Elmo Benedetto

El Naschie Ε-Infinity Cantorian Space-time, Fantappie's Group and Applications in Cosmology

In this paper starting from the Fantappie group we will consider its properties in connection with E-infinity Cantorian space-time. The cosmological consequences of such extension appear relevant, since thanks to the Fantappie group, the model of the Big Bang and that of stationary state become compatible. In particular, if we abandon the idea of the existence of only one time gauge, since we do not see the whole Universe but only a projection, the two models become compatible. In the end we will see the effects of the projective fractal geometry also on the galactic and extra-galactic dynamics; in particular, we analyze the effects of Fantappies transformation on gravitational lenses and we will see that the gravitational lensing effects could be a good tool to verify this theory.

Unruh temperature with maximal acceleration

In this paper, we modify the geometry of Rindler space so as to include an upper limit on the acceleration. Caianiello and his collaborators, in a series of papers, have analyzed the corrections to the classical spacetime metrics due to the existence of a maximal acceleration. Our goal is to derive, in this context, in a very simple way, the so-called Unruh temperature.

Some remarks about underused Loedel diagrams

We emphasize that it can be didactically very useful for students to realize how a space–time diagram of an observer, moving with a constant velocity with respect to another observer, can be obtained easily by means of a standard matrix of rotation, without recourse to imaginary axes and angles. These diagrams were introduced for the first time by Loedel and their main advantage over Minkowski diagrams is that a scale factor is not necessary to convert the units of an observer to those of another observer. We show this well-known property of Loedel diagrams using a new geometric approach.

A little help for a better understanding and application of Faraday's law

In this letter, we examine Faradays law of induction, analysing the electromotive force generated by a Lorentz force and the one generated by an electric field due to a changing magnetic field. We obtain the result in a didactically simple and appealing way. The final formula is derived considering explicitly the dependence of the magnetic field on the space coordinates, which is often neglected in standard textbooks.

Projective Special Relativity

The structural facets of projective relativity are there investigated, in particular the physical meaning of hypersphere and its projection centered on an observer.

Point, Fluid and Wave Mechanics

Projective relativity mechanics is here developed in its classical cases and the meaning of the physical quantities in SPR is investigated

Steps Towards the De Sitter Relativity

It is here introduced the Erlangen program for Physics by G. Arcidiacono, where the three relativities (Galilei, Poincare and de Sitter) are a groupal “matryoshka”, i.e., three description levels of physical phenomena. The Arcidiacono transformations for the de Sitter group and the cosmological consequences are also introduced.

De Sitter Relativity: A Sixty-Year-Long Story

In this chapter we sketch out a historical overview of de Sitter Relativity, focusing on the projective version developed by the Italian mathematicians L. Fantappie and G. Arcidiacono in the early 1950s. In addition, we analyze tendencies and problems connected to de Sitter Relativity in contemporary physics.

Projective General Relativity (PGR)

Einstein equations are generalized for de Sitter 5-dimensional space, and their local projections (PGR), with some important cosmological considerations, are studied.

Navier-Stokes Equation and Computational Scheme for Non-Newtonian Debris Flow

This paper proposes a computational approach to debris flow model. In recent years, the theoretical activity on the classical Herschel-Bulkley model (1926) has been very intense, but it was in the early 80s that the opportunity to explore the computational model has enabled considerable progress in identifying the subclasses of applicability of different sets of boundary conditions and their approximations. Here we investigate analytically the problem of the simulation of uniform motion for heterogeneous debris flow laterally confined taking into account mainly the geological data and methodological suggestions derived from simulation with cellular automata and grid systems, in order to propose a computational scheme able to operate a compromise between “global” predictive capacities and computing effort.