**Author:**

(1) Ahmed Farag Ali, Essex County College and Department of Physics, Faculty of Science, Benha University.

## Table of Links

Space-time quanta and Becken Universal bound

Space-time quanta and Spectral mass gap

Conclusion, Acknowledgments, and References

## VI. PHENOMENOLOGICAL IMPLICATIONS

Phenomenological studies expect to prop information about dark matter at ILC [73]. We intuit that the fundamental structure of dark matter/energy is the space-time quanta. Previous studies suggested that a minimal length of measurements forms a dark matter candidate [74]. There is an interesting observation about the 24-cell. All permutations of vertices in 24-cell are given by factorial 24! = 6.2044 x 1023 which is quite close to the Avogadro number (6.0221 x 1023) which determines the "approximate" number of nucleons per gram of matter based on thermodynamical and statistical computations.

The relative error between the two values is around 2.9%. This may shed light on the geometric meaning of the mole unit. The number of observable stars in the universe is between 102 to 1023! [75, 76] which is again close to the number predicted by 24-cell. According to the interpretation of creating a mass of space-time quanta by vanishing uncertainty, the minimal length is expected to correspond to the electroweak length scale at which masses are created. Therefore, the minimal length is determined from the measured Higgs mass (~ 125.35 GeV/c%) [76] and substituting it in Eq. (9) that implies a minimal length as follows:

K LI～10-18m

This would give the length scale at which uncertainty vanishes to form a mass of space-time quanta. In that sense, we reinterpret the Higgs mechanism as a state in which the uncertainty vanishes to form the mass of space-time quanta. The electroweak length scale determines the unique length of the 24-cell. The effective minimal length has been interpreted recently as a charge radius of scattering for every physical particle [77]. Recent studies show that the minimum measurable charge radius measured so far is around 10-18 for the neutrinos, Higgs, W-bosons, and Z-boson, [76, 78, 79] which is consistent with our interpretations.

One notice that the permutations of the 16-cell that forms the gluons part of the 24-cell are equal to factorial 8! and the permutation of tesseract that represents Higgs, photon, W, Z, quarks, and leptons is given by factorial 16!. Based on our model, the 16-cell represents the Planck scale and the tesseract represents the electroweak scale. The multiplications of their permutations (8!16! = 8.4360689 × 1017) may explain the scale ratio between the Planck scale and the electroweak scale. The measured scale ratio between the Planck scale and the electroweak scale is approximately 1017. This may imply a quantum computational explanation of the hierarchy in nature.

This paper is available on arxiv under CC BY 4.0 DEED license.