Why space could be quantised on a different scale to matter

Abstract

The scale of quantum mechanical effects in matter is set by Planck’s constant, \hbar ℏ . This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and hence for gravity, may not be equal to \hbar ℏ . Indeed, assuming a single quantisation scale for both matter and geometry leads to the `worst prediction in physics’, namely, the huge difference between the observed and predicted vacuum energies. Conversely, assuming a different quantum of action for geometry, \beta \ll \hbar β ≪ ℏ , allows us to recover the observed density of the Universe. Thus, by measuring its present-day expansion, we may in principle determine, empirically, the scale at which the geometric degrees of freedom should be quantised.