**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

## V. SPACE-TIME QUANTA AND SPECTRAL MASS GAP

The solution of the mass gap problem as described in [62] requires proving that Yang-Mills theory exists and that the mass of all particles predicted by the theory is strictly positive. Both conditions are satisfied by the space-time quanta. According to Eq. (9), we find that the mass of space-time quanta is a real positive value. The space-time quanta is quatified by the parameter κ in Snyder algebra that was found to generate both non-commutative geometry and GUP at the same time. For Non-commutative geometry part, it is found to emerge naturally at limits of M/string theory [2] as higher dimensional corrections of ordinary Yang-Mills theory [3]. Since the space-time is locally flat, the space-time quanta must be described by a 4-polytope. We introduce a geometric and symmetric reason to consider the 24-cell as the space-time quanta. The most important reason is that 24-cell is the Weyl/Coxeter group of F4 group that can generate the standard model gauge symmetry as shown in recent studies [45]. Therefore, Yang-Mill’s theory exists as a F4 group and is explained by the space-time quanta from the first geometric principles as 24-cell. The gluon masses should be related to the 16-cell which is related to the 24-cell we explained in previous sections. We conclude that the space-time quanta introduces a geometric origin of the spectral mass gap [62]. The spectral mass gap is entirely determined by the length/radius of 24-cell according to Eq. (9). Recently, it was shown that spectral gaps exist in Hamiltonian with quasicrystal line order [63]. Quasicrystal considerations in Holography, the basic structure of nature, and cosmology are discussed in [64–71]. We think the quantum space-time may be a quasicrystal with a fundamental structure of a 24-cell. Experimental observations of quantum time quasicrystal are reported in [72]. This quasicrystal order is expected to follow from simulating Snyder’s algebra with considering 24-cell as its fundamental structure. This needs further investigation.

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