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

Abstract

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 $\varphi = (\sqrt 5 - 1)/2$. 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

$\gamma = \log 2/(\pi \sqrt 3 ) = 0.055322 \Rightarrow \varphi ^6 = 0.055728$

. This result will be shown to have far-reaching consequences for quantum physics and cosmology.