The proposed UQFT is based on an integrated quantum type scheme providing 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. It also supports the aspiration of A. Unzicker's "mathematical reality", to " R. Courant „ R. Descartes
B. Russell „ „
E. Schrödinger The principle of objectivation
W. Heisenberg Introduction to the Unified Field Theory of Elementary Particles
Note: „ „
The gravitational phenomena related theories (SRT, GRT, Big Bang and all that) are about The SMEP is about three Classical mechanics is concerned with The common denominator of all
The proposed deductive structure of five mathematical-physical and one purely mathematical quanta energy field systems is based on coherently defined mechanical or dynamical quanta (i.e., different types of mechanical or dynamical quantum forms). The five physical quanta layers are appropriately composed by two abstract (mathematical) quanta
The (top down) view of the five physical modelling layers starts from classical Partial Differential Equation (PDE) or Pseudo Differential Operator (PDO) modelling frameworks, the Layer (0), and ends by a variational " Layer (1): Classical PDE or PDO models accompanied by PDE specific potential energy (differential) operators are interpreted as approximation models by related (weak) variational representations governed by the standard mechanical energy Hilbert space H(1) with the inner product defined by the Dirichlet integral D(u,v). Layer (2): Mechanical energy Hilbert space H(1) based variational models are interpreted as approximation models in an extended H(1/2)-energy Hilbert space framework; it can be decomposed into an orthogonal sum of the mechanical energy space H(1) of layer (1) and its orthogonal companion H(1,ortho). The mechanical Hilbert space H(1) is compactly embedded into the Hilbert space H(1/2) and its orthogonal companion H(1,ortho) provides the first modelling layer for a newly proposed dynamical energy concept. The next three layers (3)-(5) require the concept of Krein spaces accompanied by (newly!) PDE model independent, self-adjoint " Layer (3): The H(1/2) energy Hilbert space framework is interpreted as an approximation modelling framework of an „ Layer (4): The „ Layer (5): The " Remark: There are several decays possible to reduce the Remark: Layer (3) enables a proof of the „3D-Navier-Stokes (millennium) problem", (BrK9); the layers (4) and (5) make the „YME gap (millennium) problem“ obsolete.
The sixth mathematical modelling layer provides the axiomaticly defined mathematical baseline quanta. This layer framework is called "
Layer (2): This modelling layer solves the non-linear, non-stationary 3D-Navier-Stokes millennium problem providing global boundedness of the underlying generalized energy inequality, (BrK9). The H(1/2) energy Hilbert space is also in line with the Teichmüller theory & the universal period mapping via quantum calculus, (NaS), and the appropriate domains of the double layer (Prandtl) potential operator as applied e.g. in aerodynamics, (LiI). Layer (3): This layer provides an alternative modelling framework to Dirac's single (electron) system model, whose energy is the sum of three terms, one representing the energy of the atom, a second representating the electro-magnetic energy of the radiation field, and a small term representing the coupling energy of the atom with the radiation field, (FeE). It overcomes several related issues resp. required modelling adaptions to the Dirac model due to discovered phenomena like the Lamb shift phenomenon. It also provides three nucleus types in line with electric resp. magnetic conductor or isolator properties enabling an appropriate link to solid state physics. Layer (4): The Mie Theory, which is basically a new physical concept of " Layer (5): The finest physical " Layer (4) & (5): Their The layer (5) framework also (a) overcomes the current physical modelling issue of the observed Landau damping phenomenon, where there are a linear and a non-linear mathematical Landau damping model, meaning that the phenomenon conceptually must arise from different physical effects (b) provides an appropriate modelling framework for phase-space behavior peculiar to collisionless systems, like the capability of stars to organize themselves in a stable arrangement, (ShF) p. 401 (c) enables an explanation of the spiral movements of stars, (ChF) p. 245, (ShF) p. 402 (d) is in line with the global nonlinear stability of the Minkowski space, (ChD) (e) is in line with current statements that about 99% of the matter in the universe is in plasma state, (ChF) p.1p (f) provides an alternative concept to the current sophisticated concepts of „ (g) provides an explanatory model (a matter generation process) for the echo of the early universe, the (h) provides an appropriate modelling framework to support Dee’s "Implosion Theory" alternatively to the "Big Bang Theory" (" Remark: According to the "Big Bang Theory" in the early universe pressures and temperature prevented the permanent establishment of elementary particles. None of the invented elementary particles of the SMEP were able to form stable objects until the universe had cooled beyond the so-called "supergravity phase". " Remark: Big Bang models follow from a number of assumptions, (1) homogeneity of space, (2) isotropy of space, (3) matter can be described as perfect fluid, (4) laws of physics are the same everywhere, (LaM) p. 7.
The proposed deductive structure of quanta fields suggests to revisit forgotten thoughts, discoveries and theories regarding (1) forgotten or questionable physical-mathematical modelling approaches (2) ignored physical discoveries (3) neglected physical-metaphysical views e.g.: (1) Weizäcker's understanding of the unity of physics; Heisenberg's mathematical formalism for an unified field theory with its cornerstones of an indefinite metric in a Hilbert space and the degeneracy (asymmetry) of the ground state, (DüH), (HeW); Schrödinger's concept of a heat bath in statistical thermodynamics, (ScE); Penrose's calculated absurdly tiny probability to produce the universe resembling the one in which we live, (PeR); Barbour's problems about time and the need for a quantum cosmology, (BaJ1); Klainerman's global nonlinear stability of the Minkowski space, (ChD); Bohm's wholeness and (2) Ehrenhaft’s discovery of the (3) Platon's theoretical philosophy in the context of the relations between "
The Krein space based hermitian (potential) operators governing the vacuum quanta field may provide an alternative (selfadjoint) operator to the Berry-Keating "quantized" classical Hamiltonian operator of a particle of mass m that is moving under the influence of a problem specific to be defined potential function V(x). The primes (excluding the integer "2", the base number of the even numbers) are a subset of the odd integers. The conceptual design of the mathematical baseline quanta of the proposed quanta field theory, the electrinos and the positrinos forming the "ground state energy quanta field", is based on the different Schnirelmann densities of the odd resp. the even integers, a half resp. zero. Physically speaking, the Schnirelmann densities determines a kind of density distributions of the (odd integer related) electrinos and the (even integer related) positrinos of a mathematical "vacuum" quanta field. The binary Goldbach conjecture states that every positive even number n>2 is the sum of two primes. The claim is, that the additional "prime number density function" with domain 0<x<1 provides an alternative two-semicircle method to the standard Hardy-Littlewood circle method to prove the binary Goldbach conjecture.
The physical Montgomery-Odlyzko law states that the distribution of the spacing between successive non-trivial zeros of the zeta function is statistically identical with the distribution of eigenvalue spacing in a "Gaussian Unitary Ensemble". The claim is that the above conceptual modelling components also enable an appropriate mathematical model, where the physical Montgomery-Odlyzko law becomes the (L(2)-space based) statistical relevant part of the zeros distribution of the zeta function on or close to the critical line.
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