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, $\hslash$. 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 $\hslash$. 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, $\beta \ll \hslash$, 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.

5 pages of main text summarising the contents of a talk given at the 4th International Conference on Holography, String Theory and Discrete Approach, Hanoi, 3rd-8th August 2020, plus an appendix giving technical the details of the model. No figures. Published version

References in corpus (8)

• Natural extension of the Generalised Uncertainty Principle
• Generalised uncertainty relations from superpositions of geometries
• Hints of Modified Gravity in Cosmos and in the Lab?
• Hausdorff dimension of a particle path in a quantum manifold
• Model Comparison tests of modified gravity from the Eöt-Wash experiment
• Reconciling a quantum gravity minimal length with lack of photon dispersion
• How does the Planck scale affect qubits?
• A solution to the soccer ball problem for generalised uncertainty relations

Cited by in corpus (8)

• How does the Planck scale affect qubits?
• Generalised Uncertainty Relations from Finite-Accuracy Measurements
• Minimal-length quantum field theory: a first-principle approach
• From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology
• Problems with Modified Commutators
• Fractal properties of particle paths due to generalised uncertainty relations
• Series solution of the time-dependent Schrödinger-Newton equations in the presence of dark energy via the Adomian Decomposition Method
• Towards a Quantum Erlangen Program