Gravity may play a bigger role in the formation of elementary particles than scientists used to think. A team of physicists from RUDN University obtained a solution to describe a semi-classical model of particle-like waves. They also calculated the ratio between the particles' gravitational interactions and their charge interactions. The results of the study were published in the journal Universe.
Due to their small size, the gravitational pull between elementary particles (electrons, protons, and neutrons) is weaker than the Coulomb force, i.e., the attraction and repulsion determined by the charge. For example, negatively charged electrons move around the nuclei of an atom containing positively charged protons. Thus, the ratio of Newtonian attraction to Coulomb repulsive force (or γ) is negligible. However, at the Planck scale, i.e. at a distance of about 1.6 x 1035 meters, these forces become comparable. A team of physicists from RUDN University has found a solution to an existing model that corresponds to particles in the Planck range.
The team used a semi-classical model based on the equations of the electromagnetic field. Solutions that contain several particles as well as solitons (stable solitary waves). In such equations, gravity is usually not considered, but is replaced by an almost arbitrarily chosen nonlinear correction. This is the main problem with these models. However, this problem can be solved by adding equations from three fundamental fields to the system. Then, according to the requirements of quantum invariance (preventing the transformation of physical values and fields from changing at the same time), the nonlinear form is strictly defined. The team from RUDN University used this method to find a solution that matches the characteristics of a typical elementary particle. The existence of such a solution would confirm the fundamental role of gravity in particle formation.
The team failed to find a charge and mass γ
"Even though we tried to calculate γ