemeinerer physikalischer Theorien. Z. Physik181, 233–260 (1964).

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    —— Attempt of an axiomatic foundation of quantum mechanics and more general theories, II. Commun. Math. Phys.4, 331–348 (1967).

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    Bourbaki, N.: Espaces vectoriels topologiques, chap. II, deuxième édition. Paris: Hermann 1966.

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    Rose, G.: Zur Orthomodularität von Wahrscheinlichkeitsfeldern. Z. Physik181, 331–332 (1964).

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    Birkhoff, G.: Lattice Theory. Amer. Math. Soc. Colloq. Publ., 25, revised (1948).

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Ludwig, G. Attempt of an axiomatic foundation of quantum mechanics and more general theories. III. Commun.Math. Phys. 9, 1–12 (1968). https://doi.org/10.1007/BF01654027

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Keywords

  • Neural Network
  • Statistical Physic
  • Complex System
  • Quantum Mechanic
  • General Theory