principal bundle or fibration A = g^{-1}Ag + g^{-1}dg, and unitarity gives g^{-1}g = 1. Now suppose there exists a system of braid groups, say a set {G_i, i = 1, ...infinity}. Now let B be a map B: G ---&gt; G', so that for elements in these groups Bg = g'. Now multiply this by g^{-1} so then g^{-1}Bg = g^{-1}g' =/= 1. Now if the operator B is defined by group elements g, B = B(g) this means that g^{-1}Bg is a nonassociative structure. In other words for a,b,c specific examples of elements g we have that g^{-1}Bg = [a,b,c] = a(bc) - (ab)c, and is an associator. These are links between nonunital related braid groups. The nonassociative system is not unitary, but it does preserve quantum information. In a coarse grained setting it also defines Bogoliubov coefficients and thermal terms found with Hawking radiation. In this way maybe the projective structures for QM and relativity are embedded in a more extensive system. In the quantum theory the electron is a point particle and it is a problem because the zero sizes of the electron create infinitely large potential energy of an electromagnetic field of the electron. However, if internal energy of the electron is the latent form of kinetic energy as shown in essay The theory of time , then infinitely large energy disappears, and the electron ceases to be the point particle. In case of free fall of the electron or any other material particle in