Abstract
We made the hypothesis that, if spacetime is composed of small hypercubes of one Planck length edge, it exists elementary wavefunctions which are equal to √ 2 exp(ix j) if it corresponds to a space dimension or equal to √ 2 exp(it) if it corresponds to a time dimension. The masses of fermions belonging to the first family of fermions are equal to integer powers of 2 (in eV/c 2) [1]. We make the hypothesis that the fermions of the 2nd and 3rd families are excited states of the fermions of the 1st family. Indeed, the fermions of the 2nd and 3rd families have masses equal to 2 n .(p 2)/2 where n is an integer [1] calculated for the first family of fermions and p is another integer. p is an integer which corresponds to the excited states of the elementary wavefunctions (the energy of the excited elementary wave functions are equal to p 2 /2; using normalized units).