Information Theory Applied to Space-Time Physics

By: Henning F. Harmuth

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Hardcover | 1 December 1992

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Information theory was developed during the last decades within electrical communications, but it is almost unknown in physics. The closest approach to information theory in physics is the "calculus of propositions", which has been used in books on the frontier of quantum mechanics and the general theory of relativity. A discussion of the principles of information theory required in this book is given in Chapter 2. The ability to think readily in terms of a finite number of discrete samples is developed over many years of using information theory and digital computers, just as the ability to think readily in terms of a continuum is developed by long use of differential calculus.

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Preface
Historical Review
Roots in the Greek World	p. 1
From Euclidean to Non-Euclidean Geometry	p. 4
Metric and Differential Geometry	p. 7
Physical Space-Time	p. 11
Information Theory Applied to Measurements
The Concept of Information	p. 18
Finite Information and Finite Resolution	p. 21
Finite Information Flow	p. 25
Finite Resolution [Delta]x and [Delta]t	p. 29
Coordinate Systems
Coordinate Systems Based on Rings	p. 40
The Belief in Three-Dimensional Space	p. 62
Right and Left Handed Structures	p. 67
Distance in Discrete Coordinate Systems	p. 71
Coordinate Systems Defined by the Metric Tensor	p. 77
Coordinate Systems with one Variable	p. 81
Time and Motion
Time and Time Differences	p. 85
Shifts and Propagation	p. 89
Velocity	p. 96
Three Time Dimensions and One Space Dimension	p. 100
Propagation in Unusual Coordinate Systems
Dyadic Metric	p. 104
Dyadic Coordinate Systems	p. 112
Standing Waves and Topology	p. 121
Observed Shifts and Their Eigenfunctions	p. 127
Nondyadic Coordinate Systems	p. 139
Motion Based on Integer Number and Dyadic Topology	p. 146
Dyadic Clocks	p. 158
Distinction of Sinusoidal Functions
Differential and Partial Equations	p. 163
Concepts of the Calculus of Finite Differences	p. 165
Concepts of the Dyadic Calculus	p. 169
Difference Calculus on General Rings	p. 185
Spectral Decomposition of Light	p. 187
Laser for Nonsinusoidal Waves	p. 192
Discrete Topologies and Difference Equations
Finite Differences and Differentials	p. 197
Dyadic Difference Quotient	p. 200
Observable Effects of Discrete Topologies	p. 202
Schrodinger and Klein-Gordon Difference Equations
Time Dependence of the Solutions of Partial Difference Equations	p. 204
Schrodinger Equation	p. 206
Physical Meaning of a Difference Equation	p. 211
Klein-Gordon Equation	p. 212
Schrodinger Difference Equation with Coulomb Field
Separation of Variables for a Centrally Symmetric Field	p. 218
Discrete Eigenvalues in a Coulomb Field	p. 220
Time Variable Solutions	p. 228
Klein-Gordon Difference Equation with Coulomb Field
Separation of Variables and Initial Value Problem	p. 230
Discrete Eigenvalues of Bosons in a Coulomb Field	p. 232
Asymptotic Solution	p. 238
Convergent Solution	p. 239
Convergence at the Origin	p. 245
Free Particles in a Coulomb Field	p. 248
Independence Relation	p. 251
Dirac Difference Equation with Coulomb Field
Iterated Dirac Equation	p. 254
Linearized Dirac Equation	p. 264
Mathematical Supplements
Transmission Capacity	p. 270
Distributive Law for Dyadic Multiplication	p. 271
Method for Dyadic Division	p. 274
Right and Left Difference Quotient	p. 275
Independence Relation in Three-Dimensional Cartesian Coordinates	p. 276
Polynomials as Solutions of Difference Equations of Second Order	p. 277
Difference Equation of the Discrete Spherical Harmonics	p. 282
Convergence of the Solution of the Klein-Gordon Equation with Coulomb Field	p. 287
Orthogonality of Eigenfunctions	p. 289
Generalization of Green's Formula	p. 292
Eigenfunctions of the Dyadic Difference Operator	p. 294
References and Bibliography	p. 297
Index	p. 303
Table of Contents provided by Blackwell. All Rights Reserved.

Information Theory Applied to Space-Time Physics

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Hardcover

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