Our universe is three-dimensional and curved (with a positive curvature) and thus may be embedded in a four-dimensional Euclidean space with coordinates x,y,z,t where the fourth dimension time t is treated as a regular dimension. One can set in this spacetime a four-dimensional underlying array of small hypercubes of one Planck length edge. With this array all elementary particles can be classified following that they are two-, three-, or four-dimensional. The elementary wavefunctions of this underlying array are equal to 2expixi for xi=x,y,z or to 2expit for t. Hence, the masses of the fermions of the first family are equal to 2n (in eV/c2) where n is an integer. The other families of fermions are excited states of the fermions of the first family and thus have masses equal to 2n.p2/2 where n and p are two integers. Theoretical and experimental masses fit within 10%.
Part of the book: Accelerators and Colliders