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A.Einstein: "For us believing in physicists, the distinction between past, present and future is only a stubbornly persistent illusion".

H. Weyl: "We are not surprised that a concrete chunk of nature, taken in its isolated phenomenal existence, challenges our analysis by its inexhaustibility and incompleteness; it is for the sake of completeness, as we have seen, that physics projects what is given onto the background of the possible", (WeH) p. 220.

M. Kaku: " Because general relativity and quantum mechanics can be derived from a small set of postulates, one or more of these postulates must be wrong. The key must be to drop one or more of these assumptions about Nature on which we have constructed general relativity and quantum mechanics. Over the years several proposals have been made to drop some of our commonsense notions about the universe: continuity, causality, unitarity, locality, point particles", (KaM) p. 12.

J. Derbyshire: "What on earth does the distribution of prime numbers have to do with the behavior of subatomic particles?", (DeJ) p. 295

M. Heidegger: "modern physics is called mathematical because, in a remarkable way, it makes use of a quite specific mathematics.  But it can proceed mathematically in this way only because, in a deeper sense, it is already itself mathematical“, (HeM).


A Krein scale based modelling framework

The proposed Krein space framework addresses the following modelling requirements

- in plasma physics there is a symmetry between the number of positively andnegatively charged interacting particles per considered volume element

- in quantum theory there is an asymmetry between the kinetics and dynamics of elementary particles and the ground state

- in the Maxwell theory there has to be a physical „electron“ (fermion) object (a priori) existing outside of the Maxwell equations framework in order to make its motion happen governed by electric and magnetic field operators accompanied by a sophisticated „displacement current“; a similar situation is given by the (a priori) „inflaton“ object in the „big bang theory“

- conceptually, the Maxwell equations (accompanied by an "a priori" electron-fermion) are the role model for the SMEP, which is basically a "A x B x C collection" of three theories. Each of those theories starts with a set of fermions. If a theory (like Maxwell or Yang-Mills theory) is invariant under transformations by a symmetry group one obtains a conservation law and quantum numbers. Gauge symmetries are locally that act differently at each space-time point. They automatically determine the interaction between particles by introducing bosons that mediate the interaction. U(1) describes the electromagnetic interaction with one boson and one quantum number; SU(2) describes the weak force interaction with 3 bosons; SU(3) describes the strong force interaction with 8 gluon bosons

- there is the mathematical "mass gap" problem of the Yang-Mills equations (a generalization of the Maxwell equations, where a chromo-electromagnetic field carries charges), Physically speaking, this is about the difference in energy between vacuum energy and the next level lowest kinematical energy level

- missing problem adequate models to understand from a theoretical perspective the Landau damping phenomenon, the extraordinarily short "beta"-decay lifespan, a valid theory of fine-structure, including both wave mechanics and spin, and the Montgomery-Odlyzko law (*)

- it has been questioned whether the NSE really describes general flows. The difficulty with ideal fluids is that in such fluids there are no frictional forces- the proportional parts of massive particle matter, plasma particle matter, the „vaccum“ and the unknown rest of the universe

- in quantum theory the elements of a single geometric Hilbert space framework provide the model of the „state“ of an elementary particle. This „state“ is described with two attributes (location and momentum); from a mathematical perspective, those attributes relate to two different Hilbert spaces within a Hilbert scale

- in GRT the Einstein space is supposed to provide the framework for a geometric model of the phenomenon „gravity“. However it is a purely metric space accompanied by infinite numbers of locally euclidian space-time „frameworks“; mathematically speaking, the Einstein space has no geometric structure, at all

- there is still Einstein’s unfinished mission going beyond quantum mechanics to discover what is missing from a true theory of the atoms, (SmL), probably supported by Bohm's concepts of an "implicite order" and an "enfolding-unfolding universe", (BoD)

- there are many time-related reasons why a wide range of attempted approaches to quantum gravity failed to be satisfactory, (AnE), (BaJ1)

- a common modelling framework for the Hilbert-Polya conjecture and the Berry-Keating conjecture.
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(*) (DeJ) p. 292: The Montgomery-Odlyzko law: "The distribution of the spacing between successive non-trivial zeros of the Riemann zeta function (suitable normalized) is statistically identical with the distribution of eigenvalue spacing in a GUE (Gaussian Unitary Ensemble) operator
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Braun, K., The mathematical and physical realities of an unified field model