In the context of the term "paradigm change" we refer to (KuT), (UnA6). The three paradigms of physics to be changed are

Paradigms 1:
The Newton and the Coulomb potentials to deal with continuously distributed mass elements exposed to external (attractive or repulsive) forces; the Debye potentials and the London dispersion interaction potentials


Paradigm 2: 
Dirac‘s energetical one-component system to model an atom and its radiation field avoiding e.g., two distinct interacting systems to explain the phenomena of emission and absorption of light by matter, the related spin(1/2) hypothesis and the fundamental problem in statistical thermodynamics: the distribution of a given amount of energy E over N identical systems


Paradigms 3: 
The Big Bang story, the law of a „constant velocity of light c" leading to the GRT (made up of fields on fields), a gaseous state of the sun, and Newton's theory of "light rays" accompanied by the three forms of redshift in astronomy and cosmology, i.e., a theory of light is not required in current cosmological models


Preliminary remarks


(1) The Planck action constant is independent from any weak or strong gravitation field. It therefore somehow mirrors the fundamental difference of physical macro and micro world, (DeH).

(2) Current matter and force particles of the universe
„All known particles in the universe can be divided into two groups: particles of spin ½, which make up the matter in the universe, and particles of spin 0, 1, and 2, which give rise to forces between matter particles. The matter particles obey what is called Pauli’s exclusion principle“, (HaS1) pp. 69/70. 

„The neutron is observed to change spontaneously into a proton, an electron, and a neutrino. This process is so rare that we can often ignore it. Neutron decay takes on the average some thousand seconds for a free neutron, whereas within a nucleus the characteristic time between nucleon-nucleon collisions is only 10 exp(-21) second“, (BeH) p. 29.       

„The word „neutrino“ has been used to represent any assumed product of decay which has half-integer spin, no charge, and neglegible mass. Whether these particles are all identical with neutrinos of  beta-decay is so far conjecture“, (BeH) p. 32.

„Charge neutrality is one of the fundamental property of plasma, the fourth state of matter: it is about the shielding of the electric (Coulomb) potential applied to the plasma. When a probe is inserted into a plasma and positive (negative) potential is applied, the probe attracts (repulses) electrons and the plasma tends to shield the electric disturbance“, (MiK).

The conceptual element in superconducting metal models is an electron-phonon interaction governed by strongly electrostatic Coulomb repulsions accompanied by an electron-phonon coupling parameter. The related Bardeen-Cooper-Schrieffer (BCS) theory is governed by a Coulomb pseudopotential, (AnJ).

(3) Dirac‘s single atom-radiation system     

Dirac’s single atom-radiation system deals with energy, which is the sum of three terms: one representing the energy of the atom, a second representating the electromagnetic energy of the radiation field, and a small term representing the coupling energy of the atom and the radiation field“, (FeE).          

(4) Ether, perfect plasma and perfect electrodynamic fields

Einstein considered Maxwell’s equations in combination with the requirement that light moves with a certain velocity as laws of physics. 

Lorentz envisioned „various kinds of ether pressures, objects would be squeezed and therefore shortened", (SuL) pp. 60-62. 

Ehrenhaft interpreted his discovery called photophoresis, as „light induces electric and magnetic charges (poles) upon the particles if they are illuminated by concentrated light preponderantly shorter wave lengths“, (EhF) p. 242. 

The existence of quantum fluctuations dynamics in a „world“ without a time arrow and without entropy has been verified by the Casimir and the Lamb shift effects.  
        
(5) SMEP and gauge invariance

In SMEP (Standard Model of Elementary Particles) symmetry plays a key role. Conceptually, the SMEP starts with a set of fermions (e.g. the electron in quantum electrodynamics). If a theory is invariant under transformations by a symmetry group one obtains a conservation law and quantum numbers. Gauge symmetries are local symmetries that act differently at each space-time point. They automatically determine the interaction between particles by introducing bosons that mediate the interaction. The U(1) symmetry, i.e. the complex unit circle numbers, (where probability of the wave function is conserved) describes the electromagnetic interaction with one boson (photon) and one quantum number (charge Q). The group SU(2) of complex, unitary (2x2) matrices with determinant 1 describes the weak force interaction with 3 bosons W(+), W(-), Z, while the group SU(3) of complex, unitary  matrices describes the strong force interaction with 8 gluon bosons. This means that each of the observed Nature „force“ phenomena are related to a specific gauge group. The SMEP does not provide any explanation where the related elementary „particles“ were built during the inflation phase of the current big bang story and why their mass have their specific values.

For gauge symmetries the fundamental equations are symmetric, but e.g., the ground state wave function breaks the symmetry. When a gauge symmetry is broken the gauge bosons are able to acquire an effective mass, even though gauge symmetry does not allow a boson mass in the fundamental equations. 

(6) The Higgs effect (or mechanism)

The Higgs effect (or mechanism) builds on an extended from global to local U(1)  transformations symmetry group of the underlying Lagrangian. It explains the mass of the gauge W- and Z- (weak interaction) bosons of the weak “nuclear-force”. The Higgs boson is supposed to be a heavy elementary particle (with non-zero rest mass of about 125 GeV with spin 0). The Higgs field is supposed to fill the whole universe interacting with each particle, which “moves” through it by a kind of frictional resistance, i.e. which has kinetic energy. Therefore, the Higgs effect requires a Higgs field with not vanishing amplitudes in the ground state.

„The Higgs mechanism helps in two ways. First, gauge fields can acquire mass by the symmetry breaking. Second, the undesirable Goldstone bosons (which arise in the symmetry-breaking process) can be usually gauged away”, (BlD) 10.3. This degeneracy of the physical vacuum (as a result of a “spontaneous” breakdown of symmetry) permits … nonzero vacuum expectation values (or “vacuons”), (HiP).

(7) The London dispersion forces

(Wikipedia): The term "van der Waals force" is used to describe any dipole-dipole interactions in atom/molecules. Since hydrogen bonds involve interactions between permanent dipoles, they can be considered as a type of van der Waals force (and would fall under the category of Keesom interactions). The strength of van der Waals forces varies, with dipole-dipole interactions typically being stronger than covalent or ionic bonds. "London dispersion forces" are a specific type of intermolecular force present in nonpolar molecules. They are the weakest of all molecular forces. Molecules like noble gases (e.g., He, Ar), diatomic molecules (e.g., H2), and nonpolar organic molecules experience these forces.

(8) A sun basically consisting of liquid metallic hydrogen

A gaseous structure of the sun do not allow "white light" blackbody rays passing from its interior through the observed surface of the sun to Earth. At the same time there is no direct observation of the presence of classical concepts pressure & density in the atmosphere of the sun, which may explain a phase change from gaseous hydrogen to liquid metallic hydrogen governed by London dispersion forces ((Una4) p. 73. 

The fusion process from hydrogen to helium is the energy production process of the sun. The hydrogen molecules shows only two electrons, however there is an enormous bounding energy of the electron in a hydrogen molecule, (RoP), (UnA4) p. 64.

There is no direct observations neither of the pressure nor of the density in the entire atmosphere of the sun, (UnA4) p. 59.

Ironically, astronomers admit that liquid metallic hydrogen occurs in planets like Jupiter or Saturn, (UnA4) p. 61, Wikipedia

The minimum volume of a substance on atomic level is determined by the nature of the electrons not so much by the (far larger) nucleus. ... Metals appear incompressible, but exposed to an exterior pressure they can reduce their volume. ... According to de Broglie's wave length formula for a electron such a volume reduction would lead to a reduction of the wave lengths of all electrons (i.e. basically the inverse of the mechanical momentum of those electrons) in the metal, (UnA4) pp. 63/66.

There is an interesting phenomenon when water is subjected to massive pressure: water close by a nuclear explosion gets black and opaque, (UnA4) pp. 71/72.

(9) Oceans generating microwave background

"Though liquid water has a fleeting structure, it displays an astonishingly stable network of hydrogen bonds. Thus, even as a liquid, water possesses a local lattice with short range order. The presence of hydroxyl and hydrogen bonds within water, indicate that it can simultaneously maintain two separate energy systems. These can be viewed as two very different temperatures. The analysis presented uses results from vibrational spectroscopy, extracting the force constant for the hydrogen bonded dimer. By idealizing this species as a simple diatomic structure, it is shown that hydrogen bonds within water should be able to produce thermal spectra in the far infrared and microwave regions of the electromagnetic spectrum. This simple analysis reveals that the oceans have a physical mechanism at their disposal, which is capable of generating the microwave background", (RoP2)

(10) The extraordinarily special Big Bang story      

„In order to produce an universe resembling the one in which we live, the Creator would have to aim for an absurdly tiny volume of the phase space of possible universes – about 10exp(10)exp(123) – of the entire volume, for the situation under consideration“, (PeR) p. 444.    

 „The chaotic inflation state of the early universe does not match to the second law of thermodynamics as this law requires a permanent increase of the entropy of the universe over time, while the cosmos started with an incredible low probability, but also with an incredible high ordered state“, (PeR1) pp. 122 ff.    

 „It (the expanding universe) starts with high-entropy singularity which, it seems, could have been an initial state for our actual universe, and, indeed, would be a far more probable initial state (i.e. of much larger entropy) than the Big Bang that actually occurred. The black holes that congeal together in the final stage of our envisaged collapse would, when time-reversed to an expanding universe, provide us with the image of an initial singularity consisting of multiply bifurcating white holes! A white hole is the time-reverse of a black hole, and I have indicated the sort of situation that this provides us with in Fig. 2,45. It is the total absence of such white-hole singularities that singles out our Big Bang as being so extraordinarily special“, (PeR1) p. 125.


A quick outlook

The below building blocks 1 & 2 are supposed to enable the above paradigms changes. The main conceptual change coming along with building block 1 is that the mechanical potential energy based Newton/Coulomb potential concept is replaced by a dynamic potential energy based indefinite norm based potential concept enabled by a system intrinsic potential energy operator.

The 2-component dynamic systems are governed by the complex Lorentz group SU(2)xSU(2) accompanied by the concept of Mie-pressures (i.e., system intrinsic potential differences) of dynamic quanta pairs.

The 1-component atomic dynamics system is governed by the restricted Lorentz group SU(2) (isomorphic to the unit quaternions) accompanied by the concept of a Maxwell-Mie-pressure enabling links to the SRT-Minkowski space and to "Einstein's lost key", (UnA1). In other words, the creation of the 1-component atomic system from the perfect 2-component electromagnetic system is accompanied by a symmetry breakdown from the complex Lorentz group (the main tool to prove the CPT theorem, StR)) down to the real restricted Lorentz group.


"What-if" ...

... the CMBR phenomenon and the physical mechanism of oceans generating microwave background can be interpreted as an (interaction) echo caused by system intrinsic potential differences of dynamic 2-component systems like the ground state, the perfect plasma, the perfect electromagnetic, and the hydroxyl-hydrogen systems?

... the Landau damping phenomenon (wave damping without energy dissipation by elementary particle collisions) currently explained by conceptually different (linear (Coulomb potential based force) vs. nonlinear (Landau collision operator based force)) models becomes a characteristic of perfect plasma and perfect electromagnetics in line with Ehrenhaft's phenomenon called photophoresis?

… the new concept of a "potential" (e.g. replacing the anyway ignored coupling energy between the atom and the radiation field of the Dirac theory, (FeE), and the concept of an electron-phonon interaction governed by strongly electrostatic Coulomb repulsion accompanied by an electron-phonon coupling parameter) leads to a complete different „construction“ of a „Higgs mechanism“, (AnJ)?

 ... the perfect (electron-positron) plasma and the perfect (electroton-magneton) electromagnetics quanta fields generate stars composed of mechanical 1-component atomic nucleii? ... Then, mechanical matter may be interpreted as condensed dynamic energy and the related process is governed by a symmetry breakdown from complex Lorentz group down to real restricted Lorentz group.

... the perfect (electron-positron) plasma and the perfect (electroton-magneton) electromagnetics quanta fields accompanied by the concept of explicate and implicate potential differences governed by purely dynamic energy providing an appropriate modelling framework explains a liquid metallic hydrogen sun, (RoP), (UnA4)? In this case the concept of London dispersion forces is replaced by the concept of a dynamic potential difference "force" ... Then the current physical law for an ideal gas in thermodynamics in the form P*V = k*N*T (k denotes the Boltzmann constant) becomes obsolet, and, as the pressure P becomes an explicate potential difference between two dynamic quanta systems and as the concept of kinetic energy is not required the volume V and the temperature T become obsolet, as well.

... the perfect (electron-positron) plasma resp. the perfect (electroton-magneton) electromagnetics quanta fields are interpreted as as a kind of „darkness“ resp. „brightness" fields as a foundation for a theory of light? ... Then for instance, the solar wind might be interpreted as a cold plasma quanta flow with supersonic quanta speed in a space-time continuum governed by the restricted Lorentz group.


Two new building blocks for a paradigm change

Each of the two proposed building blocks is governed by the conservation law of total (mechanical and dynamic) energy. The physical actions are governed by appropriately defined potential differences within those building blocks.

Preliminary remarks

(1) The conservation principles of energy, linear momentum, angular momentum, and electric charge are amoung the most fundamental principles of physics. … The notion „conservation“ as in „conservation of energy“ is not the same as „invariant“. They are related, …, but they are not synonymous. The momentum or energy of a system of particles may be conserved but not necessarily invariant, (NeD) pp. 1, 4. A second fundamental principle in physics is the least action principle; here physical action requires a potential difference or a pressure. There is no action just due to the presence of energy or a potential.

(2) The invariant quantities in energy conservation laws are governed by functionals. The simplest model of functionals is a constant. In a Hilbert space framework such a functional is provided by its norm. 

(3) The probably most fundamental mathematical theorem in physics is E. Noether‘s theorem. It effects a huge class of conservation laws governing symmetries of space, time, and „internal“ variables. Noether’s theorem relates conservation to invariance, and thus to symmetry. This theorem provides the mathematical foundation of the whole quantum mechanics. However, the conservation of electric charge emerges from a more abstract symmetry called „gauge invariance“.

(4) An indefinite metric in a Hilbert space is one of the unconventional features of Heisenberg's "Introduction to the Unified Field Theory of Elementary Particles", (HeW). 
 

Building block 1 
... is an integrated hierarchical ordered Krein space based scheme of energetical quanta systems accompanied by

- a new dynamic energy type
- Krein space intrinsic concepts of potential and potential differences
- a Krein space intrinsic self-adjoint potential operator
- dynamic energy fields complementary to mechanical (kin./pot.) energy fields
- Krein-space based dynamic fields with related dynamic quanta systems
- 2-component (quanta pair) and 1-component (quanta) systems 
- a priori „ground state“ & „perfect plasma“ quanta pair systems
- quanta pair systems governed by the complex Lorentz group SU(2) x SU(2) 
- quanta system governed by the restricted Lorentz group SU(2)
- implicate intra-quanta system dynamics 
- explicate inter-quanta systems dynamics
- dynamic energy generated by intra-quanta potential differences 
- mechanical actions triggered by inter-quanta potential differences 
- a cohesive „Mie pressure“ of a generalized electromagnetic „ether physics“.


Building block 2 
... is the energetical H(1/2) Hilbert space approximation system of the system scheme of building block 1 accompanied by dynamic fluid particles and

- a new "mass element" as distributional function of the H(-1/2) Hilbert space
- a well-posed NSE system aligned with Plemelj's enhanced Newton potential
- a properly defined Prandtl operator (incl. domain) for the Neumann problem
- a resolved d'Alembert "paradox", in fact the failure of the Euler equation (the    model of an ideal incompressible fluid) as a model for fluid-solid interaction
- a nonlinear dynamic potential operator interpreted as compact disturbance of     the mechanical Laplacian potential operator, (BrK0) p. 11
- mechanics / dynamics governed by Fourier waves / Calderon wavelets
- an alignment with the global nonlinear stability of the Minkowski space
- ...
- ... (BrK10). 


 New physical realities

The claim is that the new paradigms allow consistent new or alternative explanations of essential phenomena and hypotheses like the CMBR, the Landau damping, the size of Bohr’s magneton, the spin hypothesis, the beta-decay, and Ehrenhaft’s photophoresis. It also indicates a new role of „Nature“ constants as observable results of physical actions or calculated values from those (e.g. the Planck action constant) triggered by inter-quanta potential differences, (UnA2).

Related selected notes

Intra-action dynamics within the Krein space based quanta systems   

Note (cohesive Mie-pressure): The Maxwell fields can carry energy from one place to another. It describes the electricity dynamics of an a priori existing charged elementary particle (electron) in an idealized semiconductor world governed by an electric and a magnetic field induced by the sum of a line current (in an electrical conductor world) and a so-called displacement current (a cross-section line reduced 1st order approximation of an electrical insulator world accompanied by the notions of „time“ and „distance“). Mathematically speaking, the energy tensor of the electromagnetic fields is only known outside of such an electron (particle) enegetical system.

Note: In the notations of the proposed UFT the above "electron" is called a "electroton".

Note (The self-energy problem of an electroton, (UnA6) p. 100): The electroton quanta system solves the "self-energy problem" of Dirac's electron system providing an explanation of the beta decay process.

Note: The "perfect plasma" quanta pair system "explains" the decay of a neutron into an electron and a proton.  


Inter-action dynamics between the Krein space based quanta systems  

Note: The symmetry break down from the complex Lorentz group to the (real) restricted Lorentz group becomes a characteristic of the inter-action dynamics between purely dynamic 2-component quanta systems and 1-component mechanical quanta systems accompanied by the concept of mechanical energy and the Minkowski space-time continuum. SU(2) is isometric to the unit quaternions S(3). This puts the spot on the Courant conjecture, which would show that the four-dimensional Minkowski physical Minkowski space-time world of classical physics enjoys an essential distinction, (CoR) p. 763. 

Note: The three Dirac 2.0 systems are accompanied by a „symmetry break down“ from SU(2) x SU(2) to SU(2), the symmetry group of the Klein-Gordon equations. 

Note The group SU(2) is isometric to the unit quaternions S(3). The quaternions provide an appropriate field to address the „translation-rotation“ (linear and angular rotation) „permutation“ requirement. The perhaps primary application of quaternions is the quaternion rotation operator. This is a special quaternion triple-product (unit quaternions and rotating imaginary vector) competing with the conventional (Euler) matrix rotation operator, (KuJ). Its outstanding advantages compared to the Euler geometry are

- the axes of rotation and angles of rotation are independent from the                underlying coordinate system and directly readable
- there is no need to take care about the sequencing of the rotary axes.

Note: The math. proof of the CPT invariance phenomenon, the only fundamental law of nature requiring a „time arrow“, is enabled by the complex Lorentz transform (StR). In other words, as long as there are no decay processes of atomic nuclei in scope the laws of Nature allow a "reverse of time".

Note: The transitions from the 2-component quanta systems to the 1-component Dirac 2.0 quanta systems avoid Dirac's spin hypothesis.   

Note: The inter-action dynamics between the "perfect plasma" system and the mechanical 2-component „electromagnetic“ system (both governed by the complex Lorentz group) supports Robitaille's "Liquid Metallic Hydrogen Model of the Sun and the Solar Atmoshere", (RoP), (UnA4).

Note:  
(1) The CMBR (currently interpreted as the "echo of the early universe", (LaM)) is an essential element of theoretical and observational cosmology and one of the foundation stones of the big bang models; to the author's humble opinion, those models are extremely unrealistic because they are based on an a priori required mathematical singularity which caused for whatever reason the biggest explosion ever, (PeR) p. 444

(2) There are currently two different (!) underlying physical "force" types for the Landau damping phenomenon depending from the considered mathematical linear (Coulomb potential based "hot plasma") or nonlinear (Landau collision operator based "cold plasma") model, (BrK14) p. 18.

(3) The cosmic microwave background radiation (CMBR) and the Landau damping phenomena may be interpreted as characteristic (echo) phenomena of the EMT electroton-magneton quanta creation process from the GSM and PPM, see also (BrK14) p. 26.

Note: The mechanical 2-component „electromagnetic“ system and the non-mechanical 2-component "perfect plasma" system enable consistent explanations of the Landau damping phenomenon and the related CMBR, (LaM), and Ehrenhaft's photophoresis phenomena, (EhF). It may also enable a missing theory of light anticipating „Einstein’s lost key“, (UnA1), Dirac's large number hypothesis, (UnA1) p. 150, (UnA2) p. 85, and Dicke’s related "theory of a variable speed of light", (UnA1) p. 129, accompanied by a mechanical global nonlinear stability of the Minkowski space, (ChD).

Note (Nature constants): The UFT indicates a new role of Nature constants. They may provide physical characterizations of the borderlines within the hierarchical quanta system structure of the above five dynamic quanta systems. The obvious characteristic borderline constant between ANT and PDT is Planck's quantum of action. In this context we refer to Robitaille’s „blackbody radiation and the loss of universality: implications for Planck’s formulation and Boltzman’s constant“, (RoP3). The observed duration for the beta-decay (about 15 min) might become another Nature constant with respect to the borderline between EMT and ANT. The magnetic moment interpretation of an electroton might become another characteristic constant. Basically Unzicker's approach investigating constants of nature and questioning their origin is reversed, (UnA2) p. 3. In other words, Planck's quantum of action become the most rough "approximation" constant within the deductive structure as its formula contains the generic term "temperature" for "energy". It also contains the speed of light, which can be calculated from the two electromagnetic Nature constants, the vacuum permittivity and the vacuum permeability resp. the Bohr magneton, i.e. the size of atomic magnetic moments, (BlS) p. 4.


Inter-action dynamics between the Hilbert space based dynamic and classical fluid dynamic systems   

Note: "Plasma „matter“ is basically characterized by the following two requirements:

-   there is an interaction between two oppositely charged particle types 
-   the numbers of those two particle types may be arbitrarily small or large,
    but they need to be almost the same", (CaF) p. 1.

„The Landau damping phenomenon is a characteristic of collisionless plasmas, but it may also have applications in other fields. For instance, in the kinetic treatment of galaxy formation, stars can be considered as atoms of a plasma interacting via gravitational rather than electromagnetic forces. Instabilities of the gas of stars can cause spiral arms to form, but this process is limited by Landau damping“, (ChF) p. 245, see also (ChF) p. 402.

"Most of the visible matter in the universe exists as plasma, whereas lightning and the aurora are the only natural manifestations of the plasma state on Earth", (DeR) p. 1.

"The sun, like most stars, is composed of plasma; in its core, the kinetic energy of the atomic nuclei, dissociated from the electrons, is so great that they can overcome their mutual electrical repulsion and fuse together, releasing energy", (DeR) p. 1.

"The solar wind consists of a diffuse plasma that streams outwards from the sun and fills interplanetary space. Its density and velocity near the Earth fluctuate in time; ... The Earth's magnetic field is sufficiently strong to deflect the solar wind", (DeR) p. 82, see also (ShF) p. 372 ff.

"The kinetic description of galaxies has many similarities with that of plasmas. Because collisions between stars in galaxies are very rare, the evolution of the distribution of stars in phase space can be described by a continuity equation which has the form (5.5). Each star interacts with the rest of the galaxy through the local gravitational potential", (DeR) p. 122.

The dynamic 2-component "perfect plasma" system is in line with the baseline requirement for plasma matter associated with an "empty space potential/pressure" providing an appropriate explanation of the Landau damping phenomenon.

Note: Sommerfeld’s fine structure constant is „just“ mathematically required to ensure convergent power series representations of the solutions of Dirac equation.

Note: In (RoP2) it is shown that hydrogen bonds within water should be able to produce thermal spectra in the far infrared and microwave regions of the electromagnetic spectrum. This simple analysis reveals that the oceans have a physical mechanism at their disposal, which is capable of generating the microwave background.

Note: The pressure p in the NSE (which may be interpreted as a "potential") can be expressed in terms of the velocity u by the formula p = R(u x u), where R denotes the Riesz operator and u x u denotes a 3x3 matrix.

Note: The  H(1/2) Hilbert space plays also a key role in the Teichmüller theory and the universal period mapping via quantum calculus accompanied by  a canonical complex structure for H(1/2), (NaS). Also, the degree or a winding number of maps of the unit circle into itself corresponds to a related H(1/2) -norm enabling the statement „one cannot her the winding number“, (BoJ).

Note (The Mie theory of matter): The UFT framework supports Mie’s theory of matter, (MiG0,(MiG1),(MiG2), and his project „to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen Lagrangian, governing the state of the aether and its dynamical evolution, and conceiving of elementary particles as stable “knots” in the aether rather than independent entities“, (SmC). Mie’s nonlinear field equations allow for stable particle-like solutions using variational principles in the context of special relativity, (SmC). This is in line with Klainerman’s proof of a global nonlinear stability of the Minkowski space, (ChD). Technically speaking, the eigenpairs of the standard self-adjoint (mechanical!) Laplace operator with H(1)-domain become the model of Mie's (mechanical!) energy knots. The "complementary"  (dynamic) operator with the complementary domain in H(1/2) with respect to the H(1)-norm becomes the model of the "implicate" dynamic energy field, which is governed by the Schrödinger 2.0 operator. Technically speaking the Schrödinger 2.0 operator is "just" the Riesz transformed Schrödinger operator. For the appreciated properties of the Riesz transforms we refer to (BrK14) p. 33.

Note (The Mie theory): „The aim of the trilogy on matter theory in (MiG), (MiG1), (MiG2) was to develop a unified theory able to account for the existence and properties of electrons (as well as atoms or molecules), explain recent observations of atomic spectra, and yield field equations for gravitation“, (SmC).

Note (The Mie theory and a global nonlinear stability of the Minkowski space): „Mie aimed to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen Lagrangian. Mie’s main innovation was to consider nonlinear field equations to allow for stable particle-like solutions (now called solitons), and he clarified the use of variational principles in the context of special relativity“, (SmC). This is in line with Klainerman’s proof of a „global nonlinear stability of the Minkowski space, (ChD).

Note (The Mie theory): „Part of Mie’s project was to develop a relativistic theory of gravitation as a consequence of his generalized electromagnetic theory, and our second goal is to briefly assess this work, which reflects the conceptual resources available for developing a new account of gravitation by analogy with electro-magnetism. …. Mie characterized electromagnetic theory as “aether physics.” Mie emphasized the appeal of reducing physics to a simple set of equations governing the state of the aether and its dynamical evolution, and conceiving of elementary particles as stable “knots” in the aether rather than independent entities“, (SmC).   

Note (The Mie theory): „Die Grundannahme meiner Theorie ist, daß auch im Innern der Elektronen elektrische und magnetische Felder auftreten. Die Elektronen und demnach überhaupt die kleinsten Teilchen der Materie sind nach dieser Auffassung also mit dem Weltäther nicht wesensverschieden, sie sind nicht, wie man sich das vielleicht vor zwanzig Jahren dachte, Fremdkörper im Äther, sondern sie sind nur Stellen, wo der Äther einen ganz besonderen Zustand angenommen hat, den wir durch das Wort elektrischte Ladung bezeichnen.  ….    Man wird vielleicht denken, daß man mit der eben formulierten Grundannahme wenig anfangen könne. Sie führt aber immerhin zu einer allgemeinen Form für die Grundgleichungen der Ätherphysik, wenn man noch zwei weitere Annahmen hinzunimmt. Die erste ist, daß das Relativitätsprinzip allgemeine Gültigkeit haben soll, die zweite, daß die bisher bekannten Zustände des Äthers, nämlich elektrisches Feld, magnetisches Feld, elektrische Ladung, Ladungsstrom, vollständig ausreichen, um alle Erscheinungen in der materiellen Welt zu beschreiben“, (MiG).

Note: The Yang-Mills (gauge) theories is a generalization of the Maxwell equations phrased in the language of a U(1) gauge theory.

Note (Einstein's lost key, (UnA1)): All known tests of the GRT can be explained with the concept of a variable speed of light, (DeH), (UnA1) p. 142. Additionally, there is a „nonlinear stability of the Minkowski space“, (ChD). Approximation theory of a nonlinear operator equation in Hilbert scales is enabled by an appropriate decomposition of the nonlinear operator N=L+R into a lineralized operator L and a remaining nonlinear operator R. In this context "nonlinear energy stability" is ensured if the nonlinear variational equation representation fulfills the Garding inequality with respect to the underlying „energy norm“ induced by the linearized term L. In this case the remaining nonlinear operator R may be interpreted as a compact disturbance of the linear operator, (BrK0) pp. 11, 26, (BrK13).

Note (Mechanical mass-energy equivalence): Einstein's famous formula  E = m*c*c  may be interpreted as approximation formula, where the energy terms on both sides of the equation are interpreted as norms of the underlying weak variational representation in an appropriately defined Hilbert-Krein space framework. In other words, the Hilbert-Krein space framework (accompanied by the concept of indefinite norms) avoids the problem of infinite negative eigenvalues. This problem occurs in Dirac's relativistic invariant wave equation for an one-electron system, which allows electrons to traverse very high potential thresholds with a certain probability, e.g. (HeW1) S. 76.

Note: There are only two superfluids which can be studied in laboratory. These are the two isotopes of helium. Unlike all other substances they are unique because they remain in the liquid state even down to absolute zero in temperature, (AnJ) p. 21.