The proposed Unified Field Theory (UFT) provides an all-encompassing theory, where physical models of different physical areas are no longer decoupled and differently scaled according to their different levels of granularity, (BrK0) pp. 10-13. It is governed by two types of energy, the today’s mechanical energy (i.e., the space-time based kinetic and potential energy) and a newly proposed dynamic energy, which is timeless and spaceless. Bohm suggested a „wholeness, explicate & implicate order" principle for quantum theory, (BoD). In this context the mechanical energy is about explicate momentum and explicate potential differences of particles in a space-time continuum, while the new dynamic energy is characterized by implicate potential differences modelled by indefinite norms (i.e., the invariances of the considered quanta systems) of appropriately defined Krein spaces.

There are two order-creating principles (or mechanisms) in classical physics, the order-from-disorder principle (e.g. in statistical thermodynamics), and the order-from-order principle in classical dynamic laws (e.g. the Newton law, F = m*a), (ScE), (PlM). Bohm suggested a „wholeness, explicate & implicate order" principle for quantum theory, (BoD). The proposed Unified Field Theory (UFT) provides a deductive dynamic system structure enabling an order-from-order-creating principle starting from meta-physical (mathematical) dynamic quanta systems up to Hilbert space based classical partial differential equation (PDE) systems.

The scope of the Unified Field Theory (UFT) includes the scope of the three quantum field theories of strong interactions, of weak interactions, and of electromagnetics), the Higgs mechanism, the scope of both relativity theories, and plasma dynamics.

The variational principles of mechanics are one of the most important concepts in mathemtical physics. The related mathematical tool is the calculus of variations. The new conceptual elements of the proposed deductive structure of physics are additional (Hilbert space and Krein space based) bases layers. The current Hilbert space frameworks of the calculus of variations become approximation Hilbert sub-spaces of an extended new Hilbert space layer. This layer (building block 2) become an approximation Hilbert space layer of underlying Krein space based layers. The central differentiator between Hilbert and Krein spaces are definite vs. indefinite norms. The central physical common denominator of Hilbert resp. Krein spaces are underlying self-adjoint (mechanical resp. dynamic) operators. The central physical differentiator between Hilbert resp. Krein space based frameworks are, that the latter frameworks are without the concepts of space and time governed by the complex Lorentz transformation group.


The two linked mathematical frameworks: Krein & Hilbert scales

A Hilbert space framework may be considered as the only possible common denominator of a GRT (based on the Hilbert-Einstein action functional) and quantum mechanics. In a Hilbert space there is a definite (invariant) norm induced by its inner product. The Krein space theory is basically the theory of linear spaces with an indefinite metric. It provides the concept of an intrinsic self-adjoint "potential" operator, which is defined by the so-called J-symmetric operator and related J-inner product on all of the considered Krein space, (BoJ) p. 120 ff.. This dynamical "Hamiltonian" operator is applied to define quantum type specific "dynamic energy" inner products and corresponding dynamic quanta energy systems, (BrK0) pp. 1, 27-29, 36.

It turns out that the Krein space based dynamic quanta systems can be approximated by an energetical H(1/2) Hilbert space framework. This Hilbert space includes the domain of the self-adjoint Friedrichs extension of the (mechanical) symmetric Laplacian operator providing the concepts of a dynamic fluid particle and a related (not self-adjoint) dynamic potential operator, (BrK0) pp. 10, 11, 17-19, 38. However, this dynamic potential operator can be interpreted as a compact disturbance of the mechanical (self-adjoint) Laplacian potential operator with domain H(1). It enables a convergent energy norm estimate of the non-linear, non-stationary 3D-NSE system. It further provides a modified Schrödinger 2.0 momentum operator. This is basically the Schrödinger operator in combination with the Riesz operator: the Riesz operator commutes with translation and homothesis, and have nice properties relative to rotations. For n=1 the Riesz operator is called the Hilbert transform on R.

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., UFT related list of papers

 

                                      Earlier UFT related papers



1. The current phenomenological & conceptual structure of physics

There is a phenomenological and a conceptual structure of physics, which are mutually dependent on each other. This results into regional disciplines of physics, where physics at large scale decouples from the physics at a smaller scale accompanied by different degrees of freedom and different dynamics:

In classical mechanics one deals with three scales according to its three basic measurements: distance D, time T, mass M. In non-relativistic quantum theory and classical relativity it has two scales: D & T resp. D & M (mass M can be expressed through T & D using the Planck constant resp. T can be expressed via D using the speed of light). In relativistic quantum theory there is only one scale: distance D, (DeP) p. 551.


2. Challenges ...

a. ... in current thermomechanics / thermodynamics

Thermomechanics deals with thermal and mechanical process (Brown motion). Thermodynamics dealing with the concepts of temperature, pressure, and volume is governed by four principles, (1) thermal equilibrium, (2) energy conservation, (3) entropy, (4) unattainable absolute zero point. In all cases only closed energetical system are considered.

There is, essentially, only one problem in statistical thermodynamics: to determine the distribution of an assembly of  identical systems over the possible states in which this assembly can find itself, given that the energy of the assembly is a constant. The idea is that there is weak interaction between them, so weak that one can speak of the „private“ energy of every one of them and that the sum of their „private“ energies has to be equal E. The distinguished role of the energy is, therefore, simply that it is a constant of the motion – the one that always exists, and, in general, the only one, (ScE) pp. 1-2.

b. ... in current quantum mechanics / quantum dynamics

Quantum mechanics is concerned with states and process of matter. Quantum dynamics is concerned with motions and interactions of closed quantum systems over time. Aditionally to matter it deals with the concept of fields. Accordingly, there are decoupled matter and interaction objects (fermions & bosons) for each quantum dynamic phenomenon or modelling case (QED (interaction between matter and light), QCD, QFD, Higgs). The three SMEP systems show similar gauge symmetry properties. The Higgs system is incompatible with the SMEP systems.

c. ... in current galactic mechanics /  galactic dynamics

There seems to be no clear differentiation between galactic mechanics and galactic dynamics. Most probably, because there is no closed system to be considered. A similar unspecified situation exists in case of all „theories“ based on the so-called Big Bang „Theory“ („even though it was the biggest black hole ever, it exploded out of nowhere“, (DeK); „producing an universe resembling the one in which we live with a probability of the inverse of 10 exp (10 exp (123))“, (PeR) p. 444). The probability that God made it within six days including a beer to celebrate the work at the seventh day seems to be more likely, especially as this scenario provides also an explanation of the existence of organisms on Earth. In any case, the most mathematical tool being applied so far in galactic dynamics are ordinary differential equations depending from a „cosmic time“ parameter and a few cosmic constants like the Hubble constant.

Galactic (stellar) dynamics is the principle tool for the study of the motion of a large number of point masses orbiting under the influence of their mutual self-gravity, (BiJ) xiv. In its purest form, Landau damping represents a phase-space behavior peculiar to collisionless systems. The dynamic plasma characteric, the Landau damping also exist in the interactions of stars in a galaxy at the Lindblad resonances of a spiral downsity wave. Such resonances in an inhomogeneous medium can produce wave absorption (in space rather than in time), which does not usually happen in fluid systems in the absence of dissipative forces (an exception in the behavior of corotation resonances for density waves in a gaseous medium), (ShF) p. 402.