On the Poincaré Group at the 5th Root of Unity

Considering the predictions from the standard model of particle physics coupled with experimental results from particle accelerators, we discuss a scenario in which from the infinite possibilities in the Lie groups we use to describe particle physics, nature needs only the lower dimensional representations − an important phenomenology that we argue indicates nature is code theoretic. We show that the “quantum” deformation of the SU (2) Lie group at the 5th root of unity can be used to address the quantum Lorentz group and gives the right low dimensional physical realistic spin quantum numbers confirmed by experiments. In this manner we can describe the spacetime symmetry content of relativistic quantum fields in accordance with the well known Wigner classification. Further connections of the 5th root of unity quantization with the mass quantum number associated with the Poincaré Group and the SU (N ) charge quantum numbers are discussed as well as their implication for quantum gravity.