Das Korrespondenzprinzip in der Kosmologie. II. Klassische und relativistische Darstellungen der Weltmodelle

According to the equivalence between the FRIEDMANN equation of relativistic cosmology and the condition for the time-independence H = o of the HAMILTON ian H of an isotropic particle-system in the NEWTON ian mechanics (which equivalence is proved in the part I of our paper) we construct the corresponding classical HAMILTON ians to the relativistic world-models. Each cosmological model which is resulting from a physically meaningful gravitation theory must give a FRIEDMANN equation as the cosmological formulation of the time-independence condition of the energy H for the corresponding NEWTON ian N-particle system. In general relativity, EINSTEIN's field equations are including EINSTEIN's strong principle of equivalence and are giving the constance f = o and M = o of the gravitation-number f and of the mass M of the universe additional to FRIEDMANN's equation. – In special relativity, we have fM = o and this MILNE -universe is possessing a NEWTON ian and a general relativistic interpretation, too. – However, if the postulate together with the “cosmological principle” other principles about the world structure, too (p. e. MACH'S or DIRAC'S principle or the “perfect cosmological principle” by the steady-state cosmology), then EINSTEIN'S weak principle of equivalence can be fulfilled, only. In these world models the gravity-mass fM becomes a function of the cosmic time t [d/dt(fM) ± o] and this variability of fM is compatible with the constance H = o of the energy H of the NEWTON ian particle-system. For flat three-dimensional cosmological spaces (with H = Ḣ = o) a creation of rest-mass (M > o) is possible. This creation is the pecularity of the steady-state cosmos (with M > o, f = o) and of JORDAN'S cosmos (with M > o, f < o). The MACH -EINSTEIN -doctrine about the perfect determination of the inertia and of the space-time-metric by the cosmic gravitation is founded on the substitution of the NEWTON ian HAMILTON ian by a GAUSS -RIEMANN ian gravitation potential U^*(r_AB' v_AB) (TREDER 1972). Therefore, the FRIEDMANN equation for a universe with MACH'S principle is resulting from the analytical expression of the time-independence of this RIEMANNian potential U* = 0. In the case of such MACH-EINSTEIN's-Universes EINSTEIN'S condition 3fM = c8r between the mass A4 and the radius Y of the universe is valid additional to FRIEDMANN'S equation. For these universes, the EINSTEIN condition determinates the instantaneous value of the gravitation-number f. - The explicite form of the conditions H = o or h' = o gives the equation of motion for the cosmic fundamental particles with attraction and repulsion forces, generally.     

Gravitation und weitreichende schwache Wechselwirkungen bei Neutrino-Feldern Gedanken zu einer Theorie der solaren Neutrinos

The strange non-evidence of the solar-neutrino current by the experiments of DAVIS et al. postulates a fundamental revision of the theory of weak interactions and of its relations to gravitation theory. (We assume that the astrophysical stellar models are not completely wrong.) – Our paper is based on PAULI 's grand hypothesis about the connection between weak and gravitational interactions. According to PAULI and BLACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) FERMI -interaction constant and according to the hypotheses of PAULI, DE BROGLIE , and JORDAN the RIEMANN -EINSTEIN gravitational metric g_ik is fusioned by the four independent WEYL ian neutrino fields (β-neutrinos and β-antineutrinos, μ-neutrinos and μ-antineutrinos). This fusion gives four reference tetrads h_i^A(x^l) as neutrino-current vectors, firstly. Then, the metric g_ik is defined by the equation g_ik = η_AB h_i^Ah_η^B according to EINSTEIN 's theory of tele-parallelism in RIEMANN ian space-times. The relation of the gravitation field theory to FERMI 's theory of weak interactions becomes evident in our reference-tetrads theory of gravitation (TREDER 1967, 1971). – According to this theory the coupling of the gravitation potential h_i^A with the matter T_ιⁱ is given by a potential-like (FERMI -like) interaction term. In this interaction term two WEYL spinor-fields are operating on the matter-tensor, simultanously. Therefore, the gravitation coupling constant is PAULI 's square of the FERMI -constant. Besides of the fusion of the RIEMANN -EINSTEIN metric g_ik by four WEYL spinors we are able to construct a conformal flat metric ĝ_ik = ϕ²η_ik by fusion from each two WEYL spinors. (This hypothesis is in connection with our interpretation of EINSTEIN 's hermitian field theory as a unified field-theory of the gravitational metric g_ik and a WEYL spinor field [TREDER 1972].) Moreover, from the reference-tetrads theory is resulting that the WEYL spinors in the “new metric” ĝ_ik are interacting with the DIRAC matter current by a FERMI -like interaction term and that these WEYL spinors fulfil a wave equation in the vacuum. Therefore, we have a long-range interaction with the radiced gravitational constant \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {\frac{{tm^2 }}{{hc}}} $\end{document} as a coupling constant. That means, we have a long-range interaction which is 10¹⁸ times stronger than the gravitation interaction. – However, according to the algebraic structure of the conform-flat this long-range interaction is effective for the neutrino currents, only. And for these neutrinos the interaction is giving an EINSTEIN -like redshift of its frequences. The characteristic quantity of this “EINSTEIN shift” is a second gravitation radius â of each body: N = number of baryons, m = mass of a baryon.) This radius â is 10¹⁸ times larger than the EINSTEIN -SCHWARZSCHILD gravitation radius a = fM/c²: But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝ_ik is given by an “ansatz” which is analogous to the ansatz for determination of strong gravitational fields in our tetrads theory. That is by an ansatz which includes the “self-absorption” of the field by the matter. For all celestial bodies the “weak radius” â is much greater than its geometrical dimension. Therefore, a total EINSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long-range weak interaction potential ĝ_ik = ϕ²η_ik. That means, the cosmic neutrino radiation becomes very weak and unable for nuclear reactions. Theoretically, our hypothesis means an ansatz for unitary theory of gravitation and of weak interaction. This unitary field theory is firstly based on EINSTEIN 's hermitian field theory and secondly based on our reference-tetrads theory of gravitation.     

Genauigkeitserwartung photographischer Sternpositionen bei geschlossener Blockausgleichung

The theoretical accuracy of photographically determined star positions is studied, based on the assumption that the whole sphere is covered by a net of fields, 4 plates each, and that all the plates are adjusted simultaneously in a closed block. The influence of the number of fields on the accuracy is estimated by computing schematized spheric blocks containing only a few reference stars. If the plates are taken with a focal length of 2 meters, the block will consist of 2500 fields, and a mean accuracy of star position of 0.1 can be expected.     

Groundwater Resources In Hard Rock; Experiences from The Hvaler Study,Southeastern Norway

Investigations in a newly constructed subsea road tunnel in the Iddefjord granite at Hvaler and test-pumping of boreholes on land indicate that a topographic or geophysical anomaly is no guarantee of a substantially transmissive fracture zone. Many prominent fracture zones appear to have depressed transmissivity due to secondary swelling-clay mineral infillings. No current geophysical technique can adequately distinguish these zones from transmissive ones. Given that siting of boreholes on the basis of geology alone can be unreliable, hydrogeologists should concentrate on quantifying the chances of a successful boring, and optimizing those chances by sensible location, favourable borehole orientation and use of artificial enhancement techniques.