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

by Herbert S. Green

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.

Product Details

ISBN-13:	9783540665175
Publisher:	Springer Berlin Heidelberg
Publication date:	01/14/2000
Series:	Theoretical and Mathematical Physics
Edition description:	2000
Pages:	244
Product dimensions:	6.10(w) x 9.25(h) x 0.02(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.