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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
The proposed quanta field theory
The proposed quanta field theory is based on coherently defined physical quanta, which are different types of energetical (mechanical or dynamical) quantum elements. They are appropriately composed by two abstract (mathematical) quanta forming a "ground state energy" quanta field in line with the thoughts in (DaJ).
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.
From a top down perspective (from classical physical models down to quanta dynamics) in the proposed deductive structure of theoretical physics classical partial differential equation (PDE) 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 layer down provides the (two mechanical components) electromagnetic (electroton & magneton) Maxwell-Mie dynamics, being followed by the (two dynamical components) plasma dynamics. Therefore, the latter one becomes the baseline modelling framework for all physical dynamics in line with the significant share of „plasma matter“ in the universe, (ChF) p.1. The underlying dynamics of the "vacuum" model is based on axiomaticly defined mathematical quanta based on the fundamental different Schnirelman densities of the odd and even integers governing the corresponding "densities" of the related electrinos resp. positrinos in the mathematical "vacuum".
In particular, the integrated physical layer modelling framework
- enables a solution of the 3D-Navier-Stokes Millennium Problem of the Clay Mathematics Institute in a H(1/2) energy Hilbert space framework
- 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
- provides an appropriate single physical plasma dynamics model "explaining" the Landau damping phenomenon overcoming current untrapped vs. trapped plasma particle based modelling frameworks
- is accompanied by a H(1/2) based overall energy Hilbert space 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)
- 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 essential ingredient of the proposed quanta field theory: a second dynamical energy type avoiding the concepts of fermions and bosons
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 („Impetustheorie“, "impetus ~ momentum" (WoM)) states that a transfer of movements requires the mediation of a certain type of quantum, a "transfer force quantum".
In simple words, the proposed new structure of theoretical physics (coming along with a mathematical explanation of quantum numbers) overcomes the three decoupled worlds of fermion (kinematics) & boson (dynamics) quantum types (= quanta) and their related three decoupled theories, which is called the Standard Model of Elementary Particles requiring multiple arbitrary parameters w/o any physical meaning.
The proposed deductive structure of physics is strongly related to Weizäcker's philosophy of physics, (WeC). It also suggests to revisit forgotten thoughts, discoveries and theories, e.g., Platon's theoretical philosophy (especially the relations of idea & cosmos resp. time & astronomy, (BöG),(BöG1)), Leibniz' vis viva concept, 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, Ehrenhaft’s discovery of the photophoresis phenomenon, e.g. (BrJ), Schauberger’s implosion theory for planetary movements, e.g. (BaA), and the implosion theory as the initializer of the universe creation process, (DeK).
 Braun K., An integrated quanta field theory enabling a deductive structure of Physics |
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
Braun, K., A Krein space based quanta energy field model, supporting mathematics |
The Gordian knot: current "realities" of physical and mathematical areas
Braun, K., Current physical and mathematical realities regarding an unified field Theory |
The relation to the Riemann Hypothesis, the Hilbert-Polya (resp. the Berry-Keating) conjecture, Montgomery's pair correlation conjecture 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 provided proof of the Riemann Hypothesis is based on a decomposition of the meromorphic Zeta function (occuring in the symmetrical form of the Riemann functional equation) into a sum of integral and series representations. The "symmetrical" series representations provide a characterization of the non-trivial zeros z(n)=1/2+/-it(n) of the zeta function in relation to the vertical line (1/2-2n) +/- i*t(n).
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 a "prime number density decomposition" in the above sense provides an alternative 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 |
UFT related historical papers:
Braun K., UFT related list of papers |
