This book presents two new mathematical techniques: nonstandard logics and nonstandard metrics. The techniques are applied to current problems in physics, i.e. the hidden variable problem, the local and nonlocal problems, etc.
Abstract:
This work presents two mathematical techniques: non-standard logics and non-standard metrics. The techniques are applied to current problems in physics, such as the hidden variable problem and the local and nonlocal problems. Read more...
Author(s): Honig, William M
Series: K & E series on knots and everything 10
Publisher: World Scientific
Year: 1995
Language: English
Pages: 280
City: River Edge, NJ, Singapore
Tags: Nonstandard mathematical analysis.;Logic, Symbolic and mathematical.;Metric spaces.;Mathematical physics.;SCIENCE -- Physics -- Mathematical & Computational.;Lógica matemática.;Lógica simbólica.;Física matemática.;Analyse mathématique non standard.
Content: ""TABLE OF CONTENTS""
""Dedication ""
""PREFACE""
""A. Coloured & Basic Illustrations""
""B. Non-Coloured Text Diagrams""
""Part Zero The Basis for This Book""
""Transforming the STR and QM Paradigms""
""Part One Preview""
""1.0 Introduction and History""
""1.1 Non Standard Mathematical Methods of Part Two""
""1.1.1 Preview of Non Standard Logics""
""1.1.2 Preview of Non Standard Metrics""
""1.2 Preview of the Realistic Physics of Part Three""
""Part Two Non Standard Mathematical Methods""
""2.0 The Ubiquity Principle, & Local/Non-Local, and Local/Global Distinctions "" ""2.1 Non Standard Logics""""2.1.1 Detailed Caption""
""2.1.2 Summary""
""2.1.3 Introduction""
""2.1.4 The Similarity of the Logical Status of Axioms to the Logical Meaning of i(â?š-1)""
""2.1.5 Logical Meaning for the Forms, 2a and eb, from Set Theory ""
""2.1.6 Transfinite Ordinals in Place of Equal Symbols""
""2.1.7 Human and Operational Meanings for Imaginary Exponentials""
""2.1.8 Addition A --
Transformations Between Conflictual Axioms""
""2.1.9 Addition B --
Data and Axiom Number Fields Represented by Real and Imaginary Number Fields, Respectively"" ""2.2 Non Standard Metrics""""2.2.1 Detailed Caption""
""2.2.2 Summary""
""2.2.3 Introduction""
""2.2.4 Initial Considerations""
""2.2.5 Mathematics of Relative Metrics""
""2.2.6 Other Conditions and Mappings""
""2.2.7 Final Remarks""
""2.2.8 Addition A --
Relative Metrics Between the 2-Dimensional (x, y) vs (r, Î?) Coordinate Systems and Spaces""
""2.3 Non Standard Delta Function""
""2.3.1 Detailed Caption""
""2.3.2 Summary""
""2.3.3 Introduction""
""2.3.4 Non Standard Definition of the Delta Function""
""Part Three Applications to a Realistic Physics"" ""3.1 Dual Charged Fluids""""3.1.1 Detailed Caption""
""3.1.2 Summary""
""3.1.3 Introduction""
""3.1.4 A Two Fluid Covariant Ether""
""3.1.5 Fluid Models""
""3.2 Discrete Electromagnetic Waves, Photex, and h""
""3.2.1 Detailed Caption""
""3.2.2 Summary""
""3.2.3 Introduction""
""3.2.4 The Hertzian Dipole Radiation Pictures""
""3.2.5 Reinterpretation of the Planck & De Broglie Relations ""
""3.2.6 Experimental Tests""
""3.2.7 Physical Meaning for the Commutation Relations""
""3.2.8 Photons""
""3.2.9 Photex Rest Frames"" ""3.2.10 The Photex as the Hidden Variable of Quantum Mechanics""""3.2.11 Addition A --
Continuous and Discontinuous Wave Trains and Proca-like Dispersion Relations""
""3.3 Non-local Hidden Variable Wave Equations, Double Slits, and All That ""
""3.3.1 Detailed Caption""
""3.3.2 Summary""
""3.3.3 Introduction""
""3.3.4 Summary of a Realistic Sub-Quantum Theory""
""3.3.5 A Wave Equation for the Hidden Variable/Quantum Potential""
""3.3.6 Electron Double Slit Experiment & Quantum Potential Waves Equations (continued)""
""3.3.7 Concluding Remarks""
