Quantum Reprogramming - E. J. Post

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Résumé :
Many, perhaps most textbooks of quantum mechanics present a Copenhagen, single system angle; fewer present the subject matter as an instrument for treating ensembles, but the two methods have been silently coexisting since the mid-Thirties. This lingering dichotomy of purpose for a major physical discipline has much shrouded further insights into the foundations of quantum theory. Quantum Reprogramming resolves this long-standing dichotomy by examining the mutual relation between single systems and ensembles, assigning each its own tools for treating the subject at hand: i.e., Schr?dinger-Dirac methods for ensembles versus period integrals for single systems. A unified treatment of integer and fractional quantum Hall effects and a finite description of the electron's anomalies are mentioned as measures of justification for the chosen procedure of resolving an old-time dichotomy. The methods of presentation are, in part, elementary, with repetitive references needed to delineate differences with respect to standard methods. The parts on period integrals are developed with a perspective on elementary methods in physics, thus leading up to some standard results of de Rham theory and algebraic topology. Audience: Students of physics, mathematics, philosophers as well as outsiders with a general interest in the conceptual development of physics will find useful reading in these pages, which will stimulate further inquiry and study.

Sommaire:
I. Introductory Remarks. The Copenhagen Era. II. The Psychology of the 1925 Revolution. III. Reassessing Copenhagen. IV. Copenhagen versus Copenhagen. V. Von Neumann, Popper-EPR, Bohm, Bell, Aspect. A Sommerfeld-de Rham View of Single Systems. VI. Period Integrals: A Universal Tool of Physics. VII. Larmor and Cyclotron Aspects of Flux Quanta. VIII. Fitting Period Integrals to Physics. IX. Implications of Cooperative Behavior. X. A Tale of Fine Structure Coincidences. XI. Classical Nonclassical Asymptotics. An Attempt at Cohomological Synthesis. XII. Arrowed Time and Cyclic Time. XIII. Quantum Cohomology. XIV. Optimizing Reduction to Familiar Concepts. Ramifications of the Two-Tier View of Q.M. XV. Compatibility of Quantum Mechanics and Relativity. XVI. Quantum Understanding in Global Perspective. XVII. Absolute versus Relative Indeterminism. XVIII. The Diffeo-4 Mandate of Michelson-Sagnac. Epilogue for Extrapolating a Favor of Fortune. Notes and References. Index.