Universality of the self gravitational potential energy of any fundamental particle

TL;DR

This paper demonstrates that the self gravitational potential energy of any fundamental particle is a universal quantum determined solely by fundamental constants and the cosmological scale, independent of the particle's mass.

Contribution

It introduces a modified Weinberg relation linking quantum and cosmological parameters, establishing the universality of gravitational energy at the particle level.

Findings

Self gravitational potential energy is a universal quantum.

Energy depends only on ar, c, and the cosmological scale R.

Proposes a modified relation maintaining numerical consistency.

Abstract

Using the relation proposed by Weinberg in 1972, combining quantum and cosmological parameters, we prove that the self gravitational potential energy of any fundamental particle is a quantum, with physical properties independent of the mass of the particle. It is a universal quantum of gravitational energy, and its physical properties depend only on the cosmological scale factor R and the physical constants \hbar and c. We propose a modification of the Weinberg's relation, keeping the same numerical value, but substituting the cosmological parameter H/c by 1/R.