The foundation of deductive theoretical physics
The two new concepts of the proposed theory of quantum dynamics are:
(1) an extension of the statistical Hilbert space L(2) of quantum mechanics to H(-1/2)
(2) two Krein-space representations of the Hilbert space H(-1/2), which define the concept of a physical ether, consisting of two interconnected ground-state quantum fluctuation and plasma quantum fluctuation models with different superposition and non-superposition states.
The metaphysical prerequisite for both models is a mathematically justifiable “density” assumption regarding this concept of a „physical ether“. It includes a concept of dynamic energy that is independent of mechanical energy and independent of the concepts of the theory of motion - that is, in particular, independent of the concepts of space, time, and continuity. The laws of classical mechanics may be interpreted as aproximation solutions in Hilbert scales of underlying variational representions of quantum-mechanical laws governed by the so-called energy method.
What at first glance appears to be a cheap magic trick (the extension of the standard Hilbert space L(2) of the quantum mechanics to the quantum-mechanical Hilbert space H(-1/2)) proves to be a valid step toward resolving the problem of a missing physical interpretation of a mathematical “world-point state". The compact embedding of H(-1/2) into H(-n/2-e), e>0, which is independent of all spatial dimensions, ensures - by virtue of Sobolev’s embedding theorem - that continuous fields in classical physics can be generated by quantum-mechanical causes, regardless of the dimension of the underlying Euclidean space. The systems of this extended Hilbert space can thus accommodate the mathematical concept of the Newtonian or Coulomb potential, both of which, for mathematical reasons, only make physical sense in 3D Euclidean space. The concept of phenomenon-specific “point charges” that generate continuous fields throughout 3D Euclidean space can thus be completely replaced.
Furthermore, it has been shown that the variation equations of the 3D NSE initial boundary value problem, based on a “test space” H(-1/2), avoid existing “blow-up” solutions by means of L(2) test functions. In classical physics, the systems of the extended “test space” H(-1/2) could therefore be physically interpreted as “dynamic fluid/gas elements.”
The original work from 2023, revised in July 2026
According to Kant's „Theory of Natural Science“ in order to establish a meta-physical foundations of physics it requires an a priori conception of matter, i.e., its „form“, its necessary and universal determinations and laws that govern (predictively describe) its behavior, (PlP) p. 29. "The merely empirical concept of motion "reality" is conceived as objective thinghood (Sachheit). Here one speaks of „motion as an accient (Akzidens) of matter“, thus not a mere act (Actus) of the productive imagination, i.e., motion as description, the describing of a space (moreover, where time, specifically as quantity, is not taken into consideration at all", (PlP) p. 297.