If quantum mechanics can provide quantitative expressions of forces in conformity with the work of Erhenfest and the principle of correspondence, recognized quantitative expressions for nuclear and weak forces do not currently exist. In addition, the four basic forces do not depend on temperature, since measured in vacuum between particles.
In one of his books, Abraham Pais recalled a comment by Rutherford during the 1914-1919 period: “the Coulomb forces dominate if v (speed of alpha particles) is sufficiently small”, evidencing by these words the velocity-dependence of the strong-nuclear force. However, since Rutherford did not apparently refer to temperature, optimal conditions for nuclear fusion do not necessarily arise in disordered configurations characterized by extremely high temperatures, such as those encountered in stars like the sun. Even compared with galaxy formation, hot fusion in many stars seems the slowest and most inefficient physical phenomenon in the universe, because the sun’s ten billion year lifetime has an order of magnitude similar to the age of the universe, this circumstance having been highly beneficial for the life on earth.
Although not based on equations, Rutherford’s conclusion constitutes the essence of the “cold” approach to nuclear fusion and reactions starting from moderate energy levels, instead of extreme temperatures hardly controlling with precision the physical parameters ruling nuclear phenomena. In this view, a better theoretical understanding of these parameters will help nuclear technologies.
B. Theoretical antecedents
Eddington mentioned the concept of asymmetric affine connection in 1921 and pointed out applications in microphysics, but he did not pursue this idea . In 1922, Elie Cartan introduced geometric torsion, as the antisymmetric part of an asymmetric affine connection. In May 1929, Cartan wrote a letter to Einstein in which he recommended the use of the differential formalism he developed, but Einstein did not follow Cartan’s advice.
Between 1944 and 1950, J. Mariani published four papers dealing with astrophysical magnetism and introduced an “ansatz” structurally similar to that used in the present theory. The German word “ansatz”, used by Ernst Schmutzer (correspondence), refers to a supposed relationship between fields of distinct origin, for example geometric contrasting with physical. Einstein also used an ansatz when he identified gravitation with the 4-space metric, but he did not put it in the form of an equation, presumably because being trivial.
The organization of the paper is the following: Section II details the Lagrangian formulation and the calculus of variations. Section III is about field equations and quantitative expressions of forces. Section IV introduces the short-range force between charged particles, first referred to as strong-nuclear between nucleons. Section V is on Yukawa and complexity. Section VI details the short-range forces in both systems electron-proton and electron-neutron, evidencing a weak nuclear mechanism in LENR technologies.