THE ELECTROMAGNETIC
ORIGIN OF
QUANTUM THEORY
AND LIGHT
Second Edition
Dale M. Grimes & Craig A. Grimes
The Pennryfaania State University, USA
Foreword
Man will occasionally stumble over the truth, but most of the time he will
pick himself up and continue on.
— Winston Churchill
Einstein, Podolsky, and Rosen suggested the possibility of nonlocality of
entangled electrons in 1935; Bell proved a critical theorem in 1964 and
Aspect et al provided experimental evidence in 1982. Feynman proved nonlocality
of free electrons in 1941 by proving that an electron goes from
point A to point B by all possible paths. In this book we provide circumstantial
evidence for nonlocality of individual eigenstate electrons.
One of Webster’s definitions of pragmatism is “a practical treatment of
things.” In this sense one group of the founders of quantum theory, including
Bohr, Heisenberg, and Pauli, were pragmatists. To explain atomic-level
events, as they became known, they discarded those classical concepts that
seemed to contradict, and introduced new postulates as required. On such a
base they constructed a consistent explanation of observations on an atomic
level of dimensions. Now, nearly a century later, it is indisputable that
the mathematics of quantum theory coupled with this historic, pragmatic
interpretation adequately account for most observed atomic-scaled physical
phenomena. It is also indisputable that, in contrast with other physical
disciplines, their interpretation requires special, rather quixotic, quantum
theory axioms. For example, under certain circumstances, results precede
their cause and there is an intrinsic uncertainty of physical events: The status
of observable physical phenomena at any instant does not completely
specify its status an instant later. Such inherent uncertainty belies all other
natural philosophy. The axioms needed also require rejection of selected
portions of classical electromagnetism within atoms and retention of the
rest, and they supply no information about the field structure accompanying
photon exchanges by atoms. With this pragmatic explanation radiating
atoms are far less understood, for example, than antennas. Nonetheless
vii
viii The Electromagnetic Origin of Quantum Theory and Light
it is accepted because, prior to this work, only this viewpoint adequately
explained quantum mechanics as a consistent and logical discipline.
One ofWebster’s definitions of idealism is “the practice of forming ideals
or living under their influence.” If we interpret ideal to mean scientific logic
separate from the pragmatic view of quantum theory, another group of
founders, including Einstein, Schr¨odinger, and de Broglie, were idealists.
They believed that quantum theory should be explained by the same basic
scientific logic that enables the classical sciences. With due respect to the
work of pragmatists, at least in principle, it is easier to explain new and
unexpected phenomena by introducing new postulates than it is to derive
complete idealistic results.
In our view, the early twentieth century knowledge of the classical sciences
was insufficient for an understanding of the connection between the
classical and quantum sciences. Critical physical effects that were discovered
only after the interpretation of quantum theory was complete include
(i) the standing energy that accompanies and encompasses active, electrically
small volumes, (ii) the power-frequency relationships in nonlinear
systems, and (iii) the possible directivity of superimposed modal fields.
Neither was the model of extended eigenstate electrons seriously addressed
until (iv) nonlocality was recognized in the late 20th century. How could
it be that such significant and basic physical phenomena would not importantly
affect the dynamic interaction between interacting charged bodies?
The present technical knowledge of electromagnetic theory and electrons
include these four items. We ask if this additional knowledge affects the historical
interpretation of quantum theory, and, if so, how?We find combining
items (i) and (iv) yields Schr¨odinger’s equation as an energy conservation
law. However, since general laws are derivable from quite disparate physical
models the derivation is a necessary but insufficient condition for any proposed
model. Using (i), (iii), and (iv) the full set of electromagnetic fields
within a source-free region is derivable. Quite differently from energy conservation,
electromagnetic fields are a unique result of sources within a region
and on its boundaries, and vice versa. Consider concentric spheres: the inner
with a small radius that just circumscribes a radiating atom and the outer
of infinite radius. Imposing the measured kinematic properties of atomic
radiation as a boundary condition gives the fields on the inner sphere.
Viewing the outer shell as an ideal absorber from which no fields return,
the result is an expression for the full set of electromagnetic photon fields
at a finite radius. Postulate (iv) is that electrons are distributed entities.
An electron somehow retains its individual identity while distributing itself,
Foreword ix
with no time delay, over the full physical extent of a trapping eigenstate.
Results include that an electron traveling from point A to point B goes by
all possible routes and, when combined with electrodynamic forces, provides
atomic stability.
With these postulates the interpretation of quantum theory developed
here preserves the full applicability of electromagnetic field theory within
atoms and, in turn, permits the construction of a new understanding
of quantum theory. Both the magnitude and the consequences of phase
quadrature, radiation reaction forces have been ignored. Yet these forces,
as we show, and (iv) are responsible both for the inherent stability of isolated
atoms and for a nonlinear, regenerative drive of transitions between
eigenstates, that is, quantum jumps. The nonlinearity forces the Ritz
power-frequency relationship between eigenstates and (ii) bans radiation of
other frequencies, including transients. The radiation reaction forces require
energy reception to occur at only a single frequency.
Once absorbed, the electron spreads over all available states in what
might be called a wave function expansion. Since only one frequency has an
available radiation path, if the same energy is later emitted the expanded
wave function must collapse to the emitting-absorbing pair of eigenstates
to which the frequency applies. With this view, wave function expansion
after absorption and collapse before emission obey the classical rules of
statistical mechanics. The radiation field, not the electron, requires the
seeming difference between quantum and classical effects, i.e. wave function
collapse upon measurement.
Since we reproduce the quantum theory equations, is our argument science
or philosophy? For some, a result becomes a science, only if a critical
experiment is found and only if it survives the test. But by that argument
astronomy is and remains a philosophy. With astronomy, however, if the
philosophy consistently matches enough observations with enough variety
and contradicts none of them it becomes an accepted science. In our view
quantum theory is, in many ways, also an observational science. A philosophy
becomes a science only after it consistently matches many observations
made under a large enough variety of circumstances. Our view survives
this test.
Our interpretation differs dramatically from the historical one; our postulates
are fewer in number and consistent with classical physics. With our
postulates events precede their causes and, if all knowledge were available,
would be predictable. By our interpretation of quantum theory, however,
x The Electromagnetic Origin of Quantum Theory and Light
there is no obvious way all knowledge could become available since our
ability to characterize eigenstate electrons is simply too limited.
Webster’s dictionary defines the Law of Parsimony as an “economy
of assumption in reasoning,” which is also the connotation of “Ockham’s
razor.” Since the number of postulates necessary with this interpretation
of quantum theory are both fewer in number and more consistent with the
classical sciences by the Law of Parsimony the view presented in this book
should be accepted.
Dale M. Grimes
Craig A. Grimes
University Park, PA, USA
Contents
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Chapter 1 Classical Electrodynamics . . . . . . . . . . . . . . . . . 1
1.1 Introductory Comments . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Space and Time Dependence upon Speed . . . . . . . . . . . . . . . 2
1.3 Four-Dimensional Space Time . . . . . . . . . . . . . . . . . . . . . 4
1.4 Newton’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 The Field Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.7 Accelerating Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.8 The Electromagnetic Stress Tensor . . . . . . . . . . . . . . . . . . . 14
1.9 Kinematic Properties of Fields . . . . . . . . . . . . . . . . . . . . . 17
1.10 A Lemma for Calculation of Electromagnetic Fields . . . . . . . . . 19
1.11 The Scalar Differential Equation . . . . . . . . . . . . . . . . . . . . 21
1.12 Radiation Fields in Spherical Coordinates . . . . . . . . . . . . . . . 23
1.13 Electromagnetic Fields in a Box . . . . . . . . . . . . . . . . . . . . 26
1.14 From Energy to Electric Fields . . . . . . . . . . . . . . . . . . . . . 29
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 2 Selected Boundary Value Problems . . . . . . . . . . . 31
2.1 TravelingWaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 Scattering of a Plane Wave by a Sphere . . . . . . . . . . . . . . . . 34
2.3 Lossless Spherical Scatterers . . . . . . . . . . . . . . . . . . . . . . 40
2.4 Biconical Transmitting Antennas, General Comments . . . . . . . . 45
2.5 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.6 TEMMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.7 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.8 The Defining Integral Equations . . . . . . . . . . . . . . . . . . . . 56
2.9 Solution of the Biconical Antenna Problem . . . . . . . . . . . . . . 58
2.10 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.11 Biconical Receiving Antennas . . . . . . . . . . . . . . . . . . . . . . 67
2.12 Incoming TE Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
xi
xii The Electromagnetic Origin of Quantum Theory and Light
2.13 Incoming TMFields . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.14 Exterior Fields, Powers, and Forces . . . . . . . . . . . . . . . . . . 75
2.15 The Cross-Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.16 General Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.17 Fields of Receiving Antennas . . . . . . . . . . . . . . . . . . . . . . 86
2.18 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 88
2.19 Zero Degree Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
2.20 Non-Zero Degree Solutions . . . . . . . . . . . . . . . . . . . . . . . 92
2.21 Surface Current Densities . . . . . . . . . . . . . . . . . . . . . . . . 94
2.22 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Chapter 3 Antenna Q . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.1 Instantaneous and Complex Power in Circuits . . . . . . . . . . . . . 100
3.2 Instantaneous and Complex Power in Fields . . . . . . . . . . . . . . 103
3.3 Time Varying Power in Actual Radiation Fields . . . . . . . . . . . 105
3.4 Comparison of Complex and Instantaneous Powers . . . . . . . . . . 108
3.5 Radiation Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.6 Chu’s Q Analysis, TMFields . . . . . . . . . . . . . . . . . . . . . . 115
3.7 Chu’s Q Analysis, Exact for TMFields . . . . . . . . . . . . . . . . 120
3.8 Chu’s Q Analysis, TE Field . . . . . . . . . . . . . . . . . . . . . . . 122
3.9 Chu’s Q Analysis, Collocated TMand TEModes . . . . . . . . . . . 123
3.10 Q the Easy Way, Electrically Small Antennas . . . . . . . . . . . . . 124
3.11 Q on the Basis of Time-Dependent Field Theory . . . . . . . . . . . 125
3.12 Q of a Radiating Electric Dipole . . . . . . . . . . . . . . . . . . . . 131
3.13 Q of Radiating Magnetic Dipoles . . . . . . . . . . . . . . . . . . . . 136
3.14 Q of Collocated Electric and Magnetic Dipole Pair . . . . . . . . . . 137
3.15 Q of Collocated Pairs of Dipoles . . . . . . . . . . . . . . . . . . . . 140
3.16 Four Collocated Electric and Magnetic Multipoles . . . . . . . . . . 144
3.17 Q ofMultipolar Combinations . . . . . . . . . . . . . . . . . . . . . 148
3.18 Numerical Characterization of Antennas . . . . . . . . . . . . . . . . 152
3.19 Experimental Characterization of Antennas . . . . . . . . . . . . . . 158
3.20 Q of Collocated Electric and Magnetic Dipoles: Numerical
and Experimental Characterizations . . . . . . . . . . . . . . . . . . 162
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Chapter 4 Quantum Theory . . . . . . . . . . . . . . . . . . . . . . 170
4.1 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
4.2 Dipole Radiation Reaction Force . . . . . . . . . . . . . . . . . . . . 173
4.3 The Time-Independent Schr¨odinger Equation . . . . . . . . . . . . . 180
4.4 The Uncertainty Principle . . . . . . . . . . . . . . . . . . . . . . . . 184
4.5 The Time-Dependent Schr¨odinger Equation . . . . . . . . . . . . . . 186
Contents xiii
4.6 Quantum Operator Properties . . . . . . . . . . . . . . . . . . . . . 188
4.7 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
4.8 Harmonic Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
4.9 Electron Angular Momentum, Central Force Fields . . . . . . . . . . 194
4.10 The Coulomb Potential Source . . . . . . . . . . . . . . . . . . . . . 196
4.11 Hydrogen Atom Eigenfunctions . . . . . . . . . . . . . . . . . . . . . 199
4.12 Perturbation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 202
4.13 Non-Ionizing Transitions . . . . . . . . . . . . . . . . . . . . . . . . . 203
4.14 Absorption and Emission of Radiation . . . . . . . . . . . . . . . . . 205
4.15 Electric Dipole Selection Rules
for One Electron Atoms . . . . . . . . . . . . . . . . . . . . . . . . . 208
4.16 Electron Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
4.17 Many-Electron Problems . . . . . . . . . . . . . . . . . . . . . . . . 211
4.18 Measurement Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 214
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Chapter 5 Radiative Energy Exchanges . . . . . . . . . . . . . . . 216
5.1 Blackbody Radiation, Rayleigh–Jeans Formula . . . . . . . . . . . . 216
5.2 Planck’s Radiation Law, Energy . . . . . . . . . . . . . . . . . . . . 218
5.3 Planck’s Radiation Law,Momentum . . . . . . . . . . . . . . . . . . 220
5.4 The Zero Point Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
5.5 The Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . 226
5.6 Power-Frequency Relationships . . . . . . . . . . . . . . . . . . . . . 229
5.7 Length of the Wave Train and Radiation Q . . . . . . . . . . . . . . 233
5.8 The Extended Plane Wave Radiation Field . . . . . . . . . . . . . . 235
5.9 Gain and Radiation Pattern . . . . . . . . . . . . . . . . . . . . . . . 239
5.10 Kinematic Values of the Radiation . . . . . . . . . . . . . . . . . . . 241
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
Chapter 6 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
6.1 Telefields and Far Fields . . . . . . . . . . . . . . . . . . . . . . . . . 248
6.2 Evaluation of Sum S12 on the Axes . . . . . . . . . . . . . . . . . . 253
6.3 Evaluation of Sums S22 and S32 on the Polar Axes . . . . . . . . . . 257
6.4 Evaluation of Sum S32 in the Equatorial Plane . . . . . . . . . . . . 261
6.5 Evaluation of Sum S22 in the Equatorial Plane . . . . . . . . . . . . 263
6.6 Summary of the Axial Fields . . . . . . . . . . . . . . . . . . . . . . 265
6.7 Radiation Pattern at Infinite Radius . . . . . . . . . . . . . . . . . . 267
6.8 MultipolarMoments . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
6.9 Multipolar Photon-Field Stress and Shear . . . . . . . . . . . . . . . 275
6.10 Self-Consistent Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 285
6.11 Energy Exchanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
6.12 Self-Consistent Photon-Field Stress and Shear . . . . . . . . . . . . 291
6.13 Thermodynamic Equivalence . . . . . . . . . . . . . . . . . . . . . . 298
6.14 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
xiv The Electromagnetic Origin of Quantum Theory and Light
Chapter 7 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
7.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . 306
7.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
7.3 The Radiation Scenario . . . . . . . . . . . . . . . . . . . . . . . . . 316
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
1 Introduction to Tensors . . . . . . . . . . . . . . . . . . . . . . . . . 323
2 Tensor Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
3 Tensor Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
4 Differential Operations on Tensor Fields . . . . . . . . . . . . . . . . 328
5 Green’s Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
6 The Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
7 Equivalent Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
8 A Series Resonant Circuit . . . . . . . . . . . . . . . . . . . . . . . . 339
9 Q of Time Varying Systems . . . . . . . . . . . . . . . . . . . . . . . 341
10 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
11 Instantaneous and Complex Power in Radiation Fields . . . . . . . . 345
12 Conducting Boundary Conditions . . . . . . . . . . . . . . . . . . . 347
13 Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
14 Spherical Shell Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . 351
15 Gamma Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
16 Azimuth Angle Trigonometric Functions . . . . . . . . . . . . . . . . 356
17 Zenith Angle Legendre Functions . . . . . . . . . . . . . . . . . . . . 359
18 Legendre Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . 363
19 Associated Legendre Functions . . . . . . . . . . . . . . . . . . . . . 366
20 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
21 Recursion Relationships . . . . . . . . . . . . . . . . . . . . . . . . . 368
22 Integrals of Legendre Functions . . . . . . . . . . . . . . . . . . . . . 375
23 Integrals of Fractional Order Legendre Functions . . . . . . . . . . . 377
24 The First Solution Form . . . . . . . . . . . . . . . . . . . . . . . . . 382
25 The Second Solution Form . . . . . . . . . . . . . . . . . . . . . . . 384
26 Tables of Spherical Bessel, Neumann,
and Hankel Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 387
27 Spherical Bessel Function Sums . . . . . . . . . . . . . . . . . . . . . 392
28 Static Scalar Potentials . . . . . . . . . . . . . . . . . . . . . . . . . 395
29 Static Vector Potentials . . . . . . . . . . . . . . . . . . . . . . . . . 400
30 Full Field Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
Many of the contents ot the book are misleading. Be cautious!
Electromagnetic Origin of Quantum Theory and Light, 2nd Edition.rar
