SciPost Submission Page
Why space must be quantised on a different scale to matter
by Matthew J. Lake
|As Contributors:||Matthew J. Lake|
|Date submitted:||2020-09-01 20:15|
|Submitted by:||Lake, Matthew J.|
|Submitted to:||SciPost Physics Proceedings|
|Proceedings issue:||4th International Conference on Holography, String Theory and Discrete Approach in Hanoi|
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, $\beta \neq \hbar$, 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.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 2020-10-19 Invited Report
1. The basic idea is interesting.
2. applications related to the cosmological constant are given.
3. Tries to address some major issues in Physics.
1. Important aspects are not clearly presented.
2. No proposals to test the formalism are provided.
3. There are mathematical issues that must be clarified.
In the manuscript the author investigates the possibility that space-time is quantized on a different scale as compared to matter. The manuscript may be publishable in SciPost Physics Proceedings if the author would fully consider the following points:
1. The meaning of the term "scale" is not clear. The quantization of matter takes place on the energy level; the quantization of gravity, if possible, would involve a geometrical scale. These two scales are not overlapping, and they are distinct, unless one introduces an energy scale for gravity. The meaning of "scale" in the present approach must be clarified.
2. How does the author defines a point?
3. Usually one can associate to a point the value of a function or of an operator, and not the function itself, so that in the point x_0 we may consider the couple (x_0,f(x_0)), where f is an arbitrary function or operator, but not the couple (x_0,f(x)), where x takes all real (or complex) values, let's say. The procedures of associating entire functions (operators), be they delta or of other type, to points, must be clearly explained.
4. The author also mention "geometry wave"(s), to which the rules of standard quantum mechanics are applied, without much justification. Using Eq. (2) for the "geometry wave"(s) is at least problematic. One must make clear what is the meaning of geometry wave in the present context, and why should they obey exactly the rules of quantum mechanics for matter.
5. The "quantum of action for geometry", given by Eq. (6), is an extremely small quantity, which looks very difficult to be measured directly, or even indirectly. Still the authors may suggest some other observational effects that could provide, at least in principle, some (realistic) observational signatures for $\beta$.