## Quanta, Logic and Spacetime (Google eBook)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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### Contents

3 | |

23 | |

Group Duality Coherence and Cyclic Actions | 41 |

Natural Deduction | 73 |

5 Quantum Logic | 91 |

The Computational Resources of Quantum Logic | 137 |

A Quantum Net | 179 |

Towards a Correspondence Principle for the Quantum Net | 203 |

Dynamics I | 279 |

Dynamics II | 315 |

Comparisons Interpretations and Speculations | 377 |

429 | |

443 | |

451 | |

457 | |

A Correspondence Principle for the Quantum Net | 233 |

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action vectors algebra map algebra structure amplitude analog associated axiom basis bispinor Boolean bosons calculus chapter choice classical coalgebra commutative component continuum correspondence principle defect defined denotes diagram Dirac maps dual dynamical elements equivalent expression fermions field finite dimensional Finkelstein formal formula function gauge given hand side Hilbert space Hopf algebra infinitesimal initial acts interpretation intuitionistic isomorphism Kripke Lagrangian last equation lattice Lie algebra line bundle linear map macroscopic experimenters manifold matrix Maxwell-Boltzmann modal monomial namely natural deduction notation notion obtain operator ortholattice orthomodel orthomodular orthomodular lattice pair physical proof proposition quan quantum logic quantum set qubit replaced representation represents resolution result reticular right-hand side rules second quantization selective acts sequence sequent calculus side of equation spacetime spinor subalgebra subspaces superposition tensor product theorem theory tion transformations transition underlying vector space Weyl equations yields

### Popular passages

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).