Legge di moto nell’ultima teoria unitaria einsteiniana

Riassunto

Si deduce la legge di movimento di particelle, tra le quali si esercitano azioni gravitazionali ed elettromagnetiche, dalle equazioni di campo della teoria unitaria einsteiniana del 1953; si ritrovano cosi tutte le forze classiche dei due campi e cioè la gravitazionale newtoniana, la elettrostatica coulombiana e quella elettrodinamica di Lorentz; si hanno in più forze meno rilevanti che rappresentano l’interazione fra i due campi.

Summary

In this paper the author demonstrates that, in the motion equations of a particle, deduced from the asymmetric field equations of Einstein’s unified theory of 1953, are present the most significant forces of classical physics, that is the Newtonian force of gravity, the Coulombian electrostatic force and Lorentz’s electrodynamicforce. The author has reached this result using an integral formula previously found by him. This formula originates from the field equations of the unified theory, and strictly determines the motion of two or more particles, once assumed the singularities representing them. Prom this formula are obtained the equations of motion of particles to any degree of approximation, applying the subsequent steps method introduced by Einstein and Infeld in the gravitational problem; i.e. the fundamental tensor is expanded into an appropriate series of functions, arranged according to the integer and positive powers of λ which is the reciprocal of the light velocityin vacua as measured by an inertial frame; consequently the vector to be integrated of the found formula is expanded into a series of integer and positive powers of λ; thus recurrent motion equations are obtained. Assuming that the lowest power of λ which in the expansion of the fundamental tensor follows that of zero degree, is λ² (as in the gravitational theory), the integral formula begins to have a meaning when the factors of λ⁴ are not left aside; the motion equations of the first step therefore consist in the terms of fourth degree with respect to λ⁴. The author deduces in this way the motion equations of the first step regarding a system of two or more particles; considering also the factors of λ⁶, he determines a significant part of the equations of motion by subsequent steps. The first step equation (obtained solely by means of λ⁴ coefficients) determines the motion of a particle subject to the Newtonian force of gravity and the Coulombian electrostatic force, exerted by the remaining particles, and to a minor force representing the interaction between the gravitational and electromagnetic fields; thus one finds again the equation that in classical physics governs the motion of charged and heavy particles, if one leaves aside the interaction forces and the Lorentz force, which is of a lower magnitude order than the previous forces, as is well known. The Coulombian electrostatic force is not obtained however selecting the elementary harmonic function as potential of the electrostatic field, but a biharmonic function, just as is requested by the electromagnetic equations which ensue in the first step from the field equations. That is. the author has chosen as electrostatic potential of each particle the biharmonic function which is the sum of the classical electrostatic potential (expressed by the elementary harmonic function), with a general polynomial of second degree concerning the distance from the acting particle; the linear term of this polynomial is essential as, without it, the Coulombian force is not present in the motion equations of the first step. This additional term of the electrostatic potential begins to show both the discrepancy between the classical electromagnetic model and that implied in the 1953 formulation of Einstein’s unified theory and the interaction between gravity and electricity, thanks to a coefficient proportional to the multiplication of Cavendish constant by the charge of the particle. All the above explains the negative result obtained by Callaway in the research of the equation of motion of the first step, limited to the coefficients of λ⁴ and deduced from the 1953 formulation of the unified theory; this author adopts as a potential merely the elementary Coulomb one, leaving thus aside the additional term. The factors of λ⁶ can be grouped into three addenda: one is the sum of the interaction terms between gravitation and electricity; another addendum is the sum of terms which represent the reaction exerted on each particle by the gravitational and electromagnetic field produced by the particle itself; finally the third addendum represents Lorentz’s electrodynamic force.