  Considering that the momentum squared in the extra dimensions is the
physically relevant quantity for the generation of the Kaluza-Klein mass
states, we have reanalyzed mathematically the procedure for five dimensional
scalar fields within the Arkhani-Ahmed, Dimopoulos and Dvali scenario. We find
new sets of physically allowed boundary conditions. Beside the usual results,
they lead to new towers with non regular mass spacing, to lonely mass states
and to tachyons. We remark that, since the SO(1,4) symmetry is to be broken due
to the compactification of the extra dimensions, the speed of light could be
different in the fifth dimension. This would lead to the possible appearance of
a new universal constant besides $\hbar$ and $c$.
