An Axiomatic Basis for Quantum Mechanics

1. Front Matter

   Pages I-X

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2. The Problem of Formulating an Axiomatics for Quantum Mechanics

   • Günther Ludwig

   Pages 1-7

3. Pretheories for Quantum Mechanics

   • Günther Ludwig

   Pages 8-46

4. Base Sets and Fundamental Structure Terms for a Theory of Microsystems

   • Günther Ludwig

   Pages 47-100

5. Embedding of Ensembles and Effect Sets in Topological Vector Spaces

   • Günther Ludwig

   Pages 101-125

6. Observables and Preparators

   • Günther Ludwig

   Pages 126-151

7. Main Laws of Preparation and Registration

   • Günther Ludwig

   Pages 152-186

8. Decision Observables and the Center

   • Günther Ludwig

   Pages 187-207

9. Representation of ℬ, ℬ’ by Banach Spaces of Operators in a Hilbert Space

   • Günther Ludwig

   Pages 208-226

10. Back Matter

    Pages 227-246

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This book is the first volume of a two-volume work, which is an improved version of a preprint [47] published in German. We seek to deduce the funda­ mental concepts of quantum mechanics solely from a description of macroscopic devices. The microscopic systems such as electrons, atoms, etc. must be detected on the basis of the macroscopic behavior of the devices. This detection resembles the detection of the dinosaurs on the basis offossils. In this first volume we develop a general description of macroscopic systems by trajectories in state spaces. This general description is a basis for the special de­ scription of devices consisting of two parts, where the first part is acting on the second. The microsystems are discovered as systems transmitting the action. Axioms which describe general empirical structures of the interactions between the two parts of each device, give rise to a derivation of the Hilbert space structure of quantum mechanics. Possibly, these axioms (and consequently the Hilbert space structure) may fail to describe other realms than the structure of atoms and mole­ cules, for instance the "elementary particles". This book supplements ref. [2]. Both together not only give an extensive foundation of quantum mechanics but also a solution in principle of the measuring problem.

• Mechanics
• Space
• Space Structure
• Structure
• atoms
• behavior
• electron
• electrons
• elementary particle
• particles
• quantum mechanics

• Fachbereich Physik, Philipps-Universität, Marburg, Federal Republic of Germany

  Günther Ludwig

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