The Mass Gap of the Space‐time and its Shape

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Abstract Snyder's quantum space‐time which is Lorentz invariant is investigated. It is found that the quanta of space‐time have a positive mass that is interpreted as a positive real mass gap of space‐time. This mass gap is related to the minimal length of measurement which is provided by Snyder's algebra. Several reasons to consider the space‐time quanta as a 24‐cell are discussed. Geometric reasons include its self‐duality property and its 24 vertices that may represent the standard model of elementary particles. The 24‐cell symmetry group is the Weyl/Coxeter group of the group which was found recently to generate the gauge group of the standard model. It is found that 24‐cell may provide a geometric interpretation of the mass generation, Avogadro number, color confinement, and the flatness of the observable universe. The phenomenology and consistency with measurements is discussed.

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