based on a mathematical (axiomatic) baseline quanta dynamics model providing a deductive conceptual structure of theoretical physics
(ScE1) p. 117 : "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".
The proposed unified (quanta) field theory is based on
- a new dynamical energy type, which is (in a well-defined mathematical sense) complementary to the current mechanical energy type
- fundamental (mathematical) and composed (physical) dynamical quanta pairs
(1) the electrino-positrino (vacuum, information carrier) quanta pair
(2) the electron-positron (plasma) quanta pair
(3) the electroton-magneton (electromagnetism) quanta pair
and their related interconnected (dynamical-dynamical vacuum, plasma, and electromagnetic) and (mechanical-dynamical atomic) energy field pairs.
September 25, 2023 update: pp. 11-12
The proposed purely mathematical unified 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. In particular, the physical modelling framework
- enables a solution of the 3D-Navier-Stokes Millennium Problem of the Clay Mathematics Institute
- overcomes the physical "YME mass gap" Millennium Problem of the Clay Mathematics Institute by making those equations obsolete
- provides an appropriate mathematical model for the Landau damping phenomenon
- 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 Gordian knot: current "realities" of physical and mathematical areas
The relation to the Riemann Hypothesis and the Goldbach conjecture
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 are a subset of the odd integers. The different sets of quantum numbers of the mathematical vacuum space consisting of the "elementary particles", the electrinos and the positrinos, are governed by the odd resp. the even integers. The Snirel'man densities of the odd resp. the even integers are a half resp. zero. Physically speaking, the Snirel'man densities determines the Ddnsity distributions of the (odd integer related) electrinos and the (even integer related) positrinos.
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.
At the same time, the Krein space based hermitian (potential) operators related to 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 specifically defined "a priori" potential function V(x).
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 also provides 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.
UFT related historical papers: