In a nutshell: scope & conceptual design elements

The scope of the Unified Field Theory (UFT) includes the scope of the three (independent, just "linked because they seem to have similar characteristics", (GlJ) p. 433) quantum field theories (strong interactions, weak interactions, and electromagnetics) and the scope of the relativity theory. 

The Hilbert space theory provides the mathematical framework of quantum mechanics. The extended Krein space theory (accompanied by the concepts of an indefinite norm and an intrinsic self adjoint potential operator) provides the mathematical framework of the proposed UFT. While quantum mechanics is governed by the physical concept of mechanical energy, the proposed quanta dynamics is governed by mechanical and (newly) dynamic energy. There are several dynamic quanta systems, which are governed by an appropriately defined deductive quanta numbers scheme. The  underlying quanta numbers are appropriately defined to reflect a kind of "potential difference" between affected underlying implicate (in the sense of D. Bohm, (BoD1)) (particle,anti-particle) quanta pairs.

The real Lorentz group L has three subgroups (orthochronous, proper, orthochorous). Associated with the restricted Lorentz group is the group of 2x2 complex matrices of determinant one, which is denoted by SL(2,C).  It is isomophic to the symmetry group SU(2) and the unit quaternions S(3). It plays a key role in the special relativity theory (accompanied by the concept of the Minkowski space) and is a characteristic of the beta-decay process.

The  complex Lorentz group L(C) is associated with SU(2)xSU(2). It is essential in the proof of the PCT theorem, (StR) p. 13. It is also the (hidden) symmetry group of the Coulomb problem, (BrK0) p. 58 ff., (BrK14) pp. 14, 28. In contrast to the real Lorentz group the complex Lorentz group has just two connected (!) components accompanied by a multiplication law for pairs of 2x2 matrices, (StR) p. 14. It is supposed to govern the conservation of energy laws of the dynamic quanta systems, (BrK0) p. 31.

There are two a priori 2-component mathematical dynamic quanta systems: the a priori dynamic electrino-positrino based ground state quanta system and the electron-positron based perfect plasma quanta system, see also (BrK14) p. 26. The most aggregated Krein space based energetical systems built from those a priori systems are three types of explicate 1-component mechanical atomic nucleus quanta systems accompanied by implicate 1-component dynamic quanta systems (ref. Bohm's "wholeness and implicate & explicate orders", (BoD1)). They may be interpreted as conductor, semi-conductor, and non-conductor atomic nucleus types.

The UFT provides a

- 2-component a priori dynamic "Ground State" Model (GSM)
- 2-component a priori dynamic "Perfect Plasma" Model (PPM)
- 2-component mechanical "Electro-Magnetic" Maxwell-Mie Theory (EMT)
- 1-component mechanical "Dirac 2.0 Atomic Nucleus" Theory (ANT)
- 1-component Dynamic Fluid Theory (DFT).

It enables

- a well-posed 3D-NSE system for dynamic fluid particles by the DFT
- an enhanced Schrödinger 2.0 operator by the Riesz transform
- a "Yang-Mills" SU(2)-invariance for Dirac 2.0 (mass) particles by the ANT
- an integrated Plasma Dynamics Theory (PDT).

The symmetry break down from the complex Lorentz group transform to the (real) restricted Lorentz transform may become a characteristic of the transformation process from 2-component quanta systems to 1-component quanta systems accompanied by the concept of the Minkowski space-time continuum.


GSM & PPM
The a priori 2-component dynamic "Ground State" Model (GSM) and the a priori dynamic "Perfect Plasma" Model (PPM) may be interpreted as an Einstein-Lorentz ether, (EiA5). We note that

- 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

- there are currently two different (!) physical explanation models for the Landau damping phenomenon depending from the considered linear or nonlinear mathematical model, (BrK14) p. 18.

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.

EMT
Quote: „…. light beams must have electric stationary components in the direction of the wave front normal, and that consequently there must be stationary electric potential differences between different points along the beam; and that there must be also a stationary magnetic field in the beam of light with potential differences. Hence, the light beam must have a magnetizing effect, and the charge of a magnet should be changed by light“, (EhF1).

We note that the mechanical energy based 2-component electro-magnetic quanta field of the EMT is in line with the "photopheresis" phenomenon discovered by F. Ehrenhaft, (BrJ), (BrK14) p. 22.

ANT
In the ANT the term "Dirac 2.0 Atomic Nucleus" is chosen to anticipate that Dirac's single mechanical energy system is extended to a mechanical x dynamic energy system concept. 

Quote: "Dirac's theory of radiation is based on a very simple idea; he treats an atom and the radiation field as a single system whose energy is the sum of three terms: one representing the energy of the atom, a second representing the electromagnetic energy of the radiation field, and a small term representing the coupling energy of the atom and the radiation field", (FeE).

The Dirac 2.0 systems provide a mechanical atomic nucleus concept accompanied by the concept of implicate dynamic quanta (in the sense of D. Bohm, (BoD1)). The potential between this implicate quanta pair defines the dynamic energy of the mechanical atomic nucleus. Those systems neither require the hypothesis of an electron spin nor the existence of the fine structure constant.

The ANT puts the spot on the "Mach 2.0" principle as proposed in (UnA1) p. 156, which is essentially the Mach principle + Dirac's two large number hypotheses in the context of his "new basis for cosmology", (DiP2).

DFT
The Krein space based 1-component mechanical atomic nucleus quanta systems can be further aggregated/approximated by the purely Hilbert (energy) space system H(1/2), which is an extension of the variational mechanical standard energy Hilbert space H(1). The mechanical H(1) energy system is the domain of the Friedrichs extension of the Laplacian (potential) operator accompanied by the domain H(2), i.e. it is an extension of the classical mechanical standard energy Hilbert space H(2).

The standard Hilbert space systems H(1) resp. H(2) provides the variational resp. the classical framework for classical and quantum mechanics accompanied by the concept of Fourier waves. The complementary sub-space of the extended H(1/2) Hilbert space with respect to the H(1)-norm provides an appropriate Hilbert space based framework for quantum dynamics accompanied by the concept of wavelets. The latter ones may be interpreted as "a mathematical microscope", (BrK0) p. 19, (BrK14) p. 37, (HoM) 1.2.

Physically speaking, the compact embedding of H(1) into H(1/2) addresses "the problem of matter in the Maxwell equations, by explaining why the field possesses a granular structure and why the knots of energy remain intact in spite of the back-and-forth flux of (mechanical!) energy and momentum", (WeH) p. 171.

PDT
Plasma is that state of matter in which the atoms or molecules are found in an ionized state. The number of neutral particles (atomes or molecules) in a gas is irrelevant for the definition of a plasma. The number of positively and negatively charged particles per considered volume element may be arbitrarily small oder arbitrarily large, but both numbers need to be approximately identical (in order to have no internal macroscopic electrostatic  fields. The interactions of electrons and ions are determined by long-range electrical forces. Plasma physics is about classical statistical fluid mechanics and classical fluid dynamics. The underlying related mathematical models are grouped by different physical application areas resp. chosen mathematical tools accompanied by correspondingly defined different types of „plasma matter gases“, (BrK0) p. 60.

The a priori GSM & PPM in combination with the EMT, ANT and DFT enable an integrated Plasma Dynamics Theory (PDT) avoiding the concept of a Debye sphere.



Further notes

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: 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.

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

Note (The self-energy problem of an electroton): The UFT solves the baseline "self-energy problem" of an electroton, avoiding the spin and the iso-spin hypotheses, (UnA6) p. 100. 

Note: The UFT provides an appropriate modelling framework explaining the decay of a neutron into an electron and a proton (as part of the PPM).

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 (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.

Braun K., The deductive structure of the UFT, creative vacuum and perfect plasma, and related opportunities.pdf

 

                                                  June, 2025

Braun, K., An unified field theory enabling a deductive structure of physics.pdf

 


                                               December 2022

Braun, K., Current physical and mathematical realities regarding an unified field theory

 

                                                 August 2022


                                  

Braun K., UFT related list of papers

 

                                        Earlier UFT related papers