Three findings to model a quantum-gravitational theory

TL;DR

This paper demonstrates that fundamental particle properties and gravitational relations can be derived from a semi-classical quantum gravity model, unifying cosmological constants, particle sizes, and masses through the Schrödinger-Newton framework.

Contribution

It introduces a semi-classical gravity model that links cosmological constants, particle mass, and size, providing new insights into quantum-gravitational theory and fundamental particle properties.

Findings

Proves the equivalence of Zeldovich and Weinberg expressions for cosmological constants.

Identifies the critical mass balancing quantum spreading and gravitational collapse.

Shows particles acquire a size equal to their Compton wavelength, explaining their mass and size.

Abstract

In 1967 Zeldovich expressed the cosmological constant lambda in terms of G, m and h, the gravitational constant, the mass of a fundamental particle and Plancks constant. In 1972 Weinberg expressed m in terms of h, G, the speed of light c and the Hubble parameter H. We proved that both expressions are identical. We also found proportionality between c and H. The critical mass balancing the outward quantum mechanical spreading of the wave function, and its inward gravitational collapse, has been recently estimated. We identify this mass with Zeldovich and Weinberg mass. A semi classical gravity model is reinforced and provides an insight for the modelling of a quantum-gravitational theory. The time evolution of the peak probability density for a free particle, a wave function initially filling the whole Universe, explains the later geometrical properties of the fundamental particles. We prove that they end up acquiring a constant size given by their Compton wavelength. The size of the fundamental particles, as well as their mass, is explained. The three findings converge: Newton laws of motion and gravitation, while explaining Zeldovich and Weinberg relations, also define the mass and size of the fundamental particles when using the Schrodinger-Newton equation.