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Transcript of AMERICAN RESEARCH · PDF file 2017. 3. 16. · at Millette’s results, we see...

  • AMERICAN RESEARCH PRESS

    Pierre A. Millette

    E l a s t o d y n a m i c s o f t h e

    S p a c e t i m e C o n t i n u u m A Spacetime Physics Theory of Gravitation,

    Electromagnetism and Quantum Physics

    STCED

    ρc2 = 4κ0ε

  • American Research Press

    Pierre A. Millette

    E l a s t o d y n a m i c s o f t h e

    S p a c e t i m e C o n t i n u u m

    A Spacetime Physics Theory of Gravitation, Electromagnetism and Quantum Physics

    – S T C E D –

    Rehoboth, New Mexico, USA

    — 2017 —

  • This book is published and distributed in agreement with the Budapest Open Ini- tiative. This means that the electronic copies of the book should always be accessed for reading, download, copying, and re-distribution for any user free of charge. To order printed copies of the book, please contact the Publisher. The book can be downloaded on-line, free of charge, from the following primary web-sites:

    Progress in Physics, the American journal of physics (USA): http://ptep-online.com/index files/books.html

    The Abraham Zelmanov Journal (International): http://zelmanov.ptep-online.com/books.html

    Copyright © Pierre A. Millette, 2017

    All rights reserved. Electronic copying, print copying and distribution of this book for non-commercial, academic or individual use can be made by any user without permission or charge. Any part of this book being cited or used howsoever in other publications must acknowledge this publication. No part of this book may be re- produced in any form whatsoever (including storage in any media) for commercial use without the prior permission of the copyright holder. Requests for permission to reproduce any part of this book for commercial use must be addressed to the Author. The Author retains his rights to use this book as a whole or any part of it in any other publications and in any way the Author sees fit. This Copyright Agreement shall remain valid even if the Author transfers copyright of the book to another party.

    Cover image: The illustration representing a spacetime continuum deformation has been prepared by the author, incorporating a helix wave from Wikimedia Commons, available at Page URL: https://commons.wikimedia.org/wiki/File File URL: https://upload.wikimedia.org/wikipedia/commons/d/de/ Circular.Polarization.Circularly.Polarized.Light Attribution: By Dave3457 (Own work) [Public domain], via Wikimedia Commons.

    This book was typeset using the LATEX typesetting system.

    ISBN 978-1-59973-401-9

    American Research Press, Box 141, Rehoboth, NM 87322, USA Standard Address Number: 297-5092 Printed in the United States of America

  • Table of Contents

    Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

    Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

    Chapter 1 Strained Spacetime

    §1.1 Properties of the spacetime continuum . . . . . . . . . . . . . . . . . . . . . 17 §1.2 Strained spacetime and the natural decomposition of the

    spacetime metric tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    §1.3 Decomposition of tensor fields in strained spacetime . . . . . . . 25 §1.4 The physicality of four-dimensional spacetime. . . . . . . . . . . . . .26

    Chapter 2 Spacetime Continuum Elastodynamics

    §2.1 Model of the spacetime continuum . . . . . . . . . . . . . . . . . . . . . . . . . 27 §2.2 Stress-strain relation of the spacetime continuum . . . . . . . . . . 29 §2.3 Rest-mass energy relation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 §2.4 Dilatation-distortion decomposition of the Ricci tensor . . . . . 33 §2.5 Relation between General Relativity and STCED . . . . . . . . . . 37 §2.6 The question of relativistic mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

    Chapter 3 Spacetime Wave Equations

    §3.1 Kinematic relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 §3.2 Dynamic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 §3.3 Displacement wave equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 §3.4 Continuity equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 §3.5 Field wave equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 §3.6 Spin analysis of the wave equations . . . . . . . . . . . . . . . . . . . . . . . . 50

    Chapter 4 Electromagnetism in STCED

    §4.1 Electromagnetic field strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 §4.2 Maxwell’s equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 §4.3 Current density four-vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 §4.4 Lorenz condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 §4.5 Four-vector potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

  • 4 Table of Contents

    §4.6 Electromagnetism and the STC volume force . . . . . . . . . . . . . . 56 §4.7 Homogeneous Maxwell equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 §4.8 Electromagnetic implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

    Chapter 5 Energy in the Spacetime Continuum

    §5.1 Strain energy density of the spacetime continuum . . . . . . . . . . 61 §5.2 Physical interpretation of the strain energy density . . . . . . . . 61 §5.3 Electromagnetic strain energy density. . . . . . . . . . . . . . . . . . . . . .63 §5.4 Electromagnetic field strain energy density and the

    photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

    Chapter 6 Spacetime Continuum Volume Force

    §6.1 STC volume force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 §6.2 Linear elastic volume force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 §6.3 Discussion of linear elastic volume force results . . . . . . . . . . . . 77 §6.4 Designer STC volume forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

    Chapter 7 Quantum Mechanical Volume Force

    §7.1 Derivation of a quantum mechanical volume force . . . . . . . . . .79 §7.2 Displacements equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82 §7.3 Wave equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83 §7.4 Alternative derivation of the quantum mechanical volume

    force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

    §7.5 Alternative volume forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

    Chapter 8 Defects in the Spacetime Continuum

    §8.1 Analysis of spacetime continuum defects . . . . . . . . . . . . . . . . . . . 93 §8.2 Defects in four-dimensional spacetime. . . . . . . . . . . . . . . . . . . . . .95 §8.3 Defects and the incompatibility tensor . . . . . . . . . . . . . . . . . . . . . 95 §8.4 Defects and the volume force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 §8.5 Defects dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

    Chapter 9 Dislocations in the Spacetime Continuum

    §9.1 Analysis of spacetime continuum dislocations . . . . . . . . . . . . . 103 §9.2 Screw dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 §9.3 Edge dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

  • Table of Contents 5

    §9.4 Volterra discrete dislocation line . . . . . . . . . . . . . . . . . . . . . . . . . . 126 §9.5 deWit discrete dislocation line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 §9.6 Curved dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134

    Chapter 10 Disclinations in the Spacetime Continuum

    §10.1 Analysis of spacetime continuum disclinations . . . . . . . . . . . . 137 §10.2 Volterra dislocations and disclinations . . . . . . . . . . . . . . . . . . . . 140 §10.3 Volterra wedge disclinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 §10.4 Volterra twist disclinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 §10.5 deWit discrete disclination lines . . . . . . . . . . . . . . . . . . . . . . . . . . 158 §10.6 deWit wedge disclinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 §10.7 deWit twist disclinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

    Chapter 11 Field Theory of Defects

    §11.1 Analysis of distributions of defect densities . . . . . . . . . . . . . . . 173 §11.2 Dislocation and disclination densities . . . . . . . . . . . . . . . . . . . . . 173 §11.3 Defect densities in continua . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174 §11.4 Differential geometry of defects . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 §11.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

    Chapter 12 Wave-Particle Duality in STCED

    §12.1 Wave-particle duality in electromagnetism . . . . . . . . . . . . . . . . 179 §1