Why space could be quantised on a different scale to matter

TL;DR

This paper argues that the quantisation scale for space and gravity may differ from that of matter, which could resolve the vacuum energy discrepancy and be empirically tested through cosmic expansion measurements.

Contribution

It proposes that space and gravity might have a different quantum of action than matter, offering a potential solution to the vacuum energy problem.

Findings

Different quantisation scales can reconcile observed vacuum energy.

Measuring cosmic expansion can determine the geometric quantisation scale.

Assuming a smaller geometric quantum reduces the vacuum energy discrepancy.

Abstract

The scale of quantum mechanical effects in matter is set by Planck's constant, $\hbar$. 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 $\hbar$. 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, $\beta \ll \hbar$, 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.