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Table of Contents
Intro
Electrical communications, fluid dynamics, and some fundamental issues in physics
Content
Abstract
Zusammenfassung
1. Introduction
2. Field velocity and rest field: concepts and basic properties
2.1 Electromagnetic fields in vacuum
2.2 Field velocity
2.3 Basic properties of the rest field
2.4 Further properties of the rest field
2.5 Rest charge, rest current, and charge velocity
2.6 Classical energy velocity
2.7 Further velocity aspects
2.8 Lorentz invariances
2.9 Basal electromagnetic field
2.10 Local decomposition into oppositely propagating planar waves
3. Field velocity and rest field: further properties
3.1 Lorentz transformation of the field velocity
3.2 Lorentz transformation of the electric and magnetic rest fields
3.3 Field velocity and Einstein rules for compounding velocities
3.4 Special case: field locally at rest
3.5 Lorentz transformation of rest charge and rest current
3.6 Generalized field velocity
3.7 Velocity equivalence class and the Einstein rules for compounding velocities
3.8 Some properties for v0→c
4. Mechanistic properties of the electromagnetic field
4.1 Flow equations
4.2 Flow equations of a basal electromagnetic field
4.3 Electromagnetic fluid and relativistic interpretation
4.4 Beyond Maxwell's equations
5. Localized basal electromagnetic fields: rotating field
5.1 Nonlinear partial differential equations describing the field
5.2 Use of normalized quantities
5.3 Major characteristic values of a rotating field
5.4 Sommerfeld's fine structure constant
5.5 Incompleteness of the original formulation
5.6 Nominal values of frequency, velocity, and radius
6. Localized basal electromagnetic fields: planar field
6. 1 Determination of the general solution
6.2 Spectral properties.
6.3 Change of reference frame
6.4 Charge and polarization
6.4.1 Linear polarization
6.4.2 Circular polarization
6.5 Nominal frequency, size, energy, and momentum
6.6 Uncertainty properties
6.7 Properties as a wave packet
6.8 Further problems
6.9 Relation between electron, positron, and photon
7. Moving particles
7.1 Electron-like particle observed in different reference frames
7.1.1 A first general relation
7.1.2 A second general relation
7.1.3 Some further details
7.1.4 Charge and current densities
7.2 Behaviour in the presence of an external electrostatic field
7.2.1 Dynamic equations of an electron-like model
7.2.2 Outline of supplementary proofs
7.2.3 Comments
8. Concluding remarks
Acknowledgment
Appendix A: Reminders
A1. Some vector and matrix properties
A2. Spherical coordinates
Appendix B: Outlines of proofs of some results in main body
B1. Proof of (2.60)
B2. Proof of (3.15)
B3. Proof of (3.38)
B4. An equivalence proof for Subsection 4.1
B5. Proof of (4.16)
Appendix C: Alternative relativistic dynamics
C1. Summary of results on alternative relativistic dynamics
C2. Comparison with classical derivations
C3. Flow equations of a basal EM field: mechanistic derivation of (4.22)
Appendix D: Symmetry requirements for a rotating field
D1. Requirements in spherical coordinates
D2. Some symmetry properties in Cartesian coordinates
Appendix E: Analytic signals and related results
E1. Analytic signal
E2. Uncertainty relation
E3. Group delay and group velocity
References.
Electrical communications, fluid dynamics, and some fundamental issues in physics
Content
Abstract
Zusammenfassung
1. Introduction
2. Field velocity and rest field: concepts and basic properties
2.1 Electromagnetic fields in vacuum
2.2 Field velocity
2.3 Basic properties of the rest field
2.4 Further properties of the rest field
2.5 Rest charge, rest current, and charge velocity
2.6 Classical energy velocity
2.7 Further velocity aspects
2.8 Lorentz invariances
2.9 Basal electromagnetic field
2.10 Local decomposition into oppositely propagating planar waves
3. Field velocity and rest field: further properties
3.1 Lorentz transformation of the field velocity
3.2 Lorentz transformation of the electric and magnetic rest fields
3.3 Field velocity and Einstein rules for compounding velocities
3.4 Special case: field locally at rest
3.5 Lorentz transformation of rest charge and rest current
3.6 Generalized field velocity
3.7 Velocity equivalence class and the Einstein rules for compounding velocities
3.8 Some properties for v0→c
4. Mechanistic properties of the electromagnetic field
4.1 Flow equations
4.2 Flow equations of a basal electromagnetic field
4.3 Electromagnetic fluid and relativistic interpretation
4.4 Beyond Maxwell's equations
5. Localized basal electromagnetic fields: rotating field
5.1 Nonlinear partial differential equations describing the field
5.2 Use of normalized quantities
5.3 Major characteristic values of a rotating field
5.4 Sommerfeld's fine structure constant
5.5 Incompleteness of the original formulation
5.6 Nominal values of frequency, velocity, and radius
6. Localized basal electromagnetic fields: planar field
6. 1 Determination of the general solution
6.2 Spectral properties.
6.3 Change of reference frame
6.4 Charge and polarization
6.4.1 Linear polarization
6.4.2 Circular polarization
6.5 Nominal frequency, size, energy, and momentum
6.6 Uncertainty properties
6.7 Properties as a wave packet
6.8 Further problems
6.9 Relation between electron, positron, and photon
7. Moving particles
7.1 Electron-like particle observed in different reference frames
7.1.1 A first general relation
7.1.2 A second general relation
7.1.3 Some further details
7.1.4 Charge and current densities
7.2 Behaviour in the presence of an external electrostatic field
7.2.1 Dynamic equations of an electron-like model
7.2.2 Outline of supplementary proofs
7.2.3 Comments
8. Concluding remarks
Acknowledgment
Appendix A: Reminders
A1. Some vector and matrix properties
A2. Spherical coordinates
Appendix B: Outlines of proofs of some results in main body
B1. Proof of (2.60)
B2. Proof of (3.15)
B3. Proof of (3.38)
B4. An equivalence proof for Subsection 4.1
B5. Proof of (4.16)
Appendix C: Alternative relativistic dynamics
C1. Summary of results on alternative relativistic dynamics
C2. Comparison with classical derivations
C3. Flow equations of a basal EM field: mechanistic derivation of (4.22)
Appendix D: Symmetry requirements for a rotating field
D1. Requirements in spherical coordinates
D2. Some symmetry properties in Cartesian coordinates
Appendix E: Analytic signals and related results
E1. Analytic signal
E2. Uncertainty relation
E3. Group delay and group velocity
References.