This homepage is dedicated to my mom, who died at April 9, 2020 in the age of 93 years. In retrospect, the proposed
solution concepts of different problem areas (the Riemann Hypothesis & the inconsistent quantum theory with Einstein's gravitation theory) originate in some few simple common ideas / basic conceptual
changes to current insufficient "solution attemps".
Jan 23, 2021 update: pp. 8-9
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“. 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 (truly geometrical) Hilbert spaces, which for example avoids the Dirac „function“ concept (to model „point“ charges) with its underlying space dimension depending regularity. The aligned modelling framework between quantum theory and classical field theory requires some goodbyes from current postulates of both 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 about truly fermions resp. bosons (i.e. quantum elements with and without kinematical energy, i.e. mass), governed by their corresponding kinematical and potential energy Hilbert spaces, modelled as decomposition of H(1/2) into the sum of the kinematical energy space H(1) and its complementary sub-space with respct to the norm of the overall energy Hilbert space H(1/2). The proposed model - overcomes 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) - acknowledge the primacy of micro quantum world against the macro (classical field) cosmology world, where the Mach principle governs the gravity of masses and masses govern the variable speed of light, (DeH) - 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- acknowledge the Mach principle as a selecting principle to select the appropriate cosmology model out of the few existing physical relevant ones, (DeH) - aknowledge Bohm's property of a "particle" in case of quantum fluctuation, (BoD), chapter 4, section 9, (SmL)
From a mathematical perspective the two fundamental model changes are :
Jan 6, 2021 update: p. 2
fun, fun, fun and learning", it looks like a good point in time to share resp. enable more
fun to the readers‘ side, who showed their interest by more than
1 GB downloads per day (on average) during the last years. From (KoJ) p. 148 we quote: „ find a skillful motivation.
Then do the math and enjoy the creativity of the mind“and, with the words of master Yoda: " may the Force be with you", ...:) .For people, who are familar with the german language and who want to get some guidance to autonomous thinking in current grazy times we recommend
the latest book from A. Unzicker: „Wenn man weiß, wo der Verstand ist, hat
der Tag Struktur“. In order to support this some MS-Word based source documents of key papers are provided below.
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