This homepage is dedicated to my mom, who died at April 9, 2020 in the age of 93 years. It considers multiple research areas. In retrospect, the proposed
solution concepts originate in some few simple ideas / basic conceptual
changes to current insufficient "solutions":
changes to previous version (October 24, 2020) : p. 6
The Einstein field equations are classical non-linear,
hyperbolic PDEs defined on differentable manifolds (i.e. based on a metric space framework) coming along with the concepts
of „affine connexion“ and „external product“.
The Standard Model of Elementary Particles (SMEP) is basically about a sum of three Langragian equations, one equation, each for the considered three „Nature forces“, based on a Hilbert space framework. Quantum mechanics is basically about matter fields described in a L(2) Hilbert space framework modelling quantum states (position and momentum). Our proposed quantum gravity model is based on a properly extended pair of distributional Hilbert spaces (which for example avoids the Dirac „function“ concept to model „point“ charges). Therefore, the proposed (truly geometrical) Hilbert space framework requires some goodbyes from current postulates of the quantum and gravitation theories. The central changes are : - as the L(2) Hilbert space is reflexive, the current considered matter equations can be equivalently represented as variational equations with respect to the L(2) inner product; this representation is extended to a newly proposed quantum element
Hilbert space H(-1/2); we note that the Dirac function is only (at most,
depending from the space dimension) an element of H(-1/2-e), and that the main
gap of Dirac‘s related quantum theory of radiation is the small term
representing the coupling energy of the atom and the radiation field. - classical PDE equations are represented as variational equations in the H(-1/2) Hilbert space framework coming along with reduced regularity requirements to the correspondingly defined solutions; we note that the Einstein field equations and the wave equation are hyperbolic PDEs and that PDEs are only well defined in combination with approproiate initial and boundary value functions; we further note, that the main gap of the Einstein field equations is, that it does not fulfill Leibniz's requirement, that " there is no space, where
no matter exists"; the GRT field equations provide also solutions for
a vaccuum, i.e. the concept of "space-time" does not vanishes
in a matter-free universe. At the same point in time H. Weyl's requirement concerning a truly
infinitesimal geometry are fulfilled as well, because ... "… a truly infinitesimal geometry (wahrhafte
Nahegeometrie) … should know a transfer principle for length measurements
between infinitely close points only ...", (WeH0).The proposed model is only about truly bosons w/o mass, modelled as elements of the H(1)-complementary sub-space of the overall energy Hilbert space H(1/2). Therefore, the main gap of Dirac‘s quantum theory of radiation, i.e. the small term representing the coupling energy of the atom and the radiation field, becomes part of the H(1)-complementary (truly bosons) sub-space of the overall energy Hilbert space H(1/2) . It allows to revisit Einstein's
thoughts on ETHER AND THE THEORY OF RELATIVITY in the context of the space-time theory and the kinematics of the
special theory of relativity modelled on the Maxwell-Lorentz theory of the
electromagnetic field.
The two fundamental model changes
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