## 15 Research in Italy

### 15.1 Introduction

In previous sections, we already have encountered several contributions from Italian researchers. The publication
of the 3rd and 4th edition of Einstein’s The Meaning of Relativity in an Italian translation in 1950 and
1953^{268}
seems to have given a boost to research on UFT in Italy. Bruno Finzi went about a fresh derivation of the field equations (287*) to
(290*). He started from the Lagrangian Einstein had used in the 4th Princeton edition of his
book [156*], i.e., [cf. Section 2.3.2, Eq. (83*)]. However, he did not proceed by varying
Einstein’s Lagrangian with regard to the (asymmetric) metric but instead by varying its solenoidal
and irrotational parts, separately [201]. While arriving at the correct result, his method is no
less arbitrary than what Einstein had tried himself. As one of the major figures in research
in the geometry of relativity and unified theories, Finzi became a favoured reviewer of UFT
in Italy [473*, 202, 203*]. He made it very clear that the theory did not predict new empirical
facts: “Until now, no prevision of verifiable new physical facts have emerged from this unified
theory”,^{269}
but remained a firm believer in Einstein’s unified theory:

“The charm of this theory lies in its generality, its simplicity, and, let’s say it clearly, in its
beauty, attributes which the utmost Einsteinian synthesis possesses, more than any other
noted today.” ([473], p. 306)^{270}

^{271}[285*]. Gotusso generalized Horváth’s theory by adding another tensor to the connection: satisfying . With regard to this connection [231]. The Ricci tensor belonging to the connection introduced was not calculated.

### 15.2 Approximative study of field equations

To P. Udeschini we owe investigations closer to
physics.^{272}
In a series of papers, he followed an approximative approach to the field equations of UFT by an expansion
of the fundamental tensor starting from flat space:

From this approximative approach, Udeschini calculated an additional term for the shift of the frequency of a spectral line by the unified field due to with and the polar magnetic field:

is the Newtonian gravitational potential [656, 659*, 660*]. This result depends crucially on the interpretations for the gravitational and electromagnetic fields. If, in place of , the quantity is chosen to describe the gravitational field (potential), then the 2nd term with the magnetic field drops out of (503*) ([660], p. 446). Due to this and to further ambiguities, it makes no sense to test (503*); at best, the constant eventually needed for other experiments could be determined.L. Martuscelli studied the assignment of the electromagnetic tensor to the quantity [389]. In first approximation, , while in second approximation

with a lengthy expression for again containing derivatives of products of and and of products of . A. Zanella wrote down a formal scheme of field equations which in any order n of the approximation looked the same as in the 2nd order field equations. The r.h.s. term in, e.g., contains combination of quantities obtained in all previous orders. Convergence was not shown [723].

### 15.3 Equations of motion for point particles

While Einstein refused to accept particles as singularities of the unified field, E. Clauser, P. Udeschini, and C. Venini in Italy followed Infeld (cf. Section 9.3.3) by assuming the field equations of UFT to hold only outside the sources of mass and charge treated as singularities:

“In the equations for the unified field, no energy-tensor has been introduced: only the
external problem outside the sources of the unified field (masses and charges), assumed to
be singularities, exists” ([659], p. 74).^{273}

As mentioned in Section 10.3.2, Emilio Clauser (1917 – 1986) used the method of Einstein & Infeld in order to derive equations of motion for point particles. In [81], he had obtained an integral formula for a 2-dimensional surface integral surrounding the singularities. With its help, Clauser was able to show that from Einstein’s weak field equations for two or more “particles” all classical forces in gravitation and electromagnetism (Newton, Coulomb, and Lorentz) could be obtained [82]. In his interpretation, stood for the gravitational, for the electromagnetic field.

He expanded the fundamental tensor according to:

where with the vacuum-velocity of light .^{274}In the -th step of approximation, the field equations are: In the symmetrical part of the fundamental tensor, only terms beginning with contribute, in the skew-symmetric part terms from on. The Newtonian and Coulomb forces exerted on on a “particle“ from the others, appear in the terms together with a force independent of distance and not containing the masses of the “particles“. After laborious calculations, the Lorentz force showed up in the terms . This result is the very least one would have expected from UFT: to reproduce the effects of general relativity and of electrodynamics.

In a subsequent paper by Clauser, Einstein’s weak system for the field equations of UFT was developed in every order into a recursive Maxwell-type system for six 3-vectors corresponding to electric and magnetic fields and intensities, and to electric and magnetic charge currents [83]. Quasi-stationarity for the fields was assumed.

C. Venini expanded the weak field equations by help of the formalism generated by Clauser and calculated the components of the fundamental tensor , or rather of , directly up to 2nd approximation: , and [672]. He applied it to calculate the inertial mass in 2nd approximation and obtained the corrections of special and general relativity; unfortunately the contribution of the electrostatic field energy came with a wrong numerical factor [673]. He also calculated the field of an electrical dipole in 2nd approximation [674]. Moreover, again by use of Clauser’s equation of motion, Venini derived the perihelion precession for a charged point particle in the field of a second one. It depends on both the charges and masses of the particles. However, his formula is not developed as far as that it could have been used for an observational test [675]. In hindsight, it is astonishing how many exhausting calculations Clauser and Venini dedicated to determining the motion of point particles in UFT in view of the ambiguity in the interpretation and formulation of the theory.