Elaborate experiments failed to detect proton decay and data precision justify the abandonment of SU(5) symmetry altogether from any future theory of unification. The implication is that natural symmetry could not go beyond the product of U(1), SU(2), and SU(3) although these products do not depict complete chiral symmetry since only the left handed ones are ever found in nature. Why nature is predominantly left-handed remains a mystery. However, it is well established that mass also could arise from broken chiral symmetry. To restore complete chiral symmetry then there must be an underlying symmetry for square of energy and these can be described by using the algebra of multi-dimensional Hadamard matrices.


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