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 the previous (July 22, 2020) version: pp. 1,2,4,5
Current physical classical PDE model solutions are considered as approximation solutions to the underlying weak variational formulation in the proposed Hilbert space framework and not the other way around, e.g. (BrK6), (VeW). The weak variational models are governed by a common energy model concept (BrK), (BrK1), while the related "forces" phenomena become part of the specific corresponding classical PDE model, only. The distributional (quantum state)
Hilbert space framework resp. its underlying norm (i.e. with its
underling "length measurements") is governed by the sum of the standard
(quantum mechanics / statistics) L(2)-Hilbert space norm and an "exponentical decay" (entropy measurements, (BrK1) note 2, (BrK6)) norm, which is weaker than any distributional "polynomial decay"
norm (NiJ1). With additionally assumed regularity to the solutions of the proposed weak PDE representations (which is without any quantum theoretical physical meaning) the corresponding approximation solutions of the related classical PDE are well defined (VeW), i.e. the scalability from the "very small" quantum level to the "very large" classical level is ensured. Therefore, for example the physical concept of " force" (based on the Lagrange formalism) or the mathematical concept of "continuity" (due to the Sobolev embedding theorem) keeps being valid "on the classical PDE level" and the famous Einstein
equation E = m*c*c becomes an approximation formula, only, restricted to the
kinematical energy space H(1). We note that the Fourier analysis based applied spectral analysis methods (e.g. cosmoligical distance measurement or the Doppler effect in combination with the Hubble diagram leading to the interpretations of moving apart galaxies from each other galaxies with superluminal velocity in an expanding universe) is only defined in the „granular“ kinematical Hilbert space framework H(1), i.e. the proposed quantum gravity model allows an re-interpretation of the observed cosmological background radiation phenomenon. At the same point in time H. Weyl's requirement concerning a truly infinitesimal geometry are fulfilled as well, because ...(WeH0): "… a truly infinitesimal geometry (wahrhafte Nahegeometrie) …
should know a transfer principle for
length measurements between infinitely close points only ..."
(WeH0) Weyl H., Gravitation und Elektrizität,
Sitzungsberichte Akademie der Wissenschaften Berlin, 1918, 465-48. https://arxiv.org/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 onETHER AND THE THEORY OF RELATIVITY An Address delivered on May 5th, 1920, in the University of Leyden 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.Einstein’s field equations are hyperbolic and allow so called „time bomb solutions“ which spreads along bi-characteristic or characteristic hyper surfaces. Actual quantum theories are talking about „inflations“, which blew up the germ of the universe in the very first state. The inflation field due to these concepts are not smooth, but containing fluctuation quanta. The action of those fluctuations create traces into a large area of space. The existence of quantum fluctuations (in a „world“ without a time arrow and without entropy) has been verified by the Casimir and the Lamb shift effects. The standard „big bang“ theory assumes that the creation of the first mass particle (fermion) was the „birthday“ of the universe. This event was caused by an „inflation“ energy field triggered by a „disturbance“, called fluctuations. In the proposed quantum gravity model the „birthday“ of the „granular“, compactly embedded fermion-energy Hilbert (sub-) space H(1) of H(1/2) (coming along with the (kinematical) notions "space", "time", "action", etc.) is interpreted as first disturbance of the purely (pre-universe) boson energy field H(1,ortho) with not existing entropy. The latter one can be interpreted as the (in sync with the Casimir effect) not empty quantum vaccuum; its oscillation is the cosmic background radiation, which contains all features of dynamic energies. With the „birthday“ of the fermions the correspondingly adapted variational representation of the wave equation is then governed by the purely kinematical (fermions) energy Hilbert space H(1), while its underlying initial values are purely (undistorbed) vacuum (CBR, bosons) energy data from H(1,ortho). As a consequence, the wave equation becomes time-asymmetric and the second law of (kinematical) thermodynamics (the entropy phenomenon coming along with the notions „mass“, „time“, „space“ etc.) can be interpreted (and derived from this wave equation) as „action“ principle of the ground state energy to damp and finally eliminate (remedy the deficiency) of any kinematical energy „disturbance“.
change to previous (July 6, 2020) version: p. 1
and, with the words of master Yoda: " may the Force be with you", ...:) . For this purpose this page providing the MS-Word based source documents of some key papers. A small, closed building area to start with could be to go for " a truly proof of the observed non-linear
Landau damping phenomenon based on a variational representation of the
Boltzmann-Landau equations".
| ||||||||||||||||||||||||||||||