Unified Field Theory and Wave–Particle Theory ...

Volker A. Weberruß

Unified Field Theory and Wave–Particle Theory leading into a Comprehensive Theory of Existence Fundamentals, Applications, Technology, Philosophy, Biosystems Motivation The natural resources of chemical elements essential for life such as phosphor and chemical elements essential for technology such as indium become smaller and smaller. But how to produce vital products such as mineral fertilizers and helpful products such as electronic devices when such natural resources are running out? Certainly, recycling might be helpful, but cannot remedy the problem completely! The lack of energy such as electric power becomes bigger and bigger. But how to secure our standard of living when relatively many people claim relatively little energy? Certainly, green energy such as water energy, wind energy, and solar energy might be helpful, but cannot remedy the problem completely! Going beyond that, on the one hand, the necessity of rocket drives showing a higher power than nowadays becomes bigger and bigger. Going beyond that, on the other hand, the necessity of gravitation generators showing a higher power than nowadays becomes bigger and bigger. Therefore, in no way, it is overstated to say that mankind is confronted with big challenges. However, becoming acquainted with the out-of-the-way methods presented in this out-of-the-way work, it should not be a too big problem anymore to master the big challenges. Certainly, we first have to go through a lot of theoretical stuff. However, we become rewarded by a lot of hints supplied by the theoretical stuff pointing at ways to future technologies enabling us to master the big challenges. Don’t lose heart! One step leads to the other. Softbook Version 1.9

Volker Achim Weberruß Winterbach, January 2015

©Dr. rer. nat. Volker Achim Weberruß V.A.W. scientific consultation Im Lehenbach 18 D-73650 Winterbach [email protected]

This work was produced with LINUX using KILE and TEXLIVE. Numerics: OCTAVE. Drawings: DIGCAD. Photographs: CANON AE-1.

The Human Factor

One of the most serious problems in the history of natural sciences is that we can do calculations correctly, can do numerical computations correctly, and also can take measurements correctly, but nevertheless can misinterpret the results, eventually establishing an inaccurate theoretical construct. This then has dramatic consequences. Calculations that could be done are not done. Measurements that could be taken are not taken. Technologies that could be developed are not developed. Philosophical ideas that could be worked out are not worked out. The “human factor” influences the evolution of mankind in a lot of ways. It really is a pity. Worldwide and for a long time, my scientific colleagues have registered that Einstein’s theory of gravitation includes structural properties needed to describe electromagnetic entities, but interpret these structural properties as purely formal similarities. Worldwide and for a long time, my scientific colleagues have registered that Einstein’s theory of gravitation includes structural properties needed to describe quantum systems, but likewise interpret these structural properties as purely formal similarities. Moreover, it is an entrenched belief that Einstein’s theory of gravitation and Schr¨odinger’s/Heisenberg’s/Feynman’s theory of quantum systems have nothing to do with each other, eventually separated by an insurmountable barrier, completely preventing their unification. Moreover, it is an entrenched belief that these estimations reflect scientifically proven circumstances. It really is a pity. As a general rule, the calculations are exact. As a general rule, the numerical computations are exact. As a general rule, the measurements are exact. It is the “human factor” that here plays the crucial role. Talking about the necessity to overcome classical thinking, my scientific colleagues in many ways are deeply rooted in classical thinking. They do not realize that only a few off-the-wall ideas are needed to resolve all this in a grand unified theory, and all this logically consistent with calculations, numerical computations, and measurements. They do not realize that only a few off-the-wall ideas are needed to establish a nonlinear generalization of quantum theory and quantum field theory, here termed wave–particle theory, just like a synergetic enhancement of quantum theory and quantum field theory, here termed wave–particle synergetics, departing from this grand unified theory. Remaining defiant, I now would like to carry out the next step in familiarizing my scientific colleagues with these off-the-wall ideas presenting this out-of-the-way work extending [6, 7]. Let me here also annotate that I have published a summary of the most essential basics, which are developed here, in advance in two coherent articles [62, 63].

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Notes I

Clarification In this out-of-the-way work, on the one hand, an advanced formulary is introduced to make the versatile physical circumstances and versatile technological circumstances comprehensible, and on the other hand, a “supporting picture” is introduced to make the versatile physical circumstances and versatile technological circumstances graphically accessible. So to speak, the “supporting picture” which is developed in the chapters that follow is a useful construct of ideas that makes a complicated formulary graphically accessible. Certainly, applying the “supporting picture” which is developed in the chapters that follow, the complicated formulary in a logically consistent manner is understandable in subtle details. However, it should be left to the reader to decide whether it is concrete physics or whether it is an experimental image of the reality. Nevertheless, each reader can easily convince himself that the relations, methods, and rules that are introduced in this out-of-the-way work are applicable to a large extent. Therefore, each reader can ultimately prove for himself that this Unified Field Theory, here also denoted as generalized Einstein field theory (GEFT), completely removes the barriers up to now separating the wonderful ideas of Einstein and the wonderful ideas of Schr¨odinger, Heisenberg, and Feynman. Certainly, this out-of-the-way work contains a wealth of unusal ideas and unusal models. However, this out-of-the-way work also contains a wealth of illustrations elucidating unusal circumstances.

Acknowledgment Thanks a lot, Dorothee Klink, for the helpful language support! Give my regards to my appreciated fellows at the Max–Planck-Institut f¨ ur Metallforschung, meanwhile named Max–Planck-Institut f¨ ur Intelligente Systeme. In particular, I gratefully would like to thank Fritz Aldinger, the former director of the department “engineering ceramics” of the Max–Planck-Institut f¨ ur Metallforschung, and Joachim Bill, the interim director of the department “engineering ceramics” of the Max–Planck-Institut f¨ ur Metallforschung, for their valuable support. Furthermore, I gratefully would like to thank Arndt Simon and J¨ urgen K¨ ohler, Max-Planck-Institut f¨ ur Festk¨ orperforschung, who have been feeding me with a lot of hints concerning superconductivity. Moreover, I gratefully would like to thank Jochem Hauser, Ostfalia Hochschule f¨ ur angewandte Wissenschaften, who has been feeding me with a lot of hints concerning gravitational machines. I am also indebted to Hermann Haken, G¨ unter Mahler, and Michael Mehring for their support.

The Human Factor

III

Notes II

Terminology Regarding the terminology used in the book in hand, the following aspects should be pointed out in advance. (1) The term particle, for example, occurring within the term wave–particle system, is used in the sense corpuscular object, while the term wave, for example, also occurring within the term wave–particle system, is used in the sense oscillatory field, logically supplementing the term particle. However, at special places, the term particle is used as substitute for the term wave–particle system, then forcing us to use quotation marks, then writing “particle”. (2) The term quantum system is replaced by the term wave–particle system in order to conceptualize the central feature inseparability of wave properties and particle properties of quantum systems. (3) The term quantum mechanics is replaced by the term conventional quantum mechanics in order to conceptualize that the term wave–particle mechanics circumscribes an advanced quantum mechanics/quantum field mechanics, comprehensively completing the quantum mechanics/quantum field mechanics known from conventional lectures and conventional publications (4) The term tensor, on the one hand, is used as umbrella term for scalars, vectors, and higher-order matrices showing tensor character, eventually reflecting the common usage in mathematics, and on the other hand, is used as special term for higher-order matrices showing tensor character, eventually reflecting the common usage in physics.

Symbols Regarding the symbols used in the book in hand, the following aspects should be pointed out in advance. (1) The four-dimensional quantities of general relativity can be broken down to sets of one-dimensional quantities and three-dimensional quantities, in particular, leading to a related set of basic tensors which is best adapted to the needs of mechanical (classical) systems and quantum systems and is provided by γ00 , γ 00 , A∋ = {γi0 = γi0 }, A∋ = {γ i0 = γ 0i }, θ∋ = {γij = γji }, θ∋ = {γ ij = γ ji }, with the “calligraphic three ∋” indicating the three-space quality. (2) There are ˆ , ˆl and jˆs as well as unconventional operators such as conventional operators such as p ˆ and ˆjs which are best adapted to the needs of quantum systems, in the latter case, s distinguished by Gothic letters (black letters), determining higher “covariant” levels of description enabling manifold ways of specification eventually covering a wealth of different situations.

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The Human Factor

Box I (Symbols: mass, charge, and metric). Tµν = Einstein’s energy momentum tensor, K = Einstein’s constant, G = Newton’s constant, Tµν = generalized energy momentum tensor, K = generalized constant, gµν = metric tensor, ηµν = pseudo-Euclidean metric tensor, γµν = metric potential tensor, q µ = generalized coordinates, xµ = Cartesian coordinates, ǫ Γµν = Christoffel symbols, ∞ Rµν = Riemann tensor of curvature and Rµν = completion of Rµν to infinity (in the reduced form Rµν , the Riemann tensor of curvature is also called Ricci tensor), R = scalar of curvature, δǫǫ′ = Kronecker delta, η00 = −1, η11 = η22 = η33 = +1, ηµ6=ν = 0, xµ = {xi ; x0 }, xi = {x, y, z}, x0 = ct, {µ, ν} = {0, 1, 2, 3}, i = {1, 2, 3}; ρg = mass density, ρC = charge density, φg = mass potential, φC = charge potential, φg,C = mass–charge potential, Φ = generalized potential, U = generation tension (voltage) or vacuum tension (voltage), λC = charge adaptation factor, Φ = −γ00 /2 = φg /c2 or − φC /U or φg,C = φg /c2 − φC /U , c = light velocity; F a = Newtonian forces, E = electric field (D = ǫ0 E), H = magnetic field (B = µ0 H), A = vector potential, U = electric tension (in the context of conventional potentials), I = electric current, j = electric current density, ǫ0 = dielectric constant, µ0 = magnetic constant, εr = tensor of relative permittivity, ε = tensor of permittivity, µr = tensor of relative permeability, µ = tensor of permeability; x = position vector, v = velocity vector, V = volume, A = cross-sectional area, ds = (non-oriented) line element, ds = (oriented) line element, m0 = rest mass, m = mass, q = charge.

The Human Factor

Box II (Symbols: wave–particle theory). ψ = wave function;

in the case of classical systems: γ00 = scalar classical potential, γ 00 = imprinted scalar classical properties, A∋ (collecting the γi0 ) = vectorial classical potential, A∋ (collecting the γ i0 ) = imprinted vectorial classical properties, θ∋ (collecting the γij ) = tensorial classical potential, θ∋ (collecting the γ ij ) = imprinted tensorial classical properties (comprising classical potentials such as the vector potential A; complex functions are not necessary);

in the case of wave–particle systems: γ00 = scalar wave–particle potential := ψ, ¯ γ = imprinted scalar properties such as scalar self-interaction properties := ψ, A∋ = vectorial wave–particle potential, A∋ = imprinted vectorial properties such as vectorial self-interaction properties, θ∋ = tensorial wave–particle potential, θ∋ = imprinted tensorial properties such as spin properties; 00

(comprising classical potentials such as the vector potential A and nonclassical potentials such as linkages “vector potential A” and “wave function ψ”; in the latter case, complex functions are necessary);

ˆ = −iℏ∇ = momentum operator, p ˆl = r × p ˆ = angular momentum operator, ˆ s = actual spin operator, jˆ = θω s

ˆ s = r × ˆjs = covariantly adapted spin operator, ˆjs = −iℏθ∋ s ∇ = covariantly adapted actual spin operator, θ = tensor of inertia, θ∋ s = covariantly adapted tensor of inertia;

r = radius vector, r = amount of radius vector, e = elementary charge, ℏ = Planck’s constant.

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. . . the root evolves on which a trunk evolves forming the basis for a wealth of branches that more and more branch out taken from the VAWsc picture archive Figure I. This work is like a tree, part one, . . .

The Human Factor

. . . the root evolves on which a trunk evolves forming the basis for a wealth of branches that more and more branch out taken from the VAWsc picture archive Figure II. This work is like a tree, part two, . . .

VII

Structure of Contents Unusal ideas require an unusal structure of contents. Chapter 1 summarizes the basic ideas of generalized Einstein field theory (GEFT) and wave–particle theory (WPT), eventually defining a self-consistent concept enabling a unified description of mass, charge, and metric within macroscopic limits as well as microscopic limits. Chapter 2 deepens the basic ideas of wave–particle theory (WPT), eventually defining a specification of generalized Einstein field theory (GEFT) aiming at the theoretical description of microscopic systems (quantum systems) here also consistently called “wave–particle systems”. Chapters 3–5 present first models in the areas “atoms/molecules”, “elementary particles”, and “solid bodies”, eventually serving as first examples demonstrating the possibilities of GEFT/WPT in comparison to the possibilities of conventional quantum mechanics. In addition, Chapter 6 presents advanced extensions paving the way to quantum synergetics here also consistently called “wave–particle synergetics”, eventually further demonstrating the possibilities of GEFT/WPT. In addition, Chapter 7 presents advanced extensions paving the way to quantum technologies here also consistently called “wave–particle technologies” including antimatter technologies and artificial gravitation technologies, eventually further demonstrating the possibilities of GEFT/WPT. Beyond that, taking my hat off to novel trends of research dealing with biosystems, Chapter 8 elucidates specific extensions meeting neurological aspects of human beings and Chapter 9 elucidates specific extensions meeting genetic aspects of human beings, in this manner, also demonstrating that GEFT/WPT supplies us with an intuitive access to biosystems. Beyond that, taking my hat off to old trends of research dealing with mysticisms, Chapter 10 elucidates specific extensions meeting philosophical notions of human beings such as the notion “human soul” or the notion “God/Allah”, in this manner, also demonstrating that GEFT/WPT supplies us with an intuitive access to mysticisms. Being fully aware that the researchers of nowadays believe that a theory of unified fields, which here basically is launched, must be very complicated and cannot be derived via a simple concatenation of Einstein’s theory and Schr¨odinger’s theory, I have added Chapter 11 being responsive to objections. Last but not least, I have added some supplementary chapters completing this out-of-the-way work. Be a little bit inspired!

Contents

The Human Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XVI

Unified Field Theory 1.

Superunified Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 A Superunified Picture of Mass/Charge Physics . . . . . . . . 1.2 A Superunified Picture of Micro-/Macro-Physics . . . . . . . . 1.3 What I Here Should Say Finally: Mass–Charge Metrics . . . 1.4 What I Here Should Say Finally: Wave–Particle Metrics . . 1.5 Velocities Higher Light Speed in a Self-Interaction Bubble?

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Wave–Particle Entities . . . . . . . . . . . . . . . . . . . . 2.1 The Concept of Wave–Particle Energies . . . . . . . 2.2 The Concept of Wave–Particle Trajectories . . . . . 2.3 The Concept of Wave–Particle State Equations . . 2.4 The Concept of Wave–Particle State Information 2.5 The Concept of Wave–Particle State Topology . .

Wave–Particle Systems I 3.

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Wave–Particle Phases II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 4.1 The Wave–Particle Image of Electron/Positron Generation . . . . . . . . 324 4.2 The Wave–Particle Image of Electron–Positron Destruction . . . . . . . . 354

Wave–Particle Systems III 5.

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Wave–Particle Phases I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 3.1 The Hydrogen Atom Electron e− as First Application . . . . . . . . . . . . 176 3.2 The Hydrogen Atom Nucleus 2 H as Second Application . . . . . . . . . . . 288

Wave–Particle Systems II 4.

1 26 56 78 86 88 92

Wave–Particle Theory 2.

I

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Wave–Particle Phases III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 5.1 The Wave–Particle Image of Electric Conductivity . . . . . . . . . . . . . . 440 5.2 The Wave–Particle Image of Superconductivity . . . . . . . . . . . . . . . . . 454

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Contents

512

Advanced Topics I 6.

Wave–Particle 6.1 Synergetics 6.2 Synergetics 6.3 Synergetics

Synergetics . . . . . . . . . . . . . . of Wave–Particle Entities . . . . . . of Electron–Positron Destruction of Electron–Positron Generation .

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Advanced Topics II 7.

Wave–Particle Technology . . . . . . . . . . 7.1 Conversion of Solid Matter into Light . 7.2 Conversion of Light into Solid Matter . 7.3 Generation of Artificial Gravitation . .

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Neuronal Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Manic Potentials and Kinfolk – Empirical Approach . . . 8.2 Manic Potentials and Kinfolk – Numerical Approach . . . 8.3 Perceptive Potentials and Kinfolk – Empirical Approach 8.4 From GEFT/WPT to Neuronal Potentials . . . . . . . . . .

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Genetic Potentials . . . . . . . . . . . . . . . . . . 9.1 Chemical Code/Decimal Code . . . . . . . . 9.2 Potentials of Genetic Differentiation . . . . 9.3 Potentials of Genetic Complexity . . . . . . 9.4 From GEFT/WPT to Genetic Potentials

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Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . On the Concept of Human Soul . . . . . . . . . . . . On the Concept of God/Allah . . . . . . . . . . . . . On the Picture of Human Existence . . . . . . . . . From GEFT/WPT to Models of Human Soul . . From GEFT/WPT to Models of God/Allah . . . From GEFT/WPT to HB/HS Models of Death . From GEFT/WPT to HB/HS Models of Birth .

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751 760 760 761 762 772 778 779 786

Einstein’s Ideas versus Schr¨ odinger’s Ideas 11. Off-The-Wall Thinking 11.1 Objection and Reply . 11.2 The Way of Thinking 11.3 The Way of Modeling

705 705 712 724 742 750

Border Aspects of Human Existence 10. Life 10.1 10.2 10.3 10.4 10.5 10.6 10.7

603 610 644 686 698 704

Aspects of Biophysics II 9.

553 560 570 590 602

Aspects of Biophysics I 8.

513 524 525 525

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787 788 790 790

Contents

XI

796

Supplementary Aspects: “Particles” “As They Are” I

12. Low-Level Concepts I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797 12.1 The Electron “As It Is”: Quantum Rules? . . . . . . . . . . . . . . . . . . . . . 798 12.2 The Electron “As It Is”: Electric Dipole Moment? . . . . . . . . . . . . . . . 844 854

Supplementary Aspects: “Particles” “As They Are” II

13. Low-Level Concepts II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855 13.1 QM/QFT Views: What are Strings? . . . . . . . . . . . . . . . . . . . . . . . . . 856 13.2 GEFT/WPT Views: What are Strings? . . . . . . . . . . . . . . . . . . . . . . 856 860

Supplementary Aspects: Exciting and Evolving 14. Signal Ways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 GEFT/WPT Aspects of Single-Particle Spectroscopy 14.2 GEFT/WPT Aspects of More-Particle Spectroscopy . 14.3 GEFT/WPT Aspects of Ensemble Spectroscopy . . . . 14.4 Signal Ways: Single-Spin Precession Dynamics . . . . . 14.5 Signal Ways: Spin Ensemble Precession Dynamics . . . 14.6 Signal Ways: Magnetic Single-Spin Resonance . . . . . . 14.7 Signal Ways: Magnetic Spin Ensemble Resonance . . .

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Supplementary Aspects: Living and Dying 15. Life 15.1 15.2 15.3

Ways . . . . . . . . . . . . . . . . . On the GEFT/WPT Image of On the GEFT/WPT Image of On the GEFT/WPT Image of

................ Body/Soul . . . . . . . . Human Body/Soul . . Human Living/Dying

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17. Asked Questions and Given Answers . . . . . . . . 17.1 Questions Striking Basic Issues . . . . . . . . . . . . 17.2 Questions Striking Extended Issues: Physics . . . 17.3 Questions Striking Extended Issues: Biophysics . 17.4 Questions Striking Special Issues: Heim’s Ideas . 17.5 Critical Comments and Clarifying Answers . . . .

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CMXLII

Supplementary Aspects: Questions and Answers

Appendix

923 924 925 925 936

Supplementary Aspects: Thinking and Acting 16. Mind Ways . . . . . . . . . . . . . . . . . . . . . 16.1 On the Logic of Human Thinking . . 16.2 On the Logic of Scientific Thinking . 16.3 On the Potential Minimum Strategy

861 862 862 870 876 876 896 896

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.CMXLIII ... . . . . CMXLIII . . . . CMLV . . . . CMLVI . . . . CMLVIII . . . . CMLX 965

XII

Contents

A. Covariant Basis Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 967 B. Covariant Energy Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 979 C. Covariant Force Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MIII Annotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1009

Structure of Presentation Unusal ideas require an unusal structure of presentation. Allowing chaos in the brain accompanied by chaos on the paper means not being able to realize the mathematical/theoretical structures that govern nature. Creating order in the brain accompanied by order on the paper means being able to realize the mathematical/theoretical structures that govern nature. Certainly, chaos frequently leads to creativity. However, chaos never leads to awareness. Not chaos, order is the keyword at the end aiming at the development of a self-consistent network of rules/laws allowing a comprehensive access to nature. Not chaos, order is the keyword at the end aiming at the development of awareness. An unusal structure of presentation, reflecting order principles on low-level scales and high-level scales, not a Shakesperean way of presentation, a Goethean way of presentation, or a Brechtian way of presentation is the matrix for the argumentations and considerations introducing the unusal ideas that follow. We here take notice of the following issuses. Firstly, the work in hand is characterized by three structural instances, namely a text instance collecting thoughts, a box instance collecting formulae, and a picture instance collecting graphic images, and these are designed in such a manner that each of these widely can be considered individualy, wanting to carve out the skeleton of thoughts, the skeleton of formulae, and the skeleton of graphic images as clear as possible. Secondly, the work in hand is characterized by relatively big blocks of text, and these are designed in such a manner that streams of thoughts showing a close relationship are kept together, wanting to carve out the diverse correlations as clear as possible. Thirdly, the work in hand is characterized by different highlighting text colors, namely green pointing out groupings within a text block or between text blocks, red pointing out important issues, and violet pointing out subordinate groupings within a text block or between text blocks or pointing out subordinate issues, and these are completed by additional highlighting background colors emphasizing logical environments, namely structuring units such as the Reflections environment or the Philosophy environment. Fourthly, the work in hand is characterized by additional photographs, not really needed, but really nice, eventually inserted to liven up the complicated thoughts and the complicated formulae. Have a little bit of fun!

CMXL Contents

The supplementary chapters that follow should supply the reader with additional remarks and tools enabling a deeper access to this out-of-the-way work. Let me here especially concentrate on some supplementary aspects of discussion.

What is the main purpose of Chapter 17? Let me here elucidate some supplementary aspects of discussion, in last consequence, presenting asked questions and given answers.

Supplementary Aspects: Questions and Answers

17. Asked Questions and Given Answers

More and more people begin to realize that the picture of nature in which we are believing nowadays has fundamental deficits. Therefore, it is no miracle that more and more people begin to think of corrections of the picture of nature in which we are believing nowadays. This out-of-the-way work is the consequence of an unusal way of thinking aiming at the remdey of such deficits. Other out-of-the-way works created by other authors are pointing into similar directions [31, 32]. Naturally, unfamiliar treatments activate a lot of doubt leading to a lot of questions. Consequently, wanting to remedy the doubt regarding this out-of-the-way work, let me here additionally present a short collection of asked questions and given answers.

17.1 Questions Striking Basic Issues

Einstein’s metric fields and Hilbert’s state vectors show different characteristics. Can these really be considered as two aspects of a unity? The answer is “yes”. Einstein’s metric fields and Hilbert’s state vectors define subsets F (E) and F (H) of a functional superset F (G) that is determined by the generalized Einstein field equations, we here consult Figures 17.1 and 17.2.

A unified description of masses and charges is possible introducing an ad hoc quantity circumscribed as “tension (voltage) U ”, in particular, setting up m0 c2 = qU and m0 = m0 + λC q, λC = λC (U ). Is the tension (voltage) U related to two points of the position space? The answer is “no”. The tension (voltage) U is related to two points of the energy space, we here consult Figures 17.3 and 17.4.

CMXLIV 17. Asked Questions and Given Answers

Einstein’s metric fields (Einstein field equations) generalized metric fields (generalized Einstein field equations)

“normal form and W form”

E space

W space (specified for quantum systems)

G space

H space

Hilbert’s state vectors (Schr¨ odinger equation and more) “H state vectors”

generalized state vectors (wave–particle equations and more) “W state vectors”

GEFT/WPT and set theory: set structure of functions (“metric fields”, “state vectors”) Figure 17.1. F(E) and F(H) as subsets of a functional superset F(G).

17.1 Questions Striking Basic Issues CMXLV

mass-related energy momentum tensors mass–charge-related energy momentum tensors, exotic energy momentum tensors

E space

W space (specified for quantum systems)

G space

H space

wave–particle energy momentum tensors (related to linear operators)

wave–particle energy momentum tensors (related to linear and nonlinear operators)

GEFT/WPT and set theory: set structure of energy momentum tensors related to the set structure of functions (“metric fields”, “state vectors”) Figure 17.2. T (E) and T (H) as subsets of a functional superset T (G).

CMXLVI 17. Asked Questions and Given Answers

m0 , q = 0 the energy Ev of the vacuum edge here is set equal zero

E = m0 c2 = (q = 0)U∞

if no charge is present, an infinite term U∞ occurs so to speak, U∞ defines an infinite creation barrier for charged “particles”, opening a channel for uncharged “particles”

energy space ⇑ interrelation is fixed by c2 ⇓

observable states

E = Ev = 0 unobservable states a charge q is running through the tension (voltage) U setting up the charge energy qU , in this way, generating what we know as mass m0 and as mass energy m0 c2 making the charge q observable E = m0− c2 = (− |q− |)(− |U− |)

m0− , q− = − |q− |

⇑ interrelation is fixed by c2 and U− ⇓

+ |q+ | = q+ , m0+

observable states

E = Ev = 0

m0+ c2 = E = (+ |U+ |)(+ |q+ |)

⇑ interrelation is fixed by c2 and U+ ⇓

0 = Ev = E unobservable states

Figure 17.3. Tension (voltage) U defining distances in energy space, part one.

17.1 Questions Striking Basic Issues CMXLVII

m0 , q = 0 the energy Ev of the vacuum edge here is set equal zero

E = m0 c2 = m0 c2

if no charge is present, an infinite term U∞ occurs so to speak, U∞ defines an infinite creation barrier for charged “particles”, opening a channel for uncharged “particles”

energy space ⇑ interrelation is fixed by c2 ⇓

observable states

E = Ev = 0 unobservable states a charge q is running through the tension (voltage) U setting up the charge energy qU , in this way, generating what we know as mass m0 and as mass energy m0 c2 making the charge q observable E = m0− c2 = m0− c2 + −|q− | 2 ˜C c λ −| U − |

m0− , q− = − |q− |

⇑ interrelation is fixed by c2 and U− ⇓

+ |q+ | = q+ , m0+

observable states

E = Ev = 0

m0+ c2 = E = m0+ c2 + +|q+ | 2 ˜C c λ +|U+ |

⇑ interrelation is fixed by c2 and U+ ⇓

0 = Ev = E unobservable states

Figure 17.4. Tension (voltage) U defining distances in energy space, part two.

CMXLVIII 17. Asked Questions and Given Answers

How can we conceive that GEFT/WPT manage the unification of microscopic/macroscopic masses and charges correctly? The answer is a little bit more complicated. Therefore, let me here go a little bit more into detail. First of all, following the idea that the mass observable m0 and the charge observable q of a charged “particle” read m0 = m0 + λC q and q = q setting up the mass–charge exchange relation m0 c2 = qU defining a mass–charge energy equivalence, eventually reflecting the observation that the charge q does not occur individually, but does occur as attender of the mass m0 considering a charged “particle”, on the one hand, we realize why total decay processes of charged “particles” lead into a oneness of electromagnetic/gravitational radiation, and on the other hand, we realize why total relaxation/condensation processes of a oneness of electromagnetic/gravitational radiation lead into charged “particles” based upon a oneness of charge/mass parts, and going beyond that, we conceive why the p energy–mass formula provided by E = mc2 = γm0 c2 , where γ = 1/ 1 − v 2 /c2 , does not contradict the observation that the charge q does not occur individually, but does occur as attender of the mass m0 considering a charged “particle”, i. e. mass and charge then are team players also at velocities v near the light velocity c, and this is what an unbiased beholder would expect. Furthermore, following the above idea, we additionally conceive that the mass–charge exchange relation m0 c2 = qU defining a mass–charge energy equivalence eventually is telling us that the total energy of a charged “particle” “as it is”, m0 c2 and thus mc2 , is covering two possible field states implied by two possible sources ± |q| related to two possible tensions (voltages) ± |U |, in the latter case, defining the energetic distance relative to the vacuum edge as qU , we here again consult Figures 17.3 and 17.4. Furthermore, following the above idea, we additionally conceive that the mass–charge density ρg,C = ρg + λC ρC , which is carrying forward the mass–charge quantity mg,C = m0 + λC q, is related to the mass–charge potential φg,C = φg /c2 + φC /U , which is implying the mass–charge force Fg,C = −m′0 c2 ∇φ′g,C = −q ′ U ′ ∇φ′g,C with φ′g,C = φg /c2 + φC /U ′ finally resulting in the conventional formulation of the mass–charge force, namely Fg,C = −m′0 ∇φg − q ′ ∇φC , where the prime here indicates the parameters of the test object that is moving within the sphere of influence of the field object that is defined by the potentials φg and φC , consistently focusing on macroscopic systems, likewise fulfilling the above relations, we here also compare with Figure 17.5. Putting all these elements together, we finally conceive that microscopic/macroscopic mass and charge in combination with gravitational fields and electromagnetic fields occur as physical unity, on the one hand, structurally directly reflecting the possibility of uncharged masses just like the possibility of charged masses, and on the other hand, structurally directly reflecting the impossibility of unmassed charges, eventually meeting what we are observing.

17.1 Questions Striking Basic Issues CMXLIX

How can we conceive that GEFT/WPT manage the unification of microscopic systems and macroscopic systems correctly? The answer is a little bit more complicated, too. Therefore, let me here go a little bit more into detail, too. First of all, following the idea that macroscopic objects are characterized by relatively big energetic differences relativley to the “vacuum” so that a mixing of macroscopic objects and the warping of the “vacuum” described by metric fields does not exist, manifesting itself in the separability of macroscopic objects (“source”) and metric fields (“field”), and that microscopic objects are characterized by relatively small energetic differences relativley to the “vacuum” so that a mixing of microscopic objects and the warping of the “vacuum” described by metric fields does exist, manifesting itself in the inseparability of microscopic objects (“source”) and metric fields (“field”), on the one hand, we realize that the usage of wave–particle energy momentum tensors, which explicitly put the inseparability of microscopic objects (“source”) and metric fields (“field”) (here much better to be circumscribed as “particle properties” and “wave properties”) into concrete terms, within generalized Einstein field equations pave the way from macroscopic systems to microscopic systems, and on the other hand, we realize that the usage of the metric tensor decomposition gµν = ηµν + γµν , which implements Gallilean/Lorentzian spaces based upon Cartesian/Lorentzian reference frames and potential functions of scalar types, vectorial types, and tensorial types, within generalized Einstein field equations paves the way from Einstein’s way of thinking to Schr¨odinger’s way of thinking and more, finally identifying ψ with metric fields γ00 , we here also compare with Figures 17.5 and 17.6. Furthermore, following the above idea, we additionally conceive that the energy–momentum terms that come into being enable a generalized access to quantum systems (here much better to be circumscribed as “wave–particle systems”), and this includes basic “particle” properties such as the spin and advanced “particle” properties such as self-interactions and cross-interactions, we here also compare with Figures 17.7 and 17.8. Putting all these elements together, we finally conceive that microscopic systems and macroscopic systems based upon masses and charges in combination with gravitational fields and electromagnetic fields occur as physical unity, on the one hand, structurally directly reflecting the possibility of mechanical objects, and on the other hand, structurally directly reflecting the possibility of wave–particle objects, eventually meeting what we are observing. Going beyond that, simply try out the energy–momentum terms and you will see that all this works!

17. Asked Questions and Given Answers

R

dV ̺E = R dV ̺g,C− = R dV ρg,C− c2

ρg , ρC− (− |q|)

mass and charge generation

R

“matter”

observable states

R

metric evolution

dV ̺E = R dV ̺m− = R 2 △φg,C− dV K

dV ̺E = R dV ̺g,C+ = R dV c2 ρg,C+

mass and charge generation

R dV ̺E = dV ̺v =0

R

R

ρC+ (+ |q|), ρg

φg φC− , c2 U−

“vacuum”

metric evolution

φC+ φg , U+ c2

law of conservation of energy (balanced energies, negative values for vacuum domain): R R dV ̺g,C∓ = − dV ̺m∓ ⇓ 2 2 ρg,C∓ c = − △φg,C∓ K ⇓ 1 K ρg,C∓ c2 = − △φg,C∓ 4 2 (generalized Poissonian equation) Figure 17.5. Macroscopic systems, mechanical objects.

R dV ̺v = dV ̺E =0

unobservable states

R

dV ̺E = R dV ̺m+ = R 2 △φg,C+ dV K

U± here is the total value related to ρC±

CML

17.1 Questions Striking Basic Issues CMLI

m0 , q = − |q|

R

0 R

+ |q| = q, m0

R

dV ̺E = dV ̺g,C− = R dV ρg,C− c2 φg,C− R R dV ̺E = dV ̺g,C+ = R dV ρg,C+ c2 φg,C+

dV ̺E = R dV ̺m− = R 2 dV K △φg,C−

0

R

dV ̺E = R dV ̺m+ = R 2 dV K △φg,C+

inseparable unities = quantum-mechanical objects (putting the consequence “quantization” into concrete terms) = wave–particle objects (putting the circumstance “concatenation of wave/particle properties” into concrete terms) we here do not consider point-like mass–charge properties, eventually leading to the Schr¨ odinger formalism wave–particle objects are characterized by a relatively small energetic separation of the inherent mass–charge part and the inherent metric part, implying the inseparability of both parts and thus of “sources” and “fields” Figure 17.6. Microscopic systems, wave–particle objects.

CMLII 17. Asked Questions and Given Answers

∂ ∂ γi0 ∂x ψ +(−) 21 γ i0 ∂x

p ⇔ −i∂ψ/∂x, pˆ ∝ −i∂/∂x

in total: “particle” in an additional field

∂ ∂ γi0k ∂x ψ2 +(−) 21 γji0 ∂x

2

p2 ⇔ −i∂ψ2 /∂x, pˆ ∝ −i∂/∂x

1

p1 ⇔ −i∂ψ1 /∂x, pˆ ∝ −i∂/∂x

∂ ∂ +(−) 21 γji0 ∂x γi0k ∂x ψ1

Figure 17.7. Wave–particle energy shares. Field interactions.

17.1 Questions Striking Basic IssuesCMLIII

∂ ∂ ψ ∂x ψ − 12 γ 10 γ 10 ∂x

p ⇔ −i∂ψ/∂x, pˆ ∝ −i∂/∂x

in total: “particle” with self-interaction field

∂ ∂ ψ2 ∂x ψ1 − 12 γj10 γk10 ∂x

∂ ∂ − 12 γj10 γk10 ∂x ψ2 ∂x ψ2

2

p2 ⇔ −i∂ψ2 /∂x, pˆ ∝ −i∂/∂x

1

p1 ⇔ −i∂ψ1 /∂x, pˆ ∝ −i∂/∂x

∂ ∂ ψ1 ∂x ψ1 − 12 γj10 γk10 ∂x

∂ ∂ − 21 γj10 γk10 ∂x ψ1 ∂x ψ2

Figure 17.8. Wave–particle energy shares. Self-(cross-)interactions.

CMLIV17. Asked Questions and Given Answers

Can gravitation be considered as higher-order effect of electromagnetism or vice versa working with GEFT/WPT? The answer is “no”. A closed view at masses m0 and charges q is possible including the tension (voltage) U . For example, this becomes obvious from m0 c2 = qU . For example, this becomes obvious from m0 = m0 + λC q, λC = λC (U ). In particular, these specific circumstances are telling us that the total energy of a charged “particle” “as it is”, m0 c2 and thus mc2 , is covering two possible field states implied by two possible sources ± |q| related to two possible tensions (voltages) ± |U |, in the latter case, defining the energetic distance relative to the vacuum edge as qU . The interrelation masses–charges thus has to do with uniorientable shares of biorientable quantities comprising the tension (voltage) U , but not with higher-order effects. The interrelation gravitation–electromagnetism inherits the properties of the interrelation masses–charges and thus likewise has to do with uniorientable shares of biorientable quantities comprising the tension (voltage) U , but not with higher-order effects. The structure of the potentials, the fields, and the forces related to masses and charges directly reflects this. Let me here especially note that m0 c2 = qU drives the mass-related central potential and the charge-related central potential into a oneness comprising U following 1 1 1 1 φg = −Gm0 = −G 2 U q = −4πǫ0 G 2 U φC , r c r c 11 1 1 1 1 1 q = m0 c2 =− c2 φg . φC = 4πǫ0 r 4πǫ0 Ur 4πǫ0 G U Likewise m0 c2 = qU drives the mass-related central field and the charge-related central field into a oneness comprising U following r 1 r 1 g = −∇φg = −Gm0 3 = −G 2 U q 3 = −4πǫ0 G 2 U E, r c r c 1 r 1 1 r 1 1 E = −∇φC = q = m0 c2 =− c2 g. 4πǫ0 r3 4πǫ0 U r3 4πǫ0 G U Likewise m0 c2 = qU drives the mass-related central force and the charge-related central force into a oneness comprising U following 1 r 1 r ′ ′ F g = m0 g = −m0 ∇φg = −Gm′0 m0 3 = −G 4 U ′ U q ′ q 3 = −4πǫ0 G 4 U ′ U F C , r c r c 1 ′ r 1 1 r 1 1 F C = q ′ E = −q ′ ∇φC = qq 3 = m′0 m0 c4 ′ = − c4 ′ F g . 3 4πǫ0 r 4πǫ0 UUr 4πǫ0 G U U

17.2 Questions Striking Extended Issues: PhysicsCMLV

17.2 Questions Striking Extended Issues: Physics Solitons. GEFT/WPT deals with nonlinear energy operators and nonlinear wavefunctions. Can this be seen in connection to the notion “solitons”? The answer is “yes”. Certainly, the field equations, the wave equations, and the wave–particle equations of GEFT/WPT cover nonlinear effects of the surrounding (“nonlinear materials”) including dispersive effects of the surrounding (“dispersive nonlinear materials”), on the one hand, enabling to describe the redirection of waves (“wave scattering”), and on the other hand, enabling to describe the dissolution of waves (“wave dispersion”), and going beyond that, enabling to describe the balanced conversion of slow frequencies in fast frequencies and fast frequencies in slow frequencies such that a wave packet does not substatially alter its form during propagation (“solitons”). However, further going beyond that, these incorporate nonlinear interactions between the waves themselves, enabling the description of “particles” that decay to form waves, and vice versa, enabling the description of waves that concatenate to form “particles”, on each level of consideration, self-consistently processing matter parameters such as mass and charge decaying in the course of time or emerging in the course of time.

Wormholes. GEFT/WPT deals with space curvatures evoked by masses and charges. Can this be seen in connection to the notion “wormholes”? The answer is “yes”. Certainly, the space curvatures that are evoked by the masses of charged particles, within Galilean boundaries, described by the mass potential φg , are relatively small. However, the space curvatures that are evoked by the charges of charged particles, within Galilean boundaries, described by the Coulomb potential φC , are relatively big. Therefore, we may think about the possibility to create a really high electric potential at an operator point, entrenching oneself into the space time continuum to such an extent that a direct connection to a point far away from the operator point showing a complementary Coulomb potential is opened, eventually shorting-out two points of the space time continuum (“wormhole”). Naturally, since charges and masses form a unity leading to electric fields and gravitational fields that form a unity, we expect that the short-circuit between the two points of the space time continuum (“wormhole”) is stabilized by electric bypass effects and gravitational bypass effects.

CMLVI17. Asked Questions and Given Answers

17.3 Questions Striking Extended Issues: Biophysics Electromagnetic frequencies (emf) and the evolution of cells [67]. Electromagnetic frequencies (emf) influence the evolution of cells. Can GEFT/WPT explain this? The answer could be “electromagnetic imprinting of chemical patterns”.

Theoretical details. Applying spectra of electromagnetic frequencies (emf) to cells, you are speaking of “information fields” supplying the cells with additional information, in this context, following Royal Rife (1888–1971), especially studying microscopic levels of description.

Dear questioner, the notion “information fields” is a precursor of the notion “modes”, eventually substantiated in catastrophe theory and synergetics established by Ren´e Thom [57] and Hermann Haken [28]. As it is widely discussed in catastrophe theory and synergetics, individual elements such as molecules and cells interact with one another directly and/or indirectly embracing the surrounding such that spatio-temporal patterns evolve, for their part acting back on individual elements such as molecules and cells, eventually enforcing more or less complicated structures depending on the classes of linear effects and/or nonlinear effects, in the latter case, facilitating much more advanced structures such as self-similar structures and chaotic structures, so to speak, the whole thing is more than the individual thing. As it is also widely discussed in catastrophe theory and synergetics, “inner modes” structurally setting up such spatio-temporal patterns strongly depend on constraints, usually following control parameters, at critical points, initiating phase transitions. As it is further widely discussed in catastrophe theory and synergetics, “outer modes” applied to such a “self-organizing system” alter the statics and the dynamics of the “self-organizing system”, accompanied by an increase of the information content or a decrease of the information content, in information theory also denoted as increase of “information entropy” and decrease of “information entropy”, usually described by the formulae of Claude Shannon [52, 53] and Edwin Jaynes [36], in both cases, generalizing the term “thermodynamic entropy”, also justifying the term “information fields” in the case of “inner modes” and in the case of “outer modes”. As it is additionally discussed in wave–particle synergetics established in GEFT/WPT, all this not only applies to mesoscopic levels of description and macroscopic levels of description, all this likewise applies to microscopic levels of description, incorporating the notions “wave function”, “spin function”, and “interaction function” comprising gravitational fields and electromagnetic fields including frequencies and wave lengths.

17.3 Questions Striking Extended Issues: Biophysics CMLVII

Experimental details. Applying spectra of electromagnetic frequencies (emf) to cells, your observations show the evolution of conglomerates of cells, on the one hand, accompanied by the increase of the growth rate of dendrites of cells, and on the other hand, accompanied by the decrease of the growth rate of cells, in this context, especially using monocytes THP-1. Dear questioner, the evolution of spatio-temporal patterns of individual cells as well as the evolution of spatio-temporal patterns of composites of individual cells such as slime molds formed of individual amebas is associated with spatio-temporal patterns of chemical substances making up the surrounding, eventually interacting with one another following the principles of synergetics and wave–particle synergetics including nutrient solutions in which cell lines are artifically cultivated. Following the principles of synergetics and wave–particle synergetics, such biosystems can be described on the microscopic level, the mesoscopic level, and the macroscopic level. Following the principles of synergetics and wave–particle synergetics, such biosystems show simple chemical patterns such as homogeneous structures provided these reside near the thermodynamic equilibrium mainly related to linear effects, but elaborate chemical patterns such as wavy structures provided these reside far away from the thermodynamic equilibrium mainly related to nonlinear effects. Following the principles of synergetics and wave–particle synergetics, such biosystems are driven into states far away from the thermodynamic equilibrium related to nonlinear effects injecting excitation energy such as heat energy provided control parameters such as heat amplitudes cross critical values, finally leading from simple chemical patterns into elaborate chemical patterns. Following the principles of synergetics and wave–particle synergetics, a similar effect is directly achieved applying “outer modes” such as electromagnetic modes carrying on “outer patterns” such as harmonic patterns provided “outer patterns” such as electromagnetic modes interact with ions of the chemical surrounding and/or dipoles of the chemical surrounding, finally leading from simple chemical patterns into elaborate chemical patterns, and this is accompanied by an increase of the information content, in information theory also denoted as increase of “information entropy”. Since the latter case is consistent with your observations, the answer could be “electromagnetic imprinting of chemical patterns”. First and foremost, induced by electromagnetic frequencies (emf), chemical patterns structuring nutrient solutions should evolve, leading to maxima of the nutrient matter and minima of the nutrient matter, implying domains where cell reproduction is possible and domains where cell reproduction is not possible, finally leading to conglomerates of cells. Furthermore, within such maxima of nutrient matter, the dendrite evolution in the mean should occur raised. Moreover, within such minima of nutrient matter, the cell reproduction in the mean should occur reduced. Consistently, the “information entropy” should occur raised, too.

CMLVIII 17. Asked Questions and Given Answers

17.4 Questions Striking Special Issues: Heim’s Ideas Heim theory (HT) [33] and extended Heim theory (EHT) [21]. Aiming at a comprehensive access to elementary “particles”, HT/EHT suggest a reformulation of the 4 × 4 = 16 Einstein field equations related to 4 coordinates q µ , culminating in 4 × 4 × 4 = 64 Heim field equations related to 8 coordinates q µ , reducible to 64 − 28 = 36 Heim field equations related to 6 coordinates q µ , eventually supported by a quantized area element (“metron” ∝ ℏ2 ). Are these circumstances compatible with GEFT/WPT? The answer is “yes, accepting certain conditions” or “no, rejecting certain conditions”. Dear questioner, on the one hand, wanting to derive basic field equations of QM/QFT departing from Einstein’s field equations, and on the other hand, wanting to derive basic properties of elementary “particles” departing from Einstein’s field equations, GEFT/WPT simply resort to some advanced interpretations proceeding as follows. Firstly, the mass m0 is considered as charge-corrected mass m0 = m0 +λC q, eventually managing the transition from mass scenarios to mass–charge scenarios, and the wave function ψ is considered as metric field term γ00 implemented by the metric tensor decomposition gµν = ηµν + γµν , eventually managing the transition from curvilinear spaces to rectilinear spaces, and in combination with the charge-corrected mass m0 = m0 + λC q, also managing the transition from curvatures gµν to potentials γµν , and the equalization ψ = γ00 is possible applying “Secondly”, finally interpreting the wave function ψ as microscopic reflection of the mass potential φg related to the charge-corrected mass m0 = m0 + λC q. Secondly, the energy momentum tensor Tµν is chosen in an advanced way, namely as wave–particle energy momentum tensor explicitly putting into concrete terms that microscopic systems are wave–particle systems, in a concatenated manner, showing wave-related properties and particle-related properties, noted by the way, also implying the occurrence of Planck’s constant ℏ. All in all, applying wave–particle energy momentum tensors Tµν recasting the phenotype tensor KTµν − 12 Rgµν into the product-type tensor χµν γµν , this leads to the generalized Einstein field equations in W form Wµν (ηαβ , γαβ ) = χµν γµν , χ00 = Em0 /ℏ2 , γ00 = ψ (α, β, µ, ν = 0, 1, 2, 3 → 4 × 4 = 16 equations), and with the Cˆǫ as defined below and with the ϕǫµν (ηαβ , γαβ ) as defined below, this leads to the generalized Einstein field equations in W form P Wµν (ηαβ , γαβ ) = ǫ Cˆǫ ϕǫµν (ηαβ , γαβ ) = χµν γµν , χ00 = Em0 /ℏ2 , γ00 = ψ (ǫ, α, β, µ, ν = 0, 1, 2, 3 → 4 × 4 = 16 equations), and the product form χµν γµν applies considering relatively small space time frames, implying Cartesian (better: pseudo-Euclidean) coordinates xµ .

17.4 Questions Striking Special Issues: Heim’s IdeasCMLIX

Dear questioner, on the one hand, wanting to derive basic field equations of QM/QFT departing from Einstein’s field equations, and on the other hand, wanting to derive basic properties of elementary “particles” departing from Einstein’s field equations, HT/EHT simply resort to some involved modifications proceeding as follows. Firstly, the Riemann tensor of curvature Rµν here is decomposed in operators Cˆǫ and field functions ϕǫµν (gαβ ), in a first step, preparing the ground for eigenvalue–eigenfunction structures typical for quantum systems. Secondly, the phenotype tensor KTµν − 21 Rgµν here is decomposed in physical values λǫµν and field functions ϕǫµν (gαβ ), in a second step, preparing the ground for eigenvalue–eigenfunction structures typical for quantum systems. Thirdly, implementing the Heim idea of a quantized area element (“metron” ∝ ℏ2 ), the differential formulation must be recast into a difference formulation, also implying the occurrence of Planck’s constant ℏ. All in all, ignoring the Heim idea of a quantized area element (“metron” ∝ ℏ2 ), this leads to the Heim equations P P ˆ ǫ ǫ ǫ λǫµν ϕµν (gαβ ) ǫ Cǫ ϕµν (gαβ ) = (ǫ, µ, ν = 1, 2, 3, 4 → 4 × 4 = 16 equations), and believing in the possibility of independent λǫµν and independent ϕǫµν (gαβ ), eventually defining eigenvalues λǫµν and eigenfunctions ϕǫµν (gαβ ), this leads to the Heim equations Cˆǫ ϕǫµν (gαβ ) = λǫµν ϕǫµν (gαβ ) (ǫ, µ, ν = 1, 2, 3, 4 → 4 × 4 × 4 = 64 equations). Putting all these elements together, we firstly conceive that these circumstances are not compatible with GEFT/WPT, requiring wave–particle energy momentum tensors Tµν recasting the phenotype tensor KTµν − 21 Rgµν into the product-type tensor χµν γµν , and this even does not apply utilizing gµν = ηµν + γµν and q µ = xµ most appropriate to product forms of any kind, and we secondly conceive that these circumstances are compatible with GEFT/WPT, accepting wave–particle energy momentumP tensors Tµν recasting the phenotype tensor KTµν − 21 Rgµν into the Heim-type tensor ǫ λǫµν ϕǫµν (gαβ ), and this only does apply utilizing gµν = ηµν + γµν and q µ = xµ most appropriate to product forms of any kind. But what about the assumption of eigenvalues and eigenfunctions implying 64 (reduced: 36) equations related to 8 (reduced: 6) coordinates? Let me here float the following idea! Minimal sets of equations and related coordinates describe elementary “particles” as unity of mass–charge, gravitons, photons etc., eventually reflecting the world we are living in, telling us that it is a minimal scenario, whereas deviations from minimal sets of equations and related coordinates describe elementary “particles” as diversity of mass–charge, gravitons, photons etc., eventually reflecting a world we are not living in, telling us that it is not a minimal scenario, featuring additional coordinates, recording separation and decoupling of wave–particle features: “condensates” (Heim, Dr¨ oscher).

CMLX 17. Asked Questions and Given Answers

17.5 Critical Comments and Clarifying Answers Critical answers of members of the scientific social network “researchgate.net”. In April 2015, wanting to call attention to the special aspect “particle to antiparticle conversion” of my work, I placed the following question on the scientific social network “researchgate.net”. Is somebody interested in the conversion of electrons into positrons? A relatively broad spectrum of answers was the result. In a nutshell: “This could be possible in 5 decades or 50 decades”, ”The energy should be too high and the time windows should be too small“, “This is already realized applying methods of nuclear physics”, “The law of conservation of charge is not fulfilled”. Here is my reply to these answers. First of all, I apologize for the delay. Dear commentators, please allow me to present my reply in form of an overall discourse. Wanting to call attention to important aspects of my work, in a first step, I posed the question in the main affecting “particle to antiparticle conversion”. In the work just like in the question I focus on the basic example “electron to positron conversion”. However, the theoretical treatment and the technological suggestion that follows as direct consequence of the theoretical treatment also applies to other charged particles such as protons and ions. Dear commentators, you do think that “electron to positron conversion” cannot be realized at the moment? The technological surrounding is known! For example, the DESY and CERN groups know a lot about guiding rings and storage rings. For example, the ITER group knows a lot about fusion vessels. For example, gamma-ray and x-ray devices, which are needed here as excitation devices, are applied in medicine as a matter of course. For example, each museum exhibits ribbon generators and Braun tubes supplying us with electrons. Dear commentators, you do think that energies are too high and time windows are too small aiming at “electron to positron conversion”? The technical realization of positron generation based upon neutron beams focused on target materials leading to electron–positron pairs including the subsequent separation of electrons and positrons do not cause problems regarding energy and time windows. First estimations done by myself do show me that positron generation is also within the realm of possibility focusing on conversion by radiation.

17.5 Critical Comments and Clarifying AnswersCMLXI

Dear commentators, you do think that nuclear technologies are a good choice aiming at antimatter technologies? The technological surrounding is really expensive! The nucear fuel is really expensive! The waste disposal is really expensive! Nobody on this planet wants to live near by radioactive waste! Disposal zones such as Gorleben provoke more than one protest each year! Nuclear technologies may be acceptable within the laboratory frames of the future, but not within the industrial frames of the future. What I am looking for are antimatter technologies that are economically and ecologically acceptable allowing us to begin with the design of “consumer products”. Certainly, I am a little bit “green”. However, knowing that millions and billions of people cannot be supplied with energy and raw ore falling back on green technologies – powerfull energy plants based upon antimatter technologies were a good completion of green technologies and spaceships based upon antimatter technologies would allow the digging of raw ore on far planets –, I am a little bit “black”, too. Consequently, I am developing theoretical models leading into environmentally compatible antimatter technologies. Dear commentators, you do think that the law of conservation of charge is not fulfilled aiming at “electron to positron conversion”? Indeed, this is the central point. We all have learned that electrons and positrons must be destroyed as a pair and must be generated as a pair fulfilling the law of conservation of charge. However, this is not the full truth. The mass does not go to the happy hunting ground during the process of electron/positron destruction, it changes its entity becoming part of the radiation. The mass does not come back from the happy hunting ground during the process of electron/positron generation, the “radiative mass reflection” changes its entity, as mass becoming part of the electron and the positron. The charge is part of the mass so that similar statements apply considering the charge. In particular, the charge may change its entity becoming part of the radiation. In particular, the “radiative charge reflection” may change its entity, as charge becoming part of the electron and the positron. And all models I have developed so far are telling me that also a single positive charge or a single negative charge can be carried away by radiation or can be returned by radiation. Note that “electron to positron conversion”, on the one hand, then implies the loss of negative charges of the fuel material, and on the other hand, then implies the shift of negative charges into the radiation. Note that the energy balance then only can be positive if the negative charges that finally have to be shifted from the radiation into the fuel material are related to lower masses than the electron mass or positron mass, leading to the damage of the fuel material. Much more details are presented in DOI:10.13140/RG.2.1.3522.7684.

CMLXII 17. Asked Questions and Given Answers

Appendix

Bibliography

[A]

VAWsc Softbook Projects

1. Aldinger F., Weberruß V. A. Advanced Ceramics and Future Materials. (Wiley-VCH 2010) 2. Grafarend E. W. Map Projections. (Springer, New York Berlin Heidelberg 2006) 3. Mahler G., Weberruß V. A. Quantum Networks. (Springer, New York Berlin Heidelberg 1998) 4. Mehring M., Weberruß V. A. Object-Oriented Magnetic Resonance. (Academic Press, London 2001) 5. Weberruß V. A. ¨ Quantenphysik im Uberblick. (Oldenbourg, M¨ unchen 1998) 6. Weberruß V. A. Nichtlineare Quantenphysik. (Shaker-Verlag 2008) 7. Weberruß V. A. The Metric Field Gateway to Quantum Physics. (AVM, M¨ unchen 2012) [B]

References: Archived Material

8. Material kindly made available by CeramTec (CeramTec Platz 1–9, 73207 Plochingen, Germany) 9. Material kindly made available by Max-Planck-Institut f¨ ur Astronomie (K¨ onigstuhl 17, D-69117 Heidelberg, Germany) 10. Material kindly made available by Max-Planck-Institut f¨ ur Festk¨ orperforschung Contributors: Andersen O. K., Saha-Dasgupta T., Zurek E., Boeri L. et al. (Heisenbergstr. 1, D-70569 Stuttgart, Germany) 11. Material kindly made available by Universit¨ at Stuttgart, Physikalisches Institut Contributors: Schweizer H., Bergmann R. et al. (Pfaffenwaldring 57, D-70569 Stuttgart, Germany) [C]

References: Standard Data

12. CODATA. Recommended Value for the Electron Radius. (National Institute of Standards and Technology, Gaithersburg, USA 2014)

MIV [D]

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MVI

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67. Burckhardt J. S. Energiearme Elektromagnetische Frequenzen bewirken . . . Effekte bei Zellen . . . (Script by Jean Simon Burckhadt, received April 2015)