The quantum gravity Immirzi parameter—A general physical and topological interpretation

The paper argues that the Immirzi crucial free parameter of the spin networks theory of quantum gravity represents a definite quantum entanglement correction. In turn, this entanglement may be explained as a consequence of zero measure non-classical topology of the relevant geometrical-topological setting and the associated fiber bundle symmetry group. In particular, we show that the Immirzi parameter may be interpreted as a three-particle probability for quantum entanglement akin to Hardy’s probability for two quantum particles. We give the exact limiting value of the Immirzi parameter to be γ c = ϕ 6 = 0.05572809, where φ = (√ 5 - 1)/2 . Thus, while Hardy’s quantum entanglement was found exactly using Dirac’s conventional quantum mechanics and confirmed experimentally to be P (Hardy) = ϕ 5 = 0.090169943, we have a similar situation for the free parameter of loop quantum gravity, namely, that γ = log 2/(π √ 3 ) = 0.055322 ⇒ φ ⁶ = 0.055728 . This result will be shown to have far-reaching consequences for quantum physics and cosmology.