Information Theory and Quantum Physics: Physical Foundations for Understanding the Conscious Process / Edition 1

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Overview

In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.

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Product Details

  • ISBN-13: 9783540665175
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 1/14/2000
  • Series: Theoretical and Mathematical Physics Series
  • Edition description: 2000
  • Edition number: 1
  • Pages: 244
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.63 (d)

Table of Contents

1. First Principles.- 1.1 Relativity and Equivalence.- 1.2 Action.- 1.3 Information and Probability.- 1.4 Uncertainty and Indeterminacy.- 2. Quantal Bits.- 2.1 Creation and Annihilation.- 2.2 Classical Geometry on a Sphere.- 2.3 Spin and Rotation.- 2.3.1 The Group of Rotations.- 2.4 Lorentz Transformations.- 2.5 Translations in Space and Time.- 2.6 Elementary String Theory.- 2.7 Summary.- 3. Events in Space and Time.- 3.1 Projective Geometries.- 3.2 Classical Geometry of Space-Time.- 3.3 Changes of Observational Frame.- 3.4 Events as Quantal Information.- 3.4.1 Spin of the Photon.- 3.5 Fermions in Space-Time.- 3.5.1 Dirac’s Equation.- 3.5.2 Charged and Neutral Particles.- 3.6 Summary.- 4. Quantal ‘Tapes’.- 4.1 Representation of States of Higher Spin.- 4.1.1 ‘Tapes’ for Particles of Higher Spin.- 4.1.2 Matrices for Higher Spin.- 4.1.3 Spin 0 and 1.- 4.2 Maxwell’s Equations and the Photon.- 4.3 Systems of Fermions.- 4.4 Bosons.- 4.4.1 The Factorization Technique.- 4.4.2 The Tape Constructed from Qubits.- 4.4.3 Systems of Bosons.- 4.5 Observables with Continuous Spectra.- 4.5.1 Quasi-continuous Spectra.- 4.6 Summary.- 5. Observables and Information.- 5.1 Relativistic and Non-relativistic Approximations.- 5.1.1 Orbital Angular Momentum.- 5.2 Non-relativistic Quantum Mechanics.- 5.2.1 The Hydrogen Atom.- 5.2.2 Scattering and the S-Matrix.- 5.3 Uncertainty Relations.- 5.4 Special Relativistic Quantum Mechanics.- 5.4.1 Elastic Scattering.- 5.5 Selected and Unselected Observables.- 5.6 The Fundamental Observables of Physics.- 5.6.1 Schrödinger’s Wave Mechanics.- 5.6.2 The Heisenberg Representation.- 5.6.3 The Interaction Representation.- 5.7 Statistical Physics.- 5.7.1 Macroscopic and Microscopic Variables.- 5.8 Theory of Electrolytes.- 5.8.1 The Debye-Hückel Equation.- 5.9 Summary.- 6. Quantized Field Theories.- 6.1 Free Field Theories.- 6.1.1 Spin 1/2.- 6.1.2 Spin 0.- 6.1.3 Spin 1.- 6.2 Interacting Fields.- 6.2.1 The S-Matrix.- 6.2.2 Ordering in Time.- 6.3 Quantum Electrodynamics.- 6.4 Gauge Groups and String Theories.- 6.4.1 String Theories.- 7. Gravitation.- 7.1 Geometry in Terms of Quantal Information.- 7.1.1 The Relativistic Density Matrix.- 7.1.2 Representations for Arbitrary Spin.- 7.2 Quantum Geometry.- 7.2.1 The Curvature of Space-Time.- 7.3 Einstein’s Gravitational Field Equations.- 7.3.1 Classical Embedding of Schwarzschild’s Solution.- 7.3.2 More General Solutions of Einstein’s Equations.- 7.3.3 Lagrangian Densities.- 7.4 Quantal Embedding.- 7.5 Gauge Theories with Gravitation.- 7.6 Summary.- 8. Measurement and the Observer.- 8.1 Detectors and Measuring Devices.- 8.1.1 Theory of Measurement.- 8.2 Qubits of Fluctuating Electrolytic Potentials.- 8.2.1 The Cortex as a Quantal Turing Machine.- 8.2.2 The Qubits of Potential Fluctuations in an Electrolyte.- 8.2.3 Transmission of Information Across the Cellular Membrane.- 8.3 Cells and Membranes.- 8.3.1 Graded and Action Potentials.- 8.4 The Animal Cortex.- 8.4.1 Organization of Cells in Columns and Zones.- 8.4.2 The Subdivisions and Functions of the Cortex.- 8.5 Theory of Consciousness.- 8.6 Consciousness in Nature.- A. Appendix: Matrices.- A.1 Definitions and Elementary Properties.- A.1.1 Direct Products and Vector Subscripts.- A.1.2 The Imaginary Unit as a Matrix.- A.2 Determinants.- A.3 Eigenvalues of Matrices.- A.3.1 Reduction of a Finite Matrix to Spectral Form.- A.3.2 Representation of Observables by Matrices.- A.4 The Factorization Method.- A.5 Continuous Eigenvalues.- A.6 Parafermion Representations of Lie Algebras.

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  • Anonymous

    Posted September 29, 2002

    Quantum!

    Lots of areas of math, CS, and information science have recently required a severe reorientation because of the emergence of computers that do not rely on classical physics, but rather derive an added "power" and speed from *quantum* effects, such as superposition and entanglement. Core areas of math go into the new trend of applications. This exciting little book is well written and selfcontained. It gives an insight into this relatively new science, and it explains the math that is used,-- and how it is used. A great book for a course, or for self-study! Caution: There is a distinction betwee quantum computation and *quantum information*. While there are many books on the former, this attractive new book is on the latter, and it *is* a lovely introduction;- a very friendly invitation to the subject.

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