 |
 |
 |
 |
 |
 |
R. Courant
„Empirical evidence can never establish mathematical existence – nor can the mathematician’s demand for existence be dismissed by the physicist as useless rigor. Only a mathematical existence proof can ensure that the mathematical description of a physical phenomenon is meaningful“, (HiS) p. 148
R. Descartes
"My present design, then, is not to teach the method which each ought to follow for the right conduct of his reason, but solely to describe the way in which I have endeavored to conduct my own. They who set themselves to give precepts must of course regard themselves as possessed of greater skill than those to whom they prescribe; and if they are in the slightest particular, they subject themselves to censure. But as this tract is put forth merely as a history, or, if you will, as a tale, in which, amid some examples worthy of imitation, there will be found, perhaps, as many more which it were advisable not to follow, I hope it will prove useful to some without being hurtful to any, and that my openess will find some favor with all“, (DeR2) iii
E. Schrödinger
The principle of objectivation
"Science aims at nothing but making true and adequate statements about its object. The scientist only imposes two things, namely truth and sincerity, imposes them upon himself and upon other scientists. In the present case the object is science itself, as it has developed and has become and at present is, not as it ought to be or ought to develop in future", (ScE1) p. 117
E. Schrödinger
Form, not substance, the fundamental concept
"The new idea is that what is permanent in these ultimate particles or small aggregates is their shape and organization. The habit of everyday language deceives us and seems to require, whenever we hear the word „shape“ or „form“ pronounced, that it must be the shape or form of something, that a material substratum is required to take on a shape. Scientifically this habit goes back to Aristotle, his causa materialis and causa formalis. But when you come to the ultimate particles constituting matter, there seems to be no point in thinking of them again consisting of some material. They are, as it were, pure shape, nothing but shape; what turns up again and again in successive observations is this shape, not an individual speck of material“, (ScE3) p. 12
B. Russell
„“Substance“, in a word, is a metaphysical mistake, due to transference to the world-structure of the structure of sentences composed of a subject and a predicate.“, (RuB1) p. 212
„Hume had proved that the law of causality is not analytic, and had inferred that we could not be certain of its truth. Kant accepted the view that it is synthetic, but nevertheless maintained that it is known a priori. He maintained that arithmetic and geometry are synthetic, but are likewise a priori. He was thus led to formulate his problem in these terms:
How are synthetic judgements a priori possible?
The answer to this question, with its consequences, constitutes the main theme of The Critique of Pure Reason.
Space and time, Kant says, are not concepts; they are forms of „intuition“. (The German word is „Anschauung“, which means literally „looking at“ or „view“. The word „intuition“, though the accepted translation, is not altogether a satisfactory one)", (RuB1) p. 680
 Braun K., An integrated quanta field theory enabling a deductive structure of physics |
In a nutshell
The Gordian knot: „the principle of transfer causality“
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 principle of transfer causality is the common denominator of all dynamical models in physics. Regarding the so-called Standard Model of Elementary Particles it leads to the concept of two quantum types, the fermions and the bosons, resulting into three decoupled theories, which are basically based on decoupled electromagnetic, weak and strong interaction models of correspondingly defined decoupled fermion and boson groups (requiring multiple arbitrary (free) parameters w/o any physical meaning).
The proposed quanta field theory 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 "form a consistent picture of reality by observing nature from the cosmos to elementary particles," (UnA2).
The integrated kinematical & dynamical quanta scheme
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.
The five physical quanta layers are appropriately composed by two abstract (mathematical) quanta forming a kind of physical "ground state energy" quanta field in line with the thoughts in (DaJ).
The five hierarchical physical modelling layers
The (top down) scope of the five hierarchical physical modelling layers starts from classical Partial Differential Equation (PDE) or Pseudo Differential Operator (PDO) modelling frameworks and ends by a variational "plasma quanta dynamics" modelling framework. The respective coarser layer framework is interpreted as the approximation modelling framework of the correspondingly finer model.
The layer (1) corresponds to standard variational theory providing weak solution of classical PDE or (PDO) models accompanied by physical, model specific potential energy (differential) operators.
Layer (1): classical PDE models are approximated by related (weak) variational representations governed by the standard mechanical energy Hilbert space H(1) equipped with the Dirichlet integral inner product D(u,v)
Layer (2): mechanical energy Hilbert space H(1) based variation models are approximated 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 down require the concept of Krein spaces accompanied by (newly PDE model independent) self-adjoint potential operators (those are conceptual elements of the Krein space framework) enabling the definition of related energy Hilbert spaces:
Layer (3): the H(1/2) energy Hilbert space framework becomes the approximation modelling framework of an „atomic nucleus dynamics“ framework
Layer (4): the „atomic nucleus dynamics“ framework becomes the approximation modelling framework of an (electroton & magneton quanta pair based) "electromagnetic Maxwell-Mie dynamics" framework
Layer (5): the "electromagnetic Maxwell-Mie dynamics" framework becomes the approximation modelling framework of a (electron & positron quanta pair based) "plasma quanta dynamics".
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
The sixth mathematical modelling layer provides the axiomaticly defined mathematical baseline quanta. This layer framework is called "vacuum quanta dynamics" providing an initial a priori modelling framework based on purely mathematical „vacuum quanta“, which are called "electrinos", "positrinos", and "neutrinos". Their definition and the definition of their related energy Hilbert spaces (based on corresponding self-adjoint potential operators) is based on the different mathematical Schnirelman densities of the odd integers (density ½) and even integers (density zero) defining related "quanta numbers densities"; those govern the correspondingly defined mathematical forms called "electrino", "positrino", and „neutrino“. This design principle is in line with the observed deviation from the iso-spin-symmetry in electrodynamics, which was taken bei Heisenberg as indication for an asymmetry of the ground state, (DüH).
Proof of concept of the five physical layers
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): Dirac's theory is based on a single (electron) system model, whose energy is the sum of three terms, one representing the energy of the atom, a second representating the electromagnetic energy of the radiation field, and a small term representing the coupling energy of the atom with the radiation field). This layer provides an alternative modelling framework overcoming several known issues resp. required modelling adaptions to the Dirac model because of inconsistencies with discovered phenomena, e.g. the Lamb shift phenomenon.
Layer (4): The Mie theory is basically about a new physical concept, which Mie called "electric pressure", to overcome current model challenges of the Maxwell equations concerning the electromagnetic currents. This layer provides the concept, which may be interpreted as electric & magnetic pressures; it is in line with Leedskalnin’s claim, that magnetic and electric current is (basically) the same. It delivers an explaning of Ehrenhaft's discovery of the photophoresis phenomenon accompanied by his observations that the movement of „light particles“ in a field (in combination with an occuring centripetal force) do not run in straight lines, but run in paths in extremely regular forms, sizes and orbital frequencies. Those phenomena are also in line with Schauberger’s concept of implosion (cycloidal) movement.
Layer (5): The finest physical "plasma quanta dynamics" layer builds the baseline modelling framework for all physical dynamics. It provides a new plasma physics theory overcoming current challenges like hot, cold, and medium plasma "matter types "accompanied by different mathematical modelling frameworks required by different types of „transfer causality“ modelling needs.
The layer (5) modelling 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, (ChF) p. 248-249
(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
(d) provides an alternative concept to the current sophisticated concepts of „dark matter" & "dark energy“ and is in line with the significant (about 99%-) share of „plasma matter“ of all matter in the universe, (ChF) p.1
(e) provides an appropriate modelling framework to support Dee’s "Implosion Theory of Universe Creation" alternatively to the "Big Bang Theory" ("Even though it was the biggest black hole ever, it then exploded"), (DeK) p. 3, (PeR) p. 444.
Related forgotten thoughts, discoveries and theories
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 implicate order in physical laws, (BoD1); the current galactic kinematics assuming an universe, which is homogeneous and isotrop on large scales, modelled as an ODE depending from a cosmic time t, the Hubble function H(t), and a scale factor function a(t); the sophisticated CMBR providing the most important evidence supporting the big bang model, (BrK11)(LaM); Schauberger’s implosion theory for planetary movements, (BaA), (BrK11); Schauberger’s implosion theory as the initializer of the universe creation process, (DeK)
(2) Ehrenhaft’s discovery of the photophoresis phenomenon ("kleinste freischwebende Materieteilchen in einem konzentrierten Lichtstrahl bewegen sich auf Schraubenbahnen; zu der Bewegung um die Schraube kommt oft noch eine Bewegung um die eigene Achse hinzu"), (BrJ); Schauberger's "konzentrisch-spiralförmige Bahn von außen nach innen, deren Zentrum saugend ist, also eine zentripetale Massenbewegungsform ist", which he called implosion
(3) Platon's theoretical philosophy in the context of the relations between "idea & cosmos" resp. "time & astronomy", (BöG),(BöG1); Leibniz' vis viva and teleology concepts, (KnA); Goethe’s „data for a theory of color“ („Zur Farbenlehre“), e.g. (MüO), (NuI), (RiN); Schopenhauer’s „on vision and colours“, e.g. (HüA), (ScD) p. 33 ff.; Schopenhauer’s concept of "matter as mere visibility of the will", (ScD) p. 42; Bergson's and Shaw's rejection of "neo-darwinism & mechanism" in favour of "creative evolution (= functional adaption) & vitalism", (ShB), (BeH2); Nagel's teleology, (NaT); Bergson's view on "duration & simultaneity" regarding Einstein's relativity theory, (BeH), Schrödinger's key facts (e.g. the concept of "differentials") for the physical basis of consciousness, (ScE1).
Current physical and mathematical realities
Braun, K., Current physical and mathematical realities regarding an unified field theory |
Supporting mathematics
Braun, K., A Krein space based quanta energy field model, supporting mathematics |
Some former related papers
Braun K., UFT related list of papers |
Relations to the Riemann Hypothesis and the Goldbach conjecture
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.
Braun K., A toolbox to solve the RH and to build a non-harmonic Fourier series based two-semicircle method |
Polya Ueber eine neue Weise bestimmte Integrale in der Zahlentheorie zu gebrauchen |
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.
Braun K., The Montgomery-Odlyzko law, eigenvalue spacing in a collection of Gaussian unitary operators |
(DeJ) Derbyshire J., Number theory meets quantum mechanics |
