1. Building block 1: the Krein space based quanta systems

      a.       Intra-action dynamics   
      b.       Inter-action dynamics  

2. Building block 2: the H(1/2) Hilbert space based dynamic fluid system   

               Potential difference actions between H(1) and H(1,ortho)   


In a nutshell

Intra-action system dynamics refers to purely dynamic quanta systems, where the inter-action happens between the two dynamic quanta partners of those systems. The intra-action dynamics within the perfect plasma system (accompanied by quanta with quanta numbers < 1) is supposed to explain the Landau damping phenomenon. The intra-action system dynamics within the perfect electromagnetic system (accompanied by quanta with quanta numbers > 1) provides an appropriate modelling framework for the Mie pressure.

Inter-action dynamics is caused by potential differences between two quanta systems. The inter-action dynamics between the perfect plasma system and the perfect electromagnetic system may provide an alternative modelling framework for the CMBR and a theory of light.

The inter-action dynamics between H(1) and the 1-component dynamic Dirac 2.0 quanta system enables the definition of a Schrödinger 2.0 operator, which is basically the complexified Riesz transformed gradient operator with the Dirac 2.0 system domain.

The inter-action dynamics between H(1) and H(1,ortho) enables the definition of a dynamic fluid element, which solves the d'Alembert "paradox" in the context of ideal fluids w/o frictional forces, and the 3D-NSE problem.

The inter-action dynamics between H(1) and H(1,ortho) enables the definition of a dynamic fluid element, which solves e.g. the d'Alembert "paradox" in the context of ideal fluids w/o frictional forces, and the 3D-NSE problem. 


Affected physical topics/areas

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.  

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.

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.