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, an accelerated expansion of the universe accompanied by a hypothetical substance called "Dark Energy", 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


The overall conceptual new paradigm

The physical mechanical world is the result of symmetry breakdowns from a meta-physical (perfect plasma & perfect electrodynamics) dynamics world, which is basically governed by the symmetry break from the complex Lorentz group down to the real (restricted) Lorentz group.

The several physical decay processes may be explained by potential equalization (entropy) processes from mechanical energy systems to purely dynamic energy systems.


Two math. building blocks enabling a conceptual paradigm change

The below building blocks 1 & 2 are supposed to enable a conceptual paradigm change. Each of two proposed building blocks is governed by the conservation law of total (mechanical and dynamic) energy. The mathematical framework for building block 1 is the Krein space. The mathematical framework for building block 2 is the Hilbert space.

A physical system just governed by the conservation law of energy is insufficient to formulate any physical law. The concept of potential differences provide a model for the causes of physical actions.

Within each of the quanta systems of building block 1 there are always dynamical energy governed quanta affected. Accordingly, there is an intrinsic potential difference within each of those systems and there are also potential differences between the several hierarchical ordered dynamic quanta systems.

The physical actions within building block 2 are governed by explicate or implicate potential differences between or within the different quanta system layers.

The claim is that the related new physical 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 phenomenon, and Ehrenhaft’s photophoresis phenomenon. It also indicates a new role of „Nature“ constants as observable results of physical actions or calculated values from those as a kind of approximation constants for inter-quanta potential differences; e.g., the Planck action constant or the permittivity and the permeability constants of the mechanical 1-component Maxwell equations system (accompanied by the concepts of space, time, velocity, and mechanical mass) from which the speed of light constant in a mechanical Maxwell "vacuum" system can be calculated.


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“.

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.

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.

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).    

The building block 2 provides a purely Hilbert space based approximation framework to the Krein space based quanta field scheme accompanied by to concept of a dynamic fluid particle. It enables a well-posed non-linear, non-stationary 3D-NSE system where the standard variational mechanical energy Hilbert space H(1) is extended to the energy Hilbert space H(1/2) = H(1) x H(1,ortho). It turned out that the non-linear energy term of the 3D-NSE system is bounded with respect to the  H(1/2) energy norm as a simple consequence of the Sobolevskii inequality (BrK11), (GiY) lemma 3.2. At the same time, the dynamic fluid H(1/2) energy concept is in line with a well-defined Plemelj’s double layer potential function. The related Prandtl operator accompanied by a Hilbert scale domain H(r) (where  ½ smaller or equal than r smaller than 1) provides a unique solution of the underlying Neumann boundary value problem for the pressure p(x,t), (BrK7), (BrK11), (LiI) p. 95 ff., (PlJ).   

The Prandtl operator enables a concept of a H(1/2) energy system intrinsic potential difference. It „solves“ the source of the d’Alembert “paradox”. This is about the failure of the Euler equation as a model for fluid-solid interaction, as in incompressible fluids there are no frictional forces. In other words, the Prandtl operator enables a dynamic fluid accompanied by frictional forces, which is applicable as mathematical tool for exterior space problems in physics.

Note: Exterior space problems in physics primarily revolve around the limitations and inconsistencies between general relativity and quantum mechanics, particularly when dealing with extreme conditions and the nature of space-time itself. Key areas include the nature of dark matter  and dark energy, the unification of gravity with other forces, and the behavior of space-time at the Big Bang and black holes. Additionally, the concept of quantum gravity  and the potential for emergent space-time  are active areas of research, Wikipedia     


"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 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.

... the purely dynamic energy governed quanta fields are interpreted in the sense of H. Weyl as the whole, which has to be presupposed in order to give meaning to the mechanical particulars?

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.