Quanta, Logic and Spacetime (Google eBook)

Front Cover
World Scientific, Jan 1, 2003 - Science - 465 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 - 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
  

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Contents

Foundations
3
Quantum Sets
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
References
429
Citation Index
443
Notational Index and Glossary
451
Subject Index
457
Copyright

A Correspondence Principle for the Quantum Net
233

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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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