Quanta, Logic and Spacetime (Google eBook)

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World Scientific, Jan 1, 2003 - Science - 487 pages
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In this expanded edition of Quanta, Logic and Spacetime, the logical base is greatly broadened and quantum-computational aspects of the approach are brought to the fore. The first two parts of this edition may indeed be regarded as providing a self-contained and logic-based foundation for OCo and an introduction to OCo the enterprise known as quantum computing. The rest of the work takes on the task (as in the first edition) of computing from first principles certain dynamical expressions which turn out to compare favorably with the Lagrangian densities of the (massless) Standard Model, including gravity. The logic of this process is now subject to greater formal rigor than was possible in the first edition, and the central thesis OCo that quantum physics at a fundamental level may itself be realized as a species of quantum computation OCo is strongly underscored. Errata. Errata (159 KB). Sample Chapter(s). Foundations (207 KB). Contents: Preliminaries: Foundations: Quantum Sets; Group Duality, Coherence and Cyclic Actions; Computational Paradigms: Natural Deduction; Quantum Logic; The Computational Resources of Quantum Logic; The Plenum: A Quantum Net; Towards a Correspondence Principle for the Quantum Net; A Correspondence Principle for the Quantum Net; Dynamics I; Dynamics II; Comparisons, Interpretations and Speculations. Readership: Mathematicians and physicists."

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Quantum Sets
Group Duality Coherence and Cyclic Actions
Natural Deduction
5 Quantum Logic
The Computational Resources of Quantum Logic
A Quantum Net
Towards a Correspondence Principle for the Quantum Net
Dynamics I
Dynamics II
Comparisons Interpretations and Speculations
Citation Index
Notational Index and Glossary
Subject Index

A Correspondence Principle for the Quantum Net

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Page ii - Quantum mechanical calculations follow a simple two-step pattern: you write down the answer, and then you do the computation.
Page 3 - pure states" of the system are in one-to-one correspondence with the normalized elements of the Hilbert space (hence in one-to-one correspondence with the rays, or one-dimensional subspaces, of the said Hilbert space). A general "state" of the system is identifiable with a certain convex combination of such normalized elements or pure states (cf.
Page 19 - Contraction then produces a sum of transition amplitudes whose value is independent of the representation of 6 as a linear combination of the type shown in equation (1.3.6).

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