# Why space could be quantised on a different scale to matter

### Submission summary

 As Contributors: Matthew J. Lake Preprint link: scipost_202009_00001v4 Date accepted: 2021-08-04 Date submitted: 2021-07-08 11:09 Submitted by: Lake, Matthew J. Submitted to: SciPost Physics Proceedings Proceedings issue: Review of Particle Physics at PSI Academic field: Physics Specialties: Quantum Physics Approaches: Theoretical, Phenomenological

### 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.

Published as SciPost Phys. Proc. 4, 014 (2021)

Dear Editor(s), Please see attached the revised version of the manuscript (v4). I found it very difficult to include the requested amount of technical detail within the essay style flow of the original draft. Therefore, I included it in a separate appendix. This may be regarded as a "half-way house" between the 5 page non-technical summary of the model given in the main text, which is suitable for a wide and diverse audience, such as that attending the Hanoi conference for which it was originally written, and the 150+ page derivation of the full mathematical formalism given in refs. [16], [18] and [19]. I hope that this satisfies the remaining concerns of the referee. For clarity, all changes from v3 of the manuscript are highlighted in blue. Best wishes - Matt

### List of changes

Technical detail of the model has been added in a new appendix. Minor changes of language, in accordance with the referee's previous recommendations, have also been made within the main text. All changes from the previous version of the manuscript are highlighted in blue.

### Submission & Refereeing History

Resubmission scipost_202009_00001v4 on 8 July 2021
Resubmission scipost_202009_00001v3 on 24 April 2021
Resubmission scipost_202009_00001v2 on 3 February 2021
Submission scipost_202009_00001v1 on 1 September 2020

## Reports on this Submission

### Anonymous Report 1 on 2021-7-18 (Invited Report)

• Cite as: Anonymous, Report on arXiv:scipost_202009_00001v4, delivered 2021-07-18, doi: 10.21468/SciPost.Report.3254

### Report

The author has made an appreciable effort to improve the manuscript. The added appendix provides technical justification for arguments appearing in the main text. Statements now appear in more appropriate form. Given that this is a proceedings contribution, the manuscript can be accepted for publication in the proceedings volume of the 4th International Conference on Holography, Hanoi, Vietnam in its current form.

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