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quantum gravity
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The proposed mathematical (geometrical Hilbert space based)  "complementary" thermodynamic and ether (ground state/"quantum potential") energy model enables a quantum gravity model based on Bohm's "hidden variables" theory in line with Einstein's ether vision and his Special Relativity theory, Wheeler's gravitation & inertia conception and Schrödinger's "view of the world". At the same point in time Dirac's model of the point mass density of an idealized point mass is replaced by Plemelj's definition of a mass element.

The proposed quantum gravity theory is based on an only (energy related) Hamiltonian formalism, as the corresponding (force related) Lagrange formalism is no longer defined due to the reduced regularity assumptions to the domains of the concerned Pseudo Differential Operators. The proposed distributional Hilbert (quantum state) space H(-1/2) goes along with reduced regularity assumptions for the domain of the momentum (or pressure) operator.

The classical Yang-Mills theory is the generalization of the Maxwell theory of electromagnetism where chromo-electromagnetic field itself carries charges. As a classical field theory it has solutions which travel at the speed of light so that its quantum version should describe massless particles (gluons). However, the postulated phenomenon of color confinement permits only bound states of gluons, forming massive particles. This is the Yang-Mills mass gap. The variational representation of the Maxwell equations in the proposed "quantum state" Hilbert space framework builds on truly fermions (with mass) & bosons (w/o mass) quantum states / energies, i.e. a Yang-Mills equations model extention is no longer required.

A decomposition of the related energy Hilbert space H(1/2) provides a model for "complementary" thermodynamic energy and ether (ground state) energy. The first one is governed by Fourier's (one-parameter) waves, Kolmogorow's (statistical) turbulence model, Einstein's Special (Lorentz invariant) Relativity, Klainerman's global nonlinear stability of the Minkowski space, Vainberg's conceptions of second order surfaces in Hilbert spaces (hyperboloid (conical and hyperbolic regions) defined by corresponding potential barriers), Almgren's varifold geometry (in the context of least area problems) and the Heisenberg's uncertainly relation, while the second one is governed by Calderón's (two-parameter) wavelets (to go from scale "a" to scale "a-da"), Bohm's revisited quantum potential and Plemelj's mass element conceptions.

The thermodynamic Hilbert (energy) space H(1) is compactly embedded into the newly proposed Hilbert (energy) space H(1/2). From a statistical point of view it means that the probability to catch a quantum state/"elementary particle", which is able to collide with another one, is zero. This compactly embeddedness enables a new interpretation of the entropy phenomenon as the change process from thermo-dynamical (kinetic) energy to ether (ground state, "dark", quantum potential) energy.

In our proposed model the birth“day“ of the physical universe (which is the universe of the second law of thermodynamics additionally to the dynamical laws) is at Planck time; this is the very first interaction of created EP after „symmetry break down“ onto the physical energy Hilbert space; from that point in time the radiation is being governed by (weak variational) evolution (hyperbolic) PDO in the proposed extended Hilbert space framework.  

The physical universe model is part of the mathematical universe model, which is a steady-state model being governed by (weak variational) (elliptic) PDO equations. At the same point in time the integrated steady-state ground state energy (ether) model comes along with an explanation of the observed cosmic microwave background radiation. We note that the observed CMB is basically „only“ about electromagnetic waves, which are a very specific phenomena of our planet.  

Our proposed model is very much in line with Bohm‘s concept of „hidden variables in quantum theory“. It handles especially those physical problems dealing with extremely short distances (Planck length and shorter) and high energy (  and higher) ((BoD) p. 83). In our case the first change („mover“) of the „system“ happens/occurs at Planck (point in) „time“; the „timebefore that „point in time“ can be interpreted as a „hidden variable“ in the sense of D. Bohm. In (BoD1) Bohm shows „how many of our „self-evident“ notions of space and of time are, in fact, far from obvious and are actually learnt for experience, starting to understand the importance of measure and the need to map the relationships of these objects on to a co-ordinate grid with time playing a unique role“.  

Bohm’s concept of hidden variables overcomes current challenging consequences of main features of the quantum theory, like the fact, that there is „no wave function existing describing a state, where all physical relevant quantities are dispersionless, i.e. they are sharply defined and free from statistical fluctuations“. Bohm himself challenged his alternative model with respect to the proposed notion of a „quantum potential“ and its related „many-dimensional field“ to describe the many-body problem.  
We emphasis, that our proposed „quantum potential“ model is complementary and therefore independent from the „physical world“ Hilbert space . In other words, the extended energy Hilbert space  provides a „complementary“ thermodynamic vs. ether (ground state or dark or quantum potential) energy field model.

While the energy space H(1) (which is compactly embedded into H(1/2)) is about the concepts of event & action (and corresponding variables, including „time" & „space“, as perceived through perception and „our“ activities in space and time), the (much more larger) closed subspace H(1,ortho) is about the „energy source“ space from where perceived events and actions are generated from. By definition those „generation processes“ „happen“ independently from all only H(1) relevant variables.

                           

Braun K., RH, YME, NSE, GUT solutions, overview