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

### Submission summary

 As Contributors: Matthew J. Lake Preprint link: scipost_202009_00001v3 Date submitted: 2021-04-24 09:31 Submitted by: Lake, Matthew J. Submitted to: SciPost Physics Proceedings Proceedings issue: PSI Particle Physics 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 give a simple argument why the quantisation scale for space, and hence for gravity, cannot 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 must be quantised.

###### Current status:
Editor-in-charge assigned

### Author comments upon resubmission

Dear Editor(s),

Please see attached the revised version of the manuscript (v3), which includes the changes referred to in my earlier reply letter. For clarity, these are highlighted in blue text.

With best wishes,

Matt

### List of changes

Footnotes added in blue text.

### Submission & Refereeing History

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

### Strengths

1. Explanations on the points raised in the previous report have been provided in the response letter.

### Weaknesses

1. No significant changes have been made in the resubmitted manuscript.

### Report

The author's detailed response letter is acknowledged. However, given that there have not been significant changes in the resubmitted manuscript, save two footnotes, the status of it remains essentially the same as in the previous review. My recommendation to the Editors is to offer once more the opportunity to the author to improve the manuscript in the directions listed below.

Regarding the comments and explanations in the response letter:

- In noncommutative geometry typically the momenta are also noncommuting. This is true in most specific models and certainly a central aspect of the programme of Madore, as can be seen already in the book "An Introduction to Noncommutative Differential Geometry and its Physical Applications".

- The logical steps taken by the author to argue for the new "scale" are now better explained in the response letter. It still appears that the main claim is made in too strong terms and it must be scaled down to a proposal rather than a certainty (also in the title). Many aspects of the proposal are hard to evaluate without more rigorous explanations about the notion of "smeared points" and "smeared space" and the emergence of spacetime and geometry, or a specific theory. The author states that 150 pages of material where such explanations are made cannot be written in this contribution, which is of course true, however the reader cannot also read these 150 pages just to understand basic aspects where the proposal is based, such as the above. It is asked that some higher degree of precision is aimed at. A specific model and a clear description of the mathematical notions, geometry and the limits mentioned in the response letter is due.

- Points 4 and 5 of the previous report are answered in some detail in the response letter, to the extent that they can be addressed. Since, as far as I understand, there is no page limit in this contribution, I suggest that the author suitably implements these explanations in the manuscript.

### Requested changes

1- The issues of Lorentz invariance and emergence of spacetime (and general relativity therefore) should be discussed in more detail in the manuscript, building on the explanations in the response letter.

2- The basic notions used, such as "smeared space", "points" and the like, should be defined in more precise terms, essentially expanding and making good sense of footnote 2 in the manuscript. A specific, preferably 3+1 dimensional, model/theory where the proposal is realized should be discussed.

• validity: ok
• significance: ok
• originality: ok
• clarity: low
• formatting: reasonable
• grammar: perfect