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

Abstract The strange non‐evidence of the solar‐neutrino current by the experiments of D AVIS 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 P AULI 's grand hypothesis about the connection between weak and gravitational interactions. According to P AULI and B LACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) F ERMI ‐interaction constant and according to the hypotheses of P AULI, DE B ROGLIE , and J ORDAN the R IEMANN ‐E INSTEIN gravitational metric g ik is fusioned by the four independent W EYL 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 A h η B according to E INSTEIN 's theory of tele‐parallelism in R IEMANN ian space‐times. The relation of the gravitation field theory to F ERMI 's theory of weak interactions becomes evident in our reference‐tetrads theory of gravitation (T REDER 1967, 1971). – According to this theory the coupling of the gravitation potential h i A with the matter T ι i is given by a potential‐like (F ERMI ‐like) interaction term. In this interaction term two W EYL spinor‐fields are operating on the matter‐tensor, simultanously. Therefore, the gravitation coupling constant is P AULI 's square of the F ERMI ‐constant. Besides of the fusion of the R IEMANN ‐E INSTEIN metric g i k by four W EYL spinors we are able to construct a conformal flat metric ĝ i k = ϕ 2 η i k by fusion from each two W EYL spinors. (This hypothesis is in connection with our interpretation of E INSTEIN 's hermitian field theory as a unified field‐theory of the gravitational metric g i k and a W EYL spinor field [T REDER 1972].) Moreover, from the reference‐tetrads theory is resulting that the W EYL spinors in the “new metric” ĝ i k are interacting with the D IRAC matter current by a F ERMI ‐like interaction term and that these W EYL 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 10 18 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 E INSTEIN ‐like redshift of its frequences. The characteristic quantity of this “E INSTEIN shift” is a second gravitation radius â of each body:\documentclass{article}\pagestyle{empty}\begin{document}$$ \hat a = \sqrt {\frac{{hc}}{{fm^2 }}} \frac{{fM}}{{c^2 }} = \sqrt {\frac{{hc}}{{fm^2 }}} \;a, $$\end{document}N = number of baryons, m = mass of a baryon.) This radius â is 10 18 times larger than the E INSTEIN ‐S CHWARZSCHILD gravitation radius a = fM/c 2 :\documentclass{article}\pagestyle{empty}\begin{document}$$ \hat a = \sqrt {\frac{{hc}}{{fm^2 }}} \frac{{fM}}{{c^2 }} = \sqrt {\frac{{hc}}{{fm^2 }}} \;a,\;M \approx Nm. $$\end{document} But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝ i k 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 E INSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long‐range weak interaction potential ĝ i k = ϕ 2 η i k . 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 E INSTEIN 's hermitian field theory and secondly based on our reference‐tetrads theory of gravitation.