Artificial contradiction between cosmology and particle physics: the lambda problem
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 ; 1/10122, while the choice of Planck constant = 1 corresponds to the cosmological scale. This is due to the scale factor of 1061 that converts the Planck scale to the cosmological scale. By choosing the ratio G/c3 = 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/c2 = rg, the gravitational radius of m, is constant. For a quantum black hole we prove that Planck constant ; rg2 ; (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 ; Planck constant ; 1, while the Planck scale gives lambda ; 1/Planck constant ; 10122. This explains the lambda problem. We get two scales: the cosmological quantum black hole (QBH), size ; 1028 cm, and the quantum black hole (qbh) that includes the fundamental particles scale, size ; 10-13 cm, as well as the Planck scale, size ; 10-33 cm.