Information theory applied to space time physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore u.a.
World Scientific
1992
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 306 S. graph. Darst. |
| ISBN: | 981021278X |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text |
Information Theory Applied
To Space-Time Physics
Dr Henning F ^armuth
The Catholic University of America
School of Engineering ond Architecture
Department of Electrical Engineering
Washington, DC
World Scientific
Singapore • New Jersey • London • Hong Kong
Contents
PREFACE XI
1 Historical Review
1 1 Roots in the Greek World 1
1 2 From Euclidean to Non-Euclidean Geometry 4
1 3 Metric and Differential Geometry 7
1 4 Physical Space-Time 11
2 Information Theory Applied to Measurements
2 1 The Concept of Information 18
2 2 Finite Information and Finite Resolution 21
2 3 Finite Information Flow 25
2 4 Finite Resolution Ax and At 29
3 Coordinate Systems
3 1 Coordinate Systems Based on Rings 40
3 2 The Belief in Three-Dimensional Space 62
3 3 Right and Left Handed Structures 67
3 4 Distance in Discrete Coordinate Systems 71
3 5 Coordinate Systems Defined by the Metric Tensor 77
3 6 Coordinate Systems with one Variable - 81
Equations are numbered consecutively within each of Sections 1 1 to 12 11 Refer-
ence to an equation in a different section is made by writing the number of the section
in front of the number of the equation, eg, Eq (1 2-3) for Eq (3) in Section 1 2
Illustrations and tables are numbered consecutively within each section, with the
number of the section given first, eg, Fig 1 3-2, Table 6 3-4
References are characterized by the name of the author(s), the year of publication,
and a lower case Latin letter if more than one reference by the same author(s) is listed
for the year
4 Time and Motion
4 1 Time and Time Differences 85
4 2 Shifts and Propagation 89
4 3 Velocity 96
4 4 Three Time Dimensions and One Space Dimension 100
5 Propagation in Unusual Coordinate Systems
5 1 Dyadic Metric 104
5 2 Dyadic Coordinate Systems 112
5 3 Standing Waves and Topology 121
5 4 Observed Shifts and Their Eigenfunctions 127
5 5 Nondyadic Coordinate Systems 139
5 6 Motion Based on Integer Number and Dyadic Topology 146
5 7 Dyadic Clocks 158
6 Distinction of Sinusoidal Functions
6 1 Differential and Partial Differential Equations 163
6 2 Concepts of the Calculus of Finite Differences 165
6 3 Concepts of the Dyadic Calculus 169
6 4 Difference Calculus on General Rings 185
6 5 Spectral Decomposition of Light 187
6 6 Laser for Nonsinusoidal Waves 192
7 Discrete Topologies and Difference Equations
7 1 Finite Differences and Differentials 197
7 2 Dyadic Difference Quotient 200
7 3 Observable Effects of Discrete Topologies ' 202
8 Schrodinger and Klein-Gordon Difference Equations
8 1 Time Dependence of the Solutions of Partial Difference Equations 204
8 2 Schrodinger Equation ' 206
8 3 Physical Meaning of a Difference Equation 211
8 4 Klein-Gordon Equation 212
9 Schrodinger Difference Equation with Coulomb Field
9 1 Separation of Variables for a Centrally Symmetric Field 218
9 2 Discrete Eigenvalues in a Coulomb Field 220
9 3 Time Variable Solutions 228
10 Klein-Gordon Difference Equation with Coulomb Field
10 1 Separation of Variables and Initial Value Problem 230
10 2 Discrete Eigenvalues of Bosons in a Coulomb Field 232
10 3 Asymptotic Solution 238
10 4 Convergent Solution 239
10 5 Convergence at the Origin 245
10 6 Free Particles in a Coulomb Field 248
10 7 Independence Relation 251
11 Dirac Difference Equation with Coulomb Field
11 1 Iterated Dirac Equation 254
11 2 Linearized Dirac Equation 264
12 Mathematical Supplements
12 1 Transmission Capacity 270
12 2 Distributive Law for Dyadic Multiplication 271
12 3 Method for Dyadic Division 274
12 4 Right and Left Difference Quotient 275
12 5 Independence Relation in Three-Dimensional Cartesian
Coordinates 276
12 6 Polynomials as Solutions of Difference Equations of Second
Order 277
12 7 Difference Equation of the Discrete Spherical Harmonics 282
12 8 Convergence of the Solution of the Klein-Gordon Equation
with Coulomb Field 287
12 9 Orthogonality of Eigenfunctions 289
12 10 Generalization of Green's Formula 292
12 11 Eigenfunctions of the Dyadic Difference Operator 294
References and Bibliography 297
INDEX 303 |
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| indexdate | 2025-03-18T09:01:47Z |
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| isbn | 981021278X |
| language | English |
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| physical | XII, 306 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Harmuth, Henning F. Verfasser aut Information theory applied to space time physics Henning F. Harmuth Information theory applied to space-time physics Singapore u.a. World Scientific 1992 XII, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Champs, Théorie des (physique) ram Information, Théorie de l' ram Field theory (Physics) Information theory Informationstheorie (DE-588)4026927-9 gnd rswk-swf Raum-Zeit (DE-588)4302626-6 gnd rswk-swf Raum-Zeit (DE-588)4302626-6 s DE-604 Informationstheorie (DE-588)4026927-9 s DE-188 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006909865&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harmuth, Henning F. Information theory applied to space time physics Champs, Théorie des (physique) ram Information, Théorie de l' ram Field theory (Physics) Information theory Informationstheorie (DE-588)4026927-9 gnd Raum-Zeit (DE-588)4302626-6 gnd |
| subject_GND | (DE-588)4026927-9 (DE-588)4302626-6 |
| title | Information theory applied to space time physics |
| title_alt | Information theory applied to space-time physics |
| title_auth | Information theory applied to space time physics |
| title_exact_search | Information theory applied to space time physics |
| title_full | Information theory applied to space time physics Henning F. Harmuth |
| title_fullStr | Information theory applied to space time physics Henning F. Harmuth |
| title_full_unstemmed | Information theory applied to space time physics Henning F. Harmuth |
| title_short | Information theory applied to space time physics |
| title_sort | information theory applied to space time physics |
| topic | Champs, Théorie des (physique) ram Information, Théorie de l' ram Field theory (Physics) Information theory Informationstheorie (DE-588)4026927-9 gnd Raum-Zeit (DE-588)4302626-6 gnd |
| topic_facet | Champs, Théorie des (physique) Information, Théorie de l' Field theory (Physics) Information theory Informationstheorie Raum-Zeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006909865&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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