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

ISBN-13: 9783642630613 / Angielski / Miękka / 2012 / 244 str.

Herbert S. Green; Herbert S. Green

Opis

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.

Spis treści

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.

Blurb

In this book, H. S. Green, a former student of Max Born and well known as an author in physics and in philosophy of science, presents an individual and modern approach to theoretical physics and related fundamental problems. Starting from first principles, the links between physics and information science are unveiled step by step: modern information theory and the classical theory of the Turing machine are combined to create a new interpretation of quantum computability, which is then applied to field theory, gravitation and submicroscopic measurement theory and culminates in a detailed examination of the role of the conscious observer in physical measurements. The result is a highly readable book that unifies a wide range of scientific knowledge and is essential reading for all scientists and philosophers of science interested in the interpretation and the implications of the interaction between information science and basic physical theories.