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 1953268 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 . 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.” (, p. 306)270
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: as: 210*) and (211*) already obtained by Einstein and Straus. The field equations split into two groups related either to the gravitational potential () or to the electromagnetic field . In the identification by Udeschini, i.e., , where is a constant, the field equations then were: [653, 654, 657]), (500*) is replaced by:  . As a result, in the 2nd approximation the field equations for the gravitational and electromagnetic fields now intertwine. From his more general approach, Udeschini then reproduced the special case Schrödinger had treated in 1951 , i.e., : An electromagnetic field, small of first order, generates a gravitational field small of second order. The reciprocal case, i.e., a gravitational field small of first order cannot influence an electromagnetic field of second order .
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:[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*) (, 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 . In first approximation, , while in second approximation.
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” (, 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 , 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 . In his interpretation, stood for the gravitational, for the electromagnetic field.
He expanded the fundamental tensor according to:274 In the -th step of approximation, the field equations are:
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 . 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 . 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 . He also calculated the field of an electrical dipole in 2nd approximation . 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 . 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.