Philosophic Foundations of Quantum Mechanics

Noted philosopher offers a philosophical interpretation of quantum physics that reviews the basics of quantum mechanics and outlines their mathematical methods, blending philosophical ideas and mathematical formulations to develop a variety of concrete interpretations. 1944 edition.

Physics concerns direct analysis of the physical world, while philosophy analyzes knowledge about the physical world. This volume combines both disciplines for a philosophical interpretation of quantum physics — an interpretation free from the imprecision of metaphysics, offering a view of the atomic world and its quantum mechanical results as concrete as the visible everyday world.Written by an internationally renowned philosopher who specialized in symbolic logic and the theory of relativity, this approach consists of three parts. The first section, which requires no background in math or physics, reviews the basics of quantum mechanics, outlining their philosophical interpretation and summarizing their results. The second part, which presupposes a knowledge of calculus, outlines the mathematical methods of quantum mechanics; and the third part blends the philosophical ideas of the first part and the mathematical formulations of the second part to develop a variety of interpretations of quantum mechanics. The author presents in-depth discussions of each interpretation, constructing a conclusion in terms of three-valued logic that offers readers a satisfactory logical form of quantum mechanics.Focusing on clarification of concepts rather than developing problem-solving skills, this volume will prove enlightening to students of mathematics, physics, and the other sciences.

PART I: GENERAL CONSIDERATIONS 1. Causal laws and probability laws 2. The probability distributions 3. The principle of indeterminacy 4. The disturbance of the object by the observation 5. The determination of unobserved objects 6. Waves and corpuscles 7. Analysis of an interference experiment 8. Exhaustive and restrictive interpretationsPART II: OUTLINES OF THE MATHEMATICS OF QUANTUM MECHANICS 9. Expansion of a function in terms of an orthogonal set 10. Geometrical interpretation in the function space 11. Reversion and iteration of transformations. 12. Functions of several variables and the configuration space 13. Derivation of Schrödinger's equation from de Broglie's principle 14. "Operators, eigen-functions, and eigen-values of physical entities" 15. The commutation rule 16. Operator matrices 17. Determination of the Probability distributions 18. Time dependence of the ?-function 19. Transformation to other state functions 20. Observational determination of the ?-function 21. Mathematical theory of measurement 22. The rules of probability and the disturbance by the measurement 23. The nature of probabilities and of statistical assemblages in quantum mechanicsPART III: INTERPRETATIONS 24. Comparison of classical and quantum mechanical statistics 25. The corpuscle interpretation 26. The impossibility of a chain structure 27. The wave interpretation 28. Observational language and quantum mechanics 29. Interpretation by a restricted meaning 30. Interpretation through a three-valued logic 31. The rules of two-valued logic 32. The rules of three-valued logic 33. Suppression of causal anomalies through a three-valued logic 34. Indeterminacy in the object language 35. The limitation of measurability 36. Correlated systems 37. Conclusion Index