R. Descartes
E. Schrödinger The principle of objectivation " E. Schrödinger
B. Russell „ „
The proposed quanta field theory 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. Classical mechanics is concerned with kinematics and dynamics. The kinematics deals with the different forms of the movement of bodies in a space-time environment. Classical dynamics should explain the reasons of the connection of those different form of movements. The The proposed deductive structure of quanta fields is based on coherently defined mechanical or dynamical quanta. The physical quanta are appropriately composed by two abstract (mathematical) quanta From a top down perspective (from classical physical models down to quanta dynamics) classical Partial Differential Equation (PDE) or Pseudo Differential Equation models become approximation models of their related (weak) variational representations governed by the standard mechanical energy Hilbert space H(1) equipped with the Dirichlet integral inner product D(u,v). Those variational, purely mechanical H(1)-energy Hilbert space based models become approximation models in an extended H(1/2)-energy Hilbert space, where H(1) is compactly embedded into H(1/2). The H(1/2) energy Hilbert space based models become approximation models in an (one mechanical component) atomic nucleus dynamics framework. The next two layers down require the concept of Krein spaces. It provides the (two mechanical, i.e. electroton & magneton) electromagnetic quanta Maxwell-Mie dynamics, being followed by the (two dynamical, i.e. electron & positron) "plasma quanta dynamics". The "plasma quanta dynamics" model overcomes the current physical modelling issue of the observed Landau damping phenomenon, as there are two, a linear and non-linear, Landau damping models, which conceptually must arise from different physical effects: " The "plasma quanta dynamics" model builds the baseline modelling framework for all physical dynamics. This is in line with the significant about 99%-share of „plasma matter“ in the universe, (ChF) p.1. The underlying purely mathematical "vacuum quanta dynamics" model of the physical "plasma quanta dynamics" model provides the axiomatically defined initial In particular, the integrated physical layer modelling framework (a) enables a solution of the 3D-Navier-Stokes Millennium Problem of the Clay Mathematics Institute in a H(1/2) energy Hilbert space framework (b) overcomes the physical "YME mass gap" Millennium Problem of the Clay Mathematics Institute by making those equations obsolete resp. replaced by the electromagnetic Maxwell-Mie dynamics (c) provides a single physical plasma dynamics theory "explaining" the Landau damping phenomenon overcoming the current issue of a linear and a nonlinear theory accompanied by two different physical root causes of the phenomenon (d) provides a H(1/2) based overall energy Hilbert space in line, which is 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) (e) supports the aspiration of A. Unzicker's "mathematical reality", to "
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) neglected physical discoveries (3) 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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