On the Discrete Version of the Schwarzschild Problem

We consider a Schwarzschild type solution in the discrete Regge calculus formulation of general relativity quantized within the path integral approach. Earlier, we found a mechanism of a loose fixation of the background scale of Regge lengths. This elementary length scale is defined by the Planck scale and some free parameter of such a quantum extension of the theory. Besides, Regge action was reduced to an expansion over metric variations between the tetrahedra and, in the main approximation, is a finite-difference form of the Hilbert–Einstein action. Using for the Schwarzschild problem a priori general non-spherically symmetrical ansatz, we get finite-difference equations for its discrete version. This defines a solution which at large distances is close to the continuum Schwarzschild geometry, and the metric and effective curvature at the center are cut off at the elementary length scale. Slow rotation can also be taken into account (Lense–Thirring-like metric). Thus, we get a general approach to the classical background in the quantum framework in zero order: it is an optimal starting point for the perturbative expansion of the theory, finite-difference equations are classical, and the elementary length scale has quantum origin. Singularities, if any, are resolved.

Representative Elementary Length to Measure Soil Mass Attenuation Coefficient

With increasing demand for better yield in agricultural areas, soil physical property representative measurements are more and more essential. Nuclear techniques such as computerized tomography (CT) and gamma-ray attenuation (GAT) have been widely employed with this purpose. The soil mass attenuation coefficient (μs) is an important parameter for CT and GAT analysis. When experimentally determined (μes), the use of suitable sized samples enable to evaluate it precisely, as well as to reduce measurement time and costs. This study investigated the representative elementary length (REL) of sandy and clayey soils forμesmeasurements. Two radioactive sources were employed (241Am and137Cs), three collimators (2–4 mm diameters), and 14 thickness (x) samples (2–15 cm). Results indicated ideal thickness intervals of 12–15 and 2–4 cm for the sources137Cs and241Am, respectively. The application of such results in representative elementary area (REA) evaluations in clayey soil clods via CT indicated thatμesaverage values obtained forx > 4 cm and source241Am might induce to the use of samples which are not large enough for soil bulk density evaluations (ρs). As a consequence,ρsmight be under- or overestimated, generating inaccurate conclusions about the physical quality of the soil under study.

Sur l'existence d'une longueur élémentaire et d'un intervalle de temps élémentaire

We have briefly examined several studies which have been made concerning the introduction of an elementary length l0 and an elementary time interval t0 into physical theories. We have discussed the arguments which we have found, arguments formulated by other authors, and which support the hypotheses concerning the existence of l0 and of t0. A finite difference equation is proposed and the solutions of some problems of movement in one dimension are given.

Phänomenologische Betrachtungen zum Strahlungsgesetz / A Phenomenological Extension of the Radiation Law

The phenomenological inclusion of an elementary length leads to a generalized radion law, which includes Plancks and Eulers laws as limiting cases.

A Possible Role of Universal Length in the Theory of Weak Interactions

The discovery and role of already existing universal constants h and c in modern physics have been reviewed from a particular point of view. This viewpoint is characterized by a pattern of logic in terms of which one may possibly find a new universal constant, i.e. the elementary length. One of the main objectives of this paper is to find out whether the elementary length introduced this way would resolve inherent difficulties in relativistic quantum field theory. This has been explicitly studied in terms of the nonlocal field theory in connection with the CP violating kaon decay. This produced a relation [Formula: see text] which leads, on the one hand, to a consistent explanation of the possible mechanism of CP violation and, on the other hand, gives a result which is most probably the first direct link between the elementary length (nonlocality) and an experiment without having the inherent disorder in the small distance behavior in quantum field theory.