Information Theory and Quantum Physics: Physical Foundations for Understanding the Conscious Process (Theoretical and Mathematical Physics)

Cover......Page 1
Title Page......Page 4
ISSN 0172-5998 and Copyright......Page 5
Preface......Page 6
Contents......Page 8
1.1 Relativity and Equivalence......Page 11
1.2 Action......Page 13
1.3 Information and Probability......Page 17
1.4 Uncertainty and Indeterminacy......Page 21
2. Quanta! Bits......Page 25
2.1 Creation and Annihilation......Page 30
2.2 Classical Geometry on a Sphere......Page 32
2.3 Spin and Rotation......Page 33
2.3.1 The Group of Rotations......Page 35
2.4 Lorentz Transformations......Page 36
2 . 5 Translations in Space and Time......Page 39
2.6 Elementary String Theory......Page 42
2.7 Summary......Page 44
3. Events III Space and Time......Page 47
3.1 Projective Geometries......Page 51
3.2 Classical Geometry of Space-Time......Page 53
3.3 Changes of Observational Frame......Page 56
3.4 Events as Quantal Information......Page 58
3.4.1 Spin of the Photon......Page 60
3.5 Fermions in Space-Time......Page 61
3.5.1 Dirac's Equation......Page 64
3.5.2 Charged and Neutral Particles......Page 67
3.6 SUlIlIJlary......Page 68
4. Quantal 'Tapes'......Page 71
4.1 Representation of States of Higher Spin......Page 73
4.1.1 'Tapes' for Particles of Higher Spin......Page 75
4.1.2 Matrices for Higher Spin......Page 77
4.1.3 Spin 0 and 1......Page 78
4.2 Maxwell's Equations and the Photon......Page 81
4.3 Systems of Fermions......Page 83
4.4 Bosons......Page 85
4.4.1 The Factorization Technique......Page 86
4.4.2 The Tape Constructed from Qubits......Page 87
4.5 Observables with Continuous Spectra......Page 89
4.5.1 Quasi-continuous Spectra......Page 90
4.6 Summary......Page 91
5. Observables and Information......Page 93
5.1 Relativistic and Non-relativistic Approximations......Page 96
5.1.1 Orbital Angular Momentum......Page 97
5.2 Non-relativistic Quantum Mechanics......Page 98
5.2.1 The Hydrogen Atom......Page 99
5.2.2 Scattering and the S-Matrix......Page 102
5.3 Uncertainty Relations......Page 104
5.4 Special Relativistic Quantum Mechanics......Page 106
5.4.1 Elastic Scattering......Page 108
5.5 Selected and Unselected Observables......Page 110
5.6 The Fundamental Observables of Physics......Page 112
5.6.1 Schrodinger's Wave Mechanics......Page 113
5.6.2 The Heisenberg Representation......Page 114
5.6.3 The Interaction Representation......Page 115
5.7 Statistical Physics......Page 116
5.7.1 Macroscopic and Microscopic Variables......Page 118
5.8 Theory of Electrolytes......Page 120
5.8.1 The Debye-Hiickel Equation......Page 122
5.9 Summary......Page 123
6. Quantized Field Theories......Page 125
6.1 Free Field Theories......Page 129
6.1.1 Spin 1/2......Page 132
6,1.2 Spin 0......Page 134
6.1.3 Spin 1......Page 137
6.2 Interacting Fields......Page 139
6.2.1 The S-Matrix......Page 142
6.2.2 Ordering in Time......Page 144
6.3 Quantum Electrodynamics......Page 146
6.4 Gauge Groups and String Theories......Page 152
6.4.1 String Theories......Page 153
7. Gravitation......Page 155
7.1 Geometry in Terms of Quanta! Information......Page 158
7.1.1 The Relativistic Density Matrix......Page 160
7.1.2 Representations for Arbitrary Spin......Page 161
7.2 Quantum Geometry......Page 163
7.2.1 The Curvature of Spac-Time......Page 165
7.3.1 Classical Embedding of Schwarzschild's Solution......Page 168
7.3.2 More General Solutions of Einstein's Equations......Page 171
7.4 Quantal Embedding......Page 173
7.5 Gauge Theories with Gravitation......Page 177
7.6 Summary......Page 179
8. Measurement and the Observer......Page 181
8.1 Detectors and Measuring Devices......Page 183
8.1.1 Theory of Measurement......Page 187
8.2 Qubits of Fluctuating Electrolytic Potentials......Page 191
8.2.1 The Cortex as a Quanta! Turing Machine......Page 192
8.2.2 The Qubits of Potential Fluctuations in an Electrolyte......Page 193
8.2.3 Transmission of Information Across the Cellular Membrane......Page 196
8.3 Cells and Membranes......Page 203
8.3.1 Graded and Action Potentials......Page 206
8.4.2 The Subdivisions and Functions of the Cortex......Page 209
8.5 Theory of Consciousness......Page 212
8.6 Consciousness in Nature......Page 216
A.1 Definitions and Elementary Properties......Page 221
A.I.I Direct Products and Vector Subscripts......Page 223
A.1.2 The Imaginary Unit as a Matrix......Page 224
A.2 IJeterminants......Page 225
A.3 Eigenvalues of Matrices......Page 227
A.3.1 Reduction of a Finite Matrix to Spectral Form......Page 229
A.3.2 Representation of Observables by Matrices......Page 230
A.4 The Factorization Method......Page 231
A.S Continuous Eigenvalues......Page 233
A.6 Parafermion Representations of Lie Algebras......Page 235
A.6.I Invariants and Representations of so(2N + 1)......Page 238
Bibliography......Page 241
Back Cover......Page 255