Journal ArticleDOI
The Logic of Quantum Mechanics
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In this article, it was shown that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and in particular one can never predict both the position and the momentum of S, (Heisenberg's Uncertainty Principle) and most pairs of observations are incompatible, and cannot be made on S simultaneously.Abstract:
One of the aspects of quantum theory which has attracted the most general attention, is the novelty of the logical notions which it presupposes It asserts that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and that in particular one can never predict with certainty both the position and the momentum of S, (Heisenberg’s Uncertainty Principle) It further asserts that most pairs of observations are incompatible, and cannot be made on S, simultaneously (Principle of Non-commutativity of Observations)read more
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Journal ArticleDOI
Decoherence, einselection, and the quantum origins of the classical
TL;DR: In this article, it was shown that many of the symptoms of classicality can be induced in quantum systems by their environments, which leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information.
Book ChapterDOI
The Logic of Quantum Mechanics
TL;DR: In this article, it was shown that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and that in particular one can never predict both the position and the momentum of S, (Heisenberg's Uncertainty Principle).
Journal ArticleDOI
The mathematical foundations of quantum mechanics
TL;DR: The Mathematical Foundations of Quantum Mechanics as mentioned in this paper were the first to provide a rigorous mathematical formulation of quantum theory and a systematic comparison with classical mechanics so that the full ramifications of the quantum revolution could be clearly revealed.
Journal ArticleDOI
An operational approach to quantum probability
Edward Davies,John T. Lewis +1 more
TL;DR: In this article, the authors provide a mathematical framework for the process of making repeated measurements on continuous observables in a statistical system and make a mathematical definition of an instrument, a concept which generalises the notion of an observable and that of an operation.
Journal ArticleDOI
Conformal partial waves and the operator product expansion
F.A. Dolan,Hugh Osborn +1 more
TL;DR: By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for O(d,2) succinct expressions for the functions, conformal partial waves, representing the contribution of an operator of arbitrary scale dimension Δ and spin l together with its descendants to conformal four point functions for d = 4, recovering old results, and also for d ≥ 6 as discussed by the authors.