Artificial contradiction between cosmology and particle physics: the lambda problem

TL;DR

This paper addresses the lambda problem by analyzing the artificial contradiction caused by the conventional units in cosmology and particle physics, proposing a scale-aware approach that clarifies the relationship between quantum and cosmological scales.

Contribution

It introduces a scale-dependent interpretation of the Planck constant and related physical quantities, resolving the lambda problem and clarifying the connection between quantum and cosmological scales.

Findings

The choice of units affects the perceived contradiction between cosmology and particle physics.

A scale factor of 10^61 converts the Planck scale to the cosmological scale.

The product of lambda and Planck constant is a universal constant of order one.

Abstract

It is shown that the usual choice of units obtained by taking G = c = Planck constant = 1, giving the Planck units of mass, length and time, introduces an artificial contradiction between cosmology and particle physics: the lambda problem that we associate with Planck constant. We note that the choice of Planck constant = 1 does not correspond to the scale of quantum physics. For this scale we prove that the correct value is Planck constant \hbar; 1/10^122, while the choice of Planck constant = 1 corresponds to the cosmological scale. This is due to the scale factor of 10^61 that converts the Planck scale to the cosmological scale. By choosing the ratio G/c^3 = constant = 1, which includes the choice G = c = 1, and the momentum conservation mc = constant, we preserve the derivation of the Einstein field equations from the action principle. Then the product Gm/c^2 = rg, the gravitational radius of m, is constant. For a quantum black hole we prove that Planck constant \hbar; rg^2 \hbar; (mc)^2. We also prove that the product lambda x Planck constant is a general constant of order one, for any scale. The cosmological scale implies lambda \hbar; Planck constant \hbar; 1, while the Planck scale gives lambda \hbar; 1/Planck constant \hbar; 10^122. This explains the lambda problem. We get two scales: the cosmological quantum black hole (QBH), size \Lambda; 10^28 cm, and the quantum black hole (qbh) that includes the fundamental particles scale, size \Lambda; 10^-13 cm, as well as the Planck scale, size \Lambda; 10^-33 cm.