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
varifoldgeometry
(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 „time“
before 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.