An unified mathematical quanta field theory
A Krein spaces based unified mathematical quanta field theory is provided. From the Mie theory the concept of discrete energy knots (accompanied by a correspondingly defined kinetic energy Hilbert space) is taken providing an appropriate modelling framework for a physical problem specific (self-adjoint) kinetic energy operator. From the correspondingly defined extended Krein space framework the concept of a (self-adjoint) potential energy operator is applied. It enables the definition of a related potential energy norm on all of the Krein space.
The two quanta without "rest masses" (or better the "purely" potential energy field elements, the electrino and the positrino), may be interpreted as binary quanta information carriers enabling a link to information and consciousness theory.
From a philosophical perspective the two mathematical potential energy field elements may be interpreted as monades:
(WeH2) p. 51: „The classical philosopher of a dynamic world presentation is Leibniz. … For him the real of movement does not lie in a pure change of the location, but in a moving force „La substance est un etre capable d’action – une force primitive – overspatial, immaterial. … The last element is the dynamic point, from which the force erupts as an otherworldly power, an indecomposable strechless unit: the monade“.
(KnA) p. 55: „And so we can conclusively state the relationship of the least action principle to Kant’s Critique of Judgement in the following form: the principle of least action in its most modern generalization is a maxim of the reflective judgement.“
For Leibniz natural processes can be derived from integral principles by the method of the maximum or minimum, (KnA). Mathematically speaking, this means that the action of (otherworldly) monads as observed in natural processes are least action (approximating "forces") solutions in the physical side world.
The mathematical-dynamical & physical-kinematical "realities"
The proposed model of two perpendicular (kinetic and potential energy) worlds is about a purely mathematical dynamical world (electrinos & positrinos, quanta information) and a physical-mathematical kinematical world (physical space, physical time, physical mass / matter, physical forces), including a biological-physical world (atoms & molecules, viruses & cells, biological information, Schrödinger’s concept of biologically relevant repeated differentials (*), Husserl's concept of internal time-consciousness, (HuE)).
The differentiation between the two kinetic and potential energy worlds supports A. Unzicker’s vision „to form a consistent picture of (a mathematical) reality by observing nature from cosmos to elementary particles“, (UnA), (UnA1), (UnA2).
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The two perpendicular (kinetic and potential energy) worlds also relate to M. Harder's model of a "general duality theory" to unify relativity theory and quantum mechanics (structured space & time world vs. unstructured, not objectificable non-space & non-time world and opposite acting forces between those two worlds), requesting a narrative change in natural sciences from current upwards to down (complexity) causality thinking, (HaM). However, the proposed model is still about upwards causality thinking from mathematical world to (variational and classical) physical world, up to biological world, (WiE).
The current paradigm/narrative of physical systems
- "the behavior of a physical system depends on a scale (of energies, distances, momenta, etc.) at which the behavior is studied. Very generally speaking, the method of renormalization group is a method designed how to describe how the dynamics of some system changes when we change the scale (distance, energies) at which we probe it,. … Physics is scale dependent (requiring only a mathematical metric space framework, which has no geometric structure at all), and at each scale, we have different degrees of freedom and different dynamics, i.e. physics at a large scale decouples from the physics at a smaller scale. ...
… In classical mechanics there are three scales of distance, time, and mass. In non-relativistic quantum theory there are two scales: the mass can be expressed through «time» and «distance» using the Planck constant) and classical relativity («time» can be expressed via «distance» using the speed of light). In relativistic quantum theory there is only the scale of distance (or equivalently – the scale of (its inverse) momenta), (DeP) p. 551.
The new paradigm/narrative
The case specific (classical continuum mechanics, plasma physics, solid state physics, galactic dynamics, theory of granular structure, nucleus + electronic cloud, QED) dynamics are accompanied by phenomenologically visible "forces" resp. "force pressures" (e.g. NSE pressure, Maxwell-Mie electric pressure), the Lamb shift, which originates from quantum effects of the electromagnetic field, or gravitational/cosmic "energy potential differences" and "background radiations". The related mathematical-physical models are variational approximation solutions of an underlying mathematical solution of a Krein space (energy inner product based) variational problem.
The current role of physical constants (e.g. enabling mathematical "renormalization groups" in quantum field theory) changes to a "physical borderline role" governing the different physically relevant potential differences of the considered physical case area, (UnA2).
An only metric space (usually a Riemannian manifold) framework (in line with a scale dependent and decoupling physics) without any geometric structure concept is enhanced by a Hilbert space framework, where a simple metric with scale becomes a norm, which is induced by an (energy) Hilbert space inner product defined by two Hermitian kinetic and potential energy operators.
(*) (ScE1), Mind & Matter, p. 96: „only modifications or differentials intrude into the conscious sphere that distinguish the new incidence from previous ones and thereby unsually call for „new considerations“. … . A single experiment that is never to repeat itself is biologically irrelevant. … . Whenever the situation exhibits a relevant differential this differential and our response to it intrude into consciousness.“
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The link of the proposed plasma quanta potential model to the Riemann Hypothesis is when "Number Theory Meets Quantum Mechanics", (DeJ). Or more specifically, this is when number theory meets plasma quantum dynamics providing an appropriate mathematical model for the (physical) Montgomery-Odlyzko law.