Matter Waves, Gravitation, Particle-Wave Duality, Uncertainty, Analogies, Nikola Tesla, Rudjer ...

815 Pages·2017·22.47 MB·English

by  Miodrag Prokic

CERTAINTY of

PAR TICLE – WAVE
UNITY

or

Miodrag Prokic

1975 - 2020
National ISBN agency

National Library of Serbia

Belgrade

CIP – Catalogued in publication
National Library of Serbia

MIODRAG PROKIC

CERTAINTY of PARTICLE – WAVE UNITY or UNCERTAINTY
of PARTICLE – WAVE DUALITY / Miodrag Prokic.
- 1st edition – Switzerland, 2006
- 2nd edition – Switzerland, 2015
6 + 704 p. graphic illustr. and tables; 29,7 cm.
- (Library: MP Interconsulting; book: 2)
http://www.mpi-ultrasonics.com/
[email protected]

Circulation: 2.000 copies

International Standard Book Number
Berlin

ISO 2108

Publishers’ International ISBN Directory

ISBN 86-907593-0-1
ISBN 978-86-907593-1-6

Miodrag Prokic, CERTAINTY of PARTICLE – WAVE UNITY or
Content and graphics copyright Miodrag Prokic Switzerland, 2006. All Rights Reserved. Download the last version here:
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UNCERTAINTY of PARTICLE – WAVE DUALITY

Second edition, Switzerland, 2015

Recension:
MP Interconsulting - Switzerland

Publisher:
Miodrag Prokic

MP Interconsulting

Editor of the author issue: Miodrag Prokic

Proofreading and correction:

MP Interconsulting

Art & graphical design:

- computer text processing: Miodrag Prokic

- graphics / picture processing: Miodrag Prokic

- design: Miodrag Prokic

Cover design: Miodrag Prokic

Printed by: MP Interconsulting

Circulation: 2000 copies

ISBN 86-907593-0-1
ISBN 978-86-907593-1-6

Content and graphics copyright Miodrag Prokic Switzerland, 2006. All Rights Reserved. Download the last version here:
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INNOVATIVE ASPECTS OF PARTICLE-WAVE DUALITY, GRAVITATION, AND
ELECTROMAGNETIC THEORY ADDRESSED FROM THE POINT OF VIEW OF ELECTRIC AND
MECHANICAL ANALOGIES
Author: Miodrag Prokic
Abstract:

This book is dealing with an innovative and generalized understanding of Wave-Particle Duality of
matter, equally applicable to a micro and macro world of our Universe. An overall, multi-level system
of physics and mathematics-related analogies is presented and exploited in this book. Based on the
presented electromechanical analogies, number of hypothetical predictions are made regarding an
innovative understanding of de Broglie matter-waves phenomenology (or particle-wave duality),
generating elements for new conceptualization of Gravitation, Quantum theory, and directions for
updating Maxwell-Faraday Electromagnetic theory. New aspects of gravitation are extended to (still
hypothetical) phenomenology of masses and fields unity and coupling between electromagnetic and
mechanical, linear, and rotational motions, and to different associated and dualistic, particle-wave
states of involved motional energy members. Such approach, based on analogies, is suggesting that
field of gravitation could have a complementary field (which has not been well understood until
present, or still has not been considered or modeled as a complement to gravitation), in a similar
fashion as electric and magnetic fields are mutually coupled and complementary fields. Masses are
anyway internally composed of electromagnetic entities, such as atoms, electrons, protons, and
neutrons (and all mentioned items have spinning, orbital and/or electromagnetic moments or dipoles).
Electron and other electric charges are still partially and wrongly considered as being static
parameters (or as numbers of Coulombs), but, electric charges belong to the family of dynamic
parameters, like different mechanical moments are, and between electric charges should continuously
exist certain Radiant, electromagnetic energy flow (as Nikola Tesla speculated). This is implicating that
specific coupling and unity should exist between linear and torsional aspects of any mechanical motion
(like intrinsic coupling between electric and magnetic fields). In other words, the field of gravitation,
together with its (still hypothetical) torsional field complements should be a kind of electromagnetic
field manifestation. It is also contemplated that the gravitational force could be closely related to
formations of standing matter waves of the spatially and temporally resonating universe, acting
towards nodal, or masses agglomerating zones of such standing waves (like in cases of acoustic or
ultrasonic levitation in fluids), where the participation of electromagnetic forces or fields is still not
appropriately considered.

Then, the understanding of probabilistic and other ontological roots and foundations of the
contemporary Orthodox Quantum theory (which is presently the only widely and officially accepted
theory dealing with particle-wave duality) is differently and innovatively addressed and updated
showing that such theory can also be more realistic and deterministic than probabilistic, if certain more
appropriate mathematical modeling will be applied. It is also shown why present Orthodox Quantum
theory mathematically works well, but only in its own, self-defined boundaries, and in an artificially
assembled mathematical environment, and being with not sufficiently clear conceptual structure, not
having enough causal and common-sense grounds. Innovative mathematical modeling and upgraded
wave-particle duality concepts, as practiced in this book, are resulting in formulation of more general
forms of Schrödinger and Dirac-like matter-waves equations than presently known, but without using
assumptions of modern probabilistic Quantum theory, and being on the level of an elementary
mathematics. The generalization of Schrödinger equation is achieved, first by using powerful
mathematical modeling of physics-related wave-functions in the form of Complex and Hypercomplex
Analytic Signal functions or Phasors (created based on Hilbert transformation), and by respecting
specific and universally applicable relations between wave-packet, group, and phase velocity. In
addition, the rest energy and rest mass are not considered being the part of the wave-packet model
(resulting that de Broglie particle-wave phenomenology should only be related to states of motional
energy). The meaning of stochastic and probabilistic quantum mechanical wavefunction is equally
well explained, void of most of its probability or statistics décor. Hidden grounds of probability-like
behaviors (in modern Quantum theory) are coming from an “in-average” mathematical modeling of
particle-wave duality (or unity) phenomenology, using the framework of Probability, Statistics and
Signal Analysis on the way that basic conservation laws of Physics are effectively, and “in-average”
satisfied. Such Orthodox Quantum theory is (on certain isomorphic way) respecting energy and
moments conservation laws, while an instantaneous, real time-space-dependent signal phase is not
considered, or not known, because of the nature and limitations of applied mathematical modeling,
and because of presumed stochastic, ontological nature of mentioned phenomenology (without taking
into account that elements of condensed matter in our Universe also have spontaneous tendency to
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communicate and synchronize, internally and externally). This is producing “magic effects” that after
certain time of playing with isolated particles (regarding diffraction experiments) we get results like
experimenting with waves in fluids. It is also explained why present probabilistic wave function
modeling works sufficiently well (since it is created as an isomorphic mathematical processing, that is
conveniently hybridized and effectively guided by principles, concepts and laws already well known in
Classical Mechanics, Mathematics and Signal Analysis). The new natural fields unification platform,
proposed here, is initially based on exploiting united multi-level analogies and basic continuous
symmetries between different natural couples of mutually original and spectral, or conjugate domains
(such as Fourier-transform couples: time-frequency, momentum-position, electric-magnetic charges,
angle-orbital-momentum, etc.), being followed by an appropriate conceptual and mathematical
upgrading and integration into Physics.

Uncertainty relations (in this book) are also generalized and treated as the matching (or mismatching)
absolute intervals relations between original and spectral signal durations (and between their
elementary parts, similar as being treated in cases of signals synthesis) while explaining and
extending this concept much further than presently exercised in Orthodox Quantum theory (since we
can apply mentioned relations both to a micro and macro-Universe). Consequently, the particle-wave
duality concept, here presented more as the particle-wave unity, is extended to any situation where
motional or time-dependent energy flow is involved (regardless of its origin). This way, any change of
motional (or driving) energy is immanently coupled with associated de Broglie matter waves, creating
inertia-like waving effects, where mentioned inertial effects could manifest gravitational, mechanical,
electromagnetic, or some other nature, depending on participants involved in an interaction.
Something similar (regarding producing matter waves) is also valid for linear and spinning, or orbital
moments’ variations. In fact, in this book all kind of ordinary, mechanical, and electromagnetic
oscillations and waves, known in Physics, are considered as forms of de Broglie matter waves.

Using an oversimplified formulation, in this book we will find that de Broglie matter waves always have
their stationary, stable, or “packing”, standing waves places when rotating inside number of micro-
domains inside of particles’ structures (or inside atoms and elementary particles). Such internally
captured matter-waves structure is also naturally externally extended, active and electromagnetically
connected with other masses and atoms (this way explaining Gravitation), and it exist in all situations
when particles are changing their previous energies or states of motions. In other words, particles are
matter waves creations when involved matter waves establish kind of self-closed, stationary, and
standing waves, rotating and spinning structures, this way becoming “self-localized and self-stabilized
energy agglomerations” in a limited space.

In this book (mostly formulated using the language of mathematics), we will avoid complicated
mathematical analyses to facilitate the conceptual, intuitive, and common-sense understanding of
Physics by a wide public interested in the same field. Thus, the author hopes, the initial scholastic and
dogmatic critics of ideas presented in this book could be avoided, to grant the priority to conceptual,
common sense, innovative and intuitive understanding of presented ideas (which can be later
additionally and better developed). Another objective (of the author of this book) is that this book
could serve, as much as possible, as a challenging and brainstorming, inspiring and indicative
framework, and reminder for formulating and starting new projects and analyses that would be far-
reaching and more rigorous then initiated here. Certain chapters of this book have origins from partially
rewritten and updated version of the author’s B. S. diploma work (cited literature under [3]).

Briefly summarizing, in this book will be elaborated and underlined that Modern Physics, and
especially Quantum Theory, would be much different, more predictive, natural, and more causal if:

1. We consider Mobility system of electromechanical analogies (as presented in the first Chapter
of this book), as a generally applicable, starting, and indicative platform for creating, modeling
comparing and harmonizing relations between different domains in Physics.

2. We accept that all kind of matter-waves, oscillations and vibrations should always have certain
carrier matter state, fluidic medium, or spatial matrix, being especially important and
necessary for electromagnetic waves and photons when propagating in a vacuum. Certain
revitalized, fluidic ether should always exist. In a close relation with ether is A. Einstein
Relativity theory, which should be remodeled and reestablished, starting only from (also
innovated and better generalized) Maxwell-Faraday electromagnetic theory (see more in
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Chapter 3.). Second Order, Classical, Differential Wave Equation is relevant and applicable to
all kind of matter-waves known in micro and macro world of Physics, and it is very well
connected with Schrödinger family of equations, which can be smoothly developed from the
first one.
3. We should present all kind of matter-waves known in Physics using complex (or
hypercomplex) waves, signals, and Phasors, which are created as Analytic Signal functions
(based on Hilbert transform). See, for instance, in Chapter 4.0, under “4.0.11. Generalized
Wave Functions and Unified Field Theory “, how Analytic Signal Phasors can be formulated
and applied. See also in Chapter 10., similar ideas about wave-particle duality and matter-
wave Phasors, being equally applicable and relevant in a micro and macro world of Physics,
presented under 10.1 “Hypercomplex Analytic Signal functions and interpretation of
energy-momentum 4-vectors in relation to matter-waves and particle-wave duality”.
Wave-Particle Duality, as elaborated in this book, has a lot of common-sense grounds, and it
could be creatively united, with “de Broglie-Bohm” and “Both-particle-and-wave view”,
meaning that statistical and probabilistic Orthodox Quantum theory is not the best and only
choice for describing microphysics world (see more here:
https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory).
4. We consider quantizing in Physics as closely related to situations, structures and motions with
intrinsic periodicities, resonance-related events, and structural standing waves formations.
Generalized quantizing situations, relevant modeling and rules should be described by
Kotelnikov-Shannon-Nyquist-Whittaker-Fourier signal analysis and be equally well applicable
in a micro and macro world of Physics (see more in Chapters 4.0 and 10. and in literature
under [57, 58, 59, 117, 118 and 119]).
5. We need to significantly evolve with our conceptualization, understanding, modeling, and
classification of fundamental Natural Forces. Couple of presently considered as natural forces
are too far from having good foundations.
6. We need to accept that certain Physics related theories and concepts can and should be
reworked, redesigned, and reestablished in their fundaments, regardless how many
publications and official recognitions are already waisted or invested there, until present time.
This is especially applicable on Quantum and Relativistic theories.
7. We better apply Probability and Statistics in the final modeling and results-concluding states of
certain deterministic and tangible conceptualization (related to Physics) for the purpose of
better results presentation, than in its very first and introductory, ontological, or founding steps.
Statistics and Probability are, and can be safely applied, in Physics only if mathematical
conditions for such accounting and modeling are satisfied (meaning to be applied on naturally
tangible or measurable, sets with big number of mutually identical elements). Statistics and
Probability should not have any relation to ontological meaning, modeling, and fundamental
conceptualization in Physics, but could be easily connected to realize a perfect accounting
and results reporting regarding global energy balance, and to an averaged quantitative
satisfaction of conservation laws valid in Physics (see related thinking in Chapter 10.).
Parseval theorem or identity is also the mathematical way expressing an exact energy
balance or accounting between different, mutually conjugate spectral domains.
The short summary describing the foundations of Electromagnetism, Gravitation and Wave-Particle
Duality, what is the content of this book, is an almost trivial statement that “atoms are the origin,
sources, and initial structures of everything what we find in a macro world of Physics”.
Developing such concept, we can specify its meaning as follows.

1. There is a smooth and continual, omnidirectional natural fields and matter waves connection,
communication, synchronization, and transition from atoms towards other atoms, masses, and
all cosmic macro structures and vice versa (including biological species).

2. Atoms are stable packing formats or structures composed of electrons, protons, and neutrons,
also presenting sets of energy states composed of spatial-temporal resonant structures.
3. Atomic, intrinsic oscillatory states, systems, or internal resonators, are characterized with self-
closed and self-stabilized standing matter-waves, being also parts or structural resonant
content of energy states of electrons, protons, and neutrons.
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4. Resonant mechanical, electromagnetic, and atomic states are mutually, externally, and
internally communicating and synchronizing by exchanging photons and other matter waves.
5. Mutually identical (by spectral overlapping), and spatially separated resonant states, systems
or devices are susceptible to realizing fast resonant, mutual synchronization.
From such initial matter states of atoms, everything else what we know within our Universe is being
smoothly and causally developed or created, as for instance:

a) Electrically charged atom constituents (electrons and protons) are creating electric fields, both
inside and outside of atoms.
b) Any kind of spatial-temporal motion of electric charges is creating associated electric currents
and magnetic fields, also both manifesting within atoms and externally (within a macro
cosmos).
c) Electric and magnetic fields, currents, fluxes and charges manifest number of mutual relations
and mutual derivatives presently described or modeled by Maxwell-Faraday and Lorentz
electromagnetic theory.
d) Everything what we specify as Wave-Particle Duality and Matter-Waves phenomenology, has
its initial roots, models and analog states within atomic states and structures, being valid
equally for a micro and macro world of Physics.
e) Gravitation presents an external “electromagnetic extension” of forces and fields acting within
atomic microstructure towards other atoms and masses, being presently scientifically
described by Newton-Coulomb force law. In simple terms, Gravitation is a kind of
electromagnetic, or rather magnetic, inductively coupled systems of mutually attracting
masses. Gravitation is also creatively, imaginatively, and intuitively described by Rudjer
Boskovic’s Universal Natural Force law, and by Nicola Tesla’s Dynamic Gravity theory, which
are mutually complementing, and being still conceptually richer sources of modeling
inspiration compared to both Newton and A. Einstein Gravitation.
f) All other phenomenology and laws of Mechanics (and Physics) are creations, consequences,
and properties of mass-energy-moments interactions, with deep electromagnetic and atomic
origins.
g) Mathematical chapters related to complex and hypercomplex, analytic signal phasors, vector
algebra, and differential geometry are fully applicable to overall phenomenology in Physics
where we operate with motions, fields, and vectors.
This book is created and structured as an open-end, ongoing brainstorming draft, where a lot of
imaginative, creative, unbounded, and positively colored goodwill should be implemented to read it
and get its messages correctly. The book is still unfinished, and many of its chapters should be
mutually better presented, united, and organized, because the author initially started to write it
sporadically and without uniting strategy (as a hobby, and unprofessionally), from his early student
days (about the year 1970), not really finalizing it until present (since this is still an evolving and very
large problematic). Even in such unfinished, and not well-synchronized state, the book contains many
challenging and indicative conclusions, messages, proposals, and possible innovations, that the
author decided to prepare it in a form that will be understandable and motivating for others involved in
the familiar kind of thinking (since such book cannot be finalized by one author, and for the duration of
one human life). For strict, already fully convinced, too serious readers, who are officially certified and
convinced experts in the field of contemporary Orthodox Quantum and Relativity theory, this book and
its author would be an easy target (for all kind of critics), but for somebody who is creatively reading
and catching (with an intellectual flexibility) only challenging concepts, ideas, and innovative
proposals, this could be quite a different intellectual and motivating experience. Simply, such a large
problematic cannot be properly and fully elaborated by one person, only during an average human life,
and this is the main reason why the book is given to the public in its present state. The author intends
to make systematic improvements, upgrading, and unification of all chapters, as long the nature
related to performing such activities would allow him. All suggestions and collaboration proposals are
welcome.

Miodrag Prokic
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III
CONTENTS
INTRODUCTION
1. PRESENTATION OF BASIC ELECTROMECHANICAL ANALOGIES ……..…... 21

2. UNDERSTANDING GRAVITATION …………………………………..……..……… 33
2.1. Some Hypothetical Force Laws ………………….………………….….…….. 39
2.2. Generalized Coulomb-Newton Force Laws ……………………….………… 43
2.2.1. What the gravitation really is ..........................................................
61
2.3. How to start accounting rotation …………………………………….….….....
2.3.1. Extended Understanding of Inertia …………………………..……….. 71
2.3.2. Rotation and stable rest-mass creation ……………..……………… 80
2.3.3. Macro-Cosmological Mater-Waves and Gravitation……………….. 92
2.4. How to unite Gravitation, Rotation and Electromagnetism ………..…..... 117
2.5. New Platforms for Understanding Gravitation ………………….….…….... 118

3. POSSIBILITIES FOR GENERALIZATION OF FARADAY-MAXWELL THEORY ... 120
3.1. Modification of Maxwell Equations …………….…………………..…..…….. 121
3.2. Generalized view about Currents, Voltages and Charges ………...…..…. 125
3.3. New, Relativistic-like Formulation of Maxwell Equations …………….….. 127
3.4. The Important Extension of Electromechanical Analogies ………….…... 131
3.4.1. The Hyperspace Communications and Light ……….……...……….. 133

4. MATTER WAVES and QUANTUM THEORY.............................. 135
4.0. WAVE FUNCTIONS, WAVE VELOCITIES AND UNCERTAINTY RELATIONS... 135
4.0.1. Signal Energy Content ……………………………………….…….….…. 137
4.0.2. Resume of Different Analytic Signal Representations ……………. 141
4.0.2.1. Relations Between Additive and Multiplicative Elements …. 142
4.0.2.2. Signal Amplitude or Envelope …………………..……….….... 143
4.0.2.3. Signal Phase …………………………………...…………….…... 143
4.0.2.4. Signal instant frequency ………………………………….……. 143
4.0.2.5. More of interesting relations ……………………...……….….. 143
4.0.2.6. Hyper-complex Analytic Signal ……………………………….. 144
4.0.3. Generalized Fourier Transform & Analytic Signal ………………..… 145
4.0.4. Meaning of Complex Analytic Signal Functions in Physics ………. 147
4.0.5. Wave Packets and mathematical strategies in formulating
Wave Velocities …………………………………..……….….…………… 150
4.0.6. Traveling Wave-Packets and Waves-Dispersion ……………………. 162
4.0.7. Wave-Packets already known in Physics ………………………..….... 165
4.0.8. Uncertainty Relations and Waveform Velocities ……………………. 169
4.0.9. Uncertainty Relations in Quantum Theory …………………………… 177

4.0.10. Wave-Group Velocities, Moving Particles and Uncertainty Relations......
177
4.0.11. Generalized Wave Functions and Unified Field Theory ……….…… 185
4.0.11.0. Wave Function, Energy, Power and Impedance …………. 187
4.0.11.1. Generalized Impedances ……………………………………... 188
4.0.11.2. Resistive Impedances ………………………………………… 189
4.0.11.3. Inductive Impedances ………………………………………… 189
4.0.11.4. Capacitive Impedances …………………………………….…. 190
4.0.11.5. R-L-C Impedances for Simple Harmonic Currents ………. 190
4.0.11.6. Power Function ………………………………………………… 192
4.0.12. Evolution of the RMS concept ………………………………………….. 195
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IV
4.0.12.1. Standard Deviation in relation to Load Impedance ……… 201
4.1. MATTER WAVES AND QUANTUM MECHANICS ……………....................... 202
4.1.1. Particle-Wave Duality Code …………………………………..……..….. 208
4.1.1.1. The Resume regarding PWDC ……………………………..…. 225
4.1.2. Matter Waves, Unity and Complementarity of Linear, Angular and
229
Fluid Motions
4.1.2.1. Example 1: Bohr’s Hydrogen Atom Model ……………..….. 256
4.1.3. Mater Waves and Conservation Laws …………………………….…... 259
4.1.3.1. Example 2: X-ray Spectrum and Reaction Forces ………... 282
4.2. INTERACTION MODELING ………………………….…………..….…………… 293
4.2.1. Elastic Collisions ……………………………….…………………………. 294
4.2.2. Example 3: Collision photon-particle (Compton Effect) …….……... 301
4.2.3. Example 4: Doppler Effect ……………………………………………… 312
4.3. MATTER WAVES AND WAVE EQUATIONS …….......................................... 316
4.3.1. Wave Energy and Mean Values ………………………………..……….. 329
4.3.2. Inertial and Reaction Forces ………………………...……………..…… 332
4.3.3. Probability and Conservation Laws …………………………….……... 334
4.3.4. Mater Waves and Unified Field Theory ……………………………….. 339
4.3.5. Wave Function and Euler-Lagrange-Hamilton Formalism ………… 342
4.3.6. Further Extensions of Wave Function and Universal Field Theory … 349
4.3.7. Mater-Wave 4-Vectors in Minkowski Space and Elements for
New Topology ……………………………………………………………… 353
4.3.8. Mass, Particle-Wave Duality and Real Sources of Gravitation ….... 358

5. UNCERTAINTY RELATIONS AND ELEMENTARY MATTER DOMAINS …....... 368
5.1. Uncertainty in Physics and Mathematics …………………………..……….. 387
5.2. Uncertainty Relations, Fields and Transformation Domains …..……...… 397
5.3. Central Differences, Uncertainty and Continuum …………..….......……… 402

6. DIFFERENT POSSIBILITIES FOR MATHEMATICAL FOUNDATIONS OF
MULTIDIMENSIONAL UNIVERSE …………………………………….……..……… 405
6.1. Hypercomplex, In-depth Analysis of the Wave Function ……………….... 415

7. CONCLUSION …………………………………….……………………….…………... 424
WORKS CITED ……………………………….…………...……………………..…….. 427

Appendix:

8. BOHR’s ATOM MODEL, GRAVITATION AND PARTICLE-WAVE DUALISM
432
8.1. New Aspects of Atom Configuration from the view of
the Bohr’s Model ………………………...…………………………...…..……… 446
8.2. Bohr’s Atom Model and Stationary States of the Nucleus …………….…. 451
8.3. Structure of the Field of Subatomic and Gravitation related Forces……. 457

9. BLACK BODY RADIATION, GRAVITATION AND PHOTONS............................ 464
10. PARTICLES AND SELF-CLOSED STANDING MATTER WAVES 556

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INTRODUCTION

The main subject of this book is related to the formulation of an updated theory of particle-
wave duality (or particle-wave unity), but indirectly this book also creates or opens the
window towards a new platform regarding an innovative understanding of Gravitation, and to
natural fields and forces unification theory. Deep roots of mentioned innovative understanding
of Gravitation (and united fields’ theory) can also be found in the heritage and publications
from Nikola Tesla and Rudjer Boskovic (see [6] and [97]). The principal attempts in this book
are presenting and exploring items and statements such as:

-Gravity and Particle–Wave Duality is based on specific couplings between linear and
angular (or rotational) motions and associated electromagnetic complexity, initially originating,
and extending from atoms towards other masses and atoms. In other words, the field of
gravitation together with its (still hypothetical) torsional field components could be a kind of
specific electromagnetic field structure, electromechanically coupled with different mass-
energy-momentum states (within a global, spatial, and temporal standing-waves structure of
an oscillating macro and microcosmic universe). Briefly summarized, we can say that de
Broglie matter-waves and wave-particle duality conceptualization is applicable both to a micro
and macro world of Physics.

-Mass is specific matter-waves energy packing or formatting state of agglomerated
atoms (internally structured as mutually coupled micro domains and atoms, all of them being
like ensembles of spatial standing waves or resonators, on a self-closed area). All mentioned
micro domains dominantly or ontologically have an electromagnetic origin, based on self-
stabilized, self-closed, mutually well synchronized matter-waves formations and field
couplings of moments-energy-mass spinning states.

-Matter Waves, are intermediary and transient states that are realizing unity,
synchronizations, and couplings between atoms and masses in linear and angular or spinning
motions within spatial-temporal structures, presenting dual, mutually orthogonal, spatial-
temporal formations of waves-alike energy-momentum states (participating in
communications and self-organized resonant synchronizations) between different matter
entities and states (in a micro and macro world of Physics). Convenient superposition of
matter waves is creating particles.

Presently (meaning from the beginning of the 21. century) official science is still considering
the biggest achievements of Physics as belonging to several islands of knowledge: 1°
Mechanics including Gravitation Theory (GT) and Einstein Relativity Theories (RT), 2°
Maxwell Electromagnetic Theory (EM), and 3° Quantum Theory (QT), including all
surrounding theories and mathematical tools in connection to them. Any new theory regarding
particle-wave duality (including the one from this book) should also be placed in the same
frames of EM, GT, RT, and QT. In addition, all new formulations, and updates of such (matter-
waves) theory should start from already known works and results related to L. de Broglie
matter waves hypothesis and M. Maric - A. Einstein, and Max Planck quantized energy
concepts. In this book, the renewed Particle-Wave Duality Concept (PWDC) is presented as
the most important link (or necessary background) towards conceptualizing Universal and
United Field theory. It is also shown that there could not be any PWDC manifestation without
the presence of a certain two-body (or many-bodies) field (or energy and moments)
interaction, meaning that PWDC is a product and a consequence of existing field couplings,
interactions (and space-time evolving forces) between moving objects, when certain state of
motion is advancing (while respecting all natural conservation laws). If we could have a
moving particle in an “absolutely empty space”, there would not be any PWDC manifestation.
Of course, here we have in mind electromagnetic and mechanics (including gravitation) related
field effects (because there is still nothing else easily comprehensible, explicitly and in details
fully confirmable, conceptually, and logically tangible on a unique way, and experimentally and
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