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Information theory applied to space-time physics

Author: Henning F Harmuth
Publisher: Singapore ; River Edge, NJ : World Scientific, ©1992.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Discusses the principles of information theory in relation to physics. Topics covered include distinction of sinusoidal functions, information theory applied to measurements, time and motion, and the  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Henning F Harmuth
ISBN: 981021278X 9789810212780
OCLC Number: 27641843
Description: xii, 306 pages : illustrations ; 23 cm
Contents: 1. Historical Review. 1.1. Roots in the Greek World. 1.2. From Euclidean to Non-Euclidean Geometry. 1.3. Metric and Differential Geometry. 1.4. Physical Space-Time --
2. Information Theory Applied to Measurements. 2.1. The Concept of Information. 2.2. Finite Information and Finite Resolution. 2.3. Finite Information Flow. 2.4. Finite Resolution [Delta]x and [Delta]t --
3. Coordinate Systems. 3.1. Coordinate Systems Based on Rings. 3.2. The Belief in Three-Dimensional Space. 3.3. Right and Left Handed Structures. 3.4. Distance in Discrete Coordinate Systems. 3.5. Coordinate Systems Defined by the Metric Tensor. 3.6. Coordinate Systems with one Variable --
4. Time and Motion. 4.1. Time and Time Differences. 4.2. Shifts and Propagation. 4.3. Velocity. 4.4. Three Time Dimensions and One Space Dimension --
5. Propagation in Unusual Coordinate Systems. 5.1. Dyadic Metric. 5.2. Dyadic Coordinate Systems. 5.3. Standing Waves and Topology. 5.4. Observed Shifts and Their Eigenfunctions. 5.5. Nondyadic Coordinate Systems. 5.6. Motion Based on Integer Number and Dyadic Topology. 5.7. Dyadic Clocks --
6. Distinction of Sinusoidal Functions. 6.1. Differential and Partial Equations. 6.2. Concepts of the Calculus of Finite Differences. 6.3. Concepts of the Dyadic Calculus. 6.4. Difference Calculus on General Rings. 6.5. Spectral Decomposition of Light. 6.6. Laser for Nonsinusoidal Waves --
7. Discrete Topologies and Difference Equations. 7.1. Finite Differences and Differentials. 7.2. Dyadic Difference Quotient. 7.3. Observable Effects of Discrete Topologies --
8. Schrodinger and Klein-Gordon Difference Equations. 8.1. Time Dependence of the Solutions of Partial Difference Equations. 8.2. Schrodinger Equation. 8.3. Physical Meaning of a Difference Equation. 8.4. Klein-Gordon Equation --
9. Schrodinger Difference Equation with Coulomb Field. 9.1. Separation of Variables for a Centrally Symmetric Field. 9.2. Discrete Eigenvalues in a Coulomb Field. 9.3. Time Variable Solutions --
10. Klein-Gordon Difference Equation with Coulomb Field. 10.1. Separation of Variables and Initial Value Problem. 10.2. Discrete Eigenvalues of Bosons in a Coulomb Field. 10.3. Asymptotic Solution. 10.4. Convergent Solution. 10.5. Convergence at the Origin. 10.6. Free Particles in a Coulomb Field. 10.7. Independence Relation --
11. Dirac Difference Equation with Coulomb Field. 11.1. Iterated Dirac Equation. 11.2. Linearized Dirac Equation --
12. Mathematical Supplements. 12.1. Transmission Capacity. 12.2. Distributive Law for Dyadic Multiplication. 12.3. Method for Dyadic Division. 12.4. Right and Left Difference Quotient. 12.5. Independence Relation in Three-Dimensional Cartesian Coordinates. 12.6. Polynomials as Solutions of Difference Equations of Second Order. 12.7. Difference Equation of the Discrete Spherical Harmonics. 12.8. Convergence of the Solution of the Klein-Gordon Equation with Coulomb Field. 12.9. Orthogonality of Eigenfunctions. 12.10. Generalization of Green's Formula. 12.11. Eigenfunctions of the Dyadic Difference Operator.
Responsibility: Henning F. Harmuth.

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