| Description |
1 online resource (xx, 465 pages) : illustrations |
| Contents |
pt. I. Preliminaries. 1. Foundations. 1.1. Physics without objects. 1.2. Observables. 1.3. Finite dimensional heuristics -- 2. Quantum sets. 2.1. Logics and lattices. 2.2. Some first-order quantum aggregates. 2.3. Quantum set theory -- 3. Group duality, coherence and cyclic actions. 3.1. The duality of groups and Hopf algebras. 3.2. Quantum versions of cyclic groups -- pt. II. Computational paradigms. 4. Natural deduction. 4.1. Natural deduction for a minimal system. 4.2. The Curry-Howard isomorphism. 4.3. The Gentzen sequent calculus -- 5. Quantum logic. 5.1. Orthologic and its model theory. 5.2. Quantum logic proper: Hilbert models. 5.3. Critique of quantum logic -- 6. The computational resources of quantum logic. 6.1. An orthological toy. 6.2. GQ: a minimal intuitionisitic propositional sequent calculus for quantum resources. 6.3. Intuitionistic orthologic and GQ. 6.4. Quantum computing in classical time: an algebraic model. 6.5. Conclusions -- pt. III. The plenum. 7. A quantum net. 7.1. Symmetries of the qubit. 7.2. A superconducting quantum net. 7.3. A geometrical approach to the net -- 8. Towards a correspondence principle for the quantum net. 8.1. Vectors. 8.2. Transport, curves and a little Chenism -- 9. A correspondence principle for the quantum net. 9.1. Spinor duality. 9.2. Variation, derivation and the Dirac maps. 9.3. The [symbol] operators. 9.4. The real subspace, frame choices and Dirac matrices. 9.5. The correspondence principle -- 10. Dynamics I. 10.1. Dynamic transport and the Lagrangian. 10.2. Problems with the Dirac operator. 10.3. Feynman path integral and field equations -- 11. Dynamics II. 11.1. The defect's new clothes. 11.2. Dynamic transport and the Lagrangian, revisited. 11.3. Resolution and rescaling -- 12. Comparisons, interpretations and speculations. 12.1. An abbreviated sketch of the Standard Model. 12.2. Asymptotic freedom and grand unification. 12.3. Superconduction and electroweak unification. 12.4. Long distance topological implications. 12.5. Quantization, connections and loop quantum gravity. 12.6. Outlook |
| Summary |
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 - and an introduction to - 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 - that quantum physics at a fundamental level may itself be realized as a species of quantum computation - is strongly underscored |
| Bibliography |
Includes bibliographical references (pages 429-441) and indexes |
| Notes |
Print version record |
| Subject |
Finkelstein, David Ritz, 1929-2016
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| SUBJECT |
Finkelstein, David Ritz, 1929-2016 fast |
| Subject |
Quantum theory.
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Special relativity (Physics)
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SCIENCE -- Physics -- Quantum Theory.
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Quantum theory
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Special relativity (Physics)
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| Form |
Electronic book
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| ISBN |
9789812794932 |
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981279493X |
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