Artificial contradiction between cosmology and particle physics: the Λ problem

Abstract

It is shown that the usual choice of units obtained by taking G=c=ℏ=1, giving the Planck’s units of mass, length and time, introduces an artificial contradiction between cosmology and particle physics: the lambda problem that we associate with ℏ. We note that the choice of ℏ=1 does not correspond to the scale of quantum physics. For this scale we prove that the correct value is ℏ≈1/10¹²², while the choice of ℏ=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/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=r _g , the gravitational radius of m, is constant. For a quantum black hole we prove that ℏ≈r ² _g ≈(mc)². We also prove that the product Λℏ is a general constant of order one, for any scale. The cosmological scale implies Λ≈ℏ≈1, while the Planck scale gives Λ≈1/ℏ≈10¹²². This explains the Λ 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.