particles. This suggests that the only free parameters in this theory are 3 length scales, corresponding to the masses in each generation.

The theory presented here can be elegantly rewritten in terms of [*Jordan matrices*]{}, i.e. $3\times3$ octonionic Hermitian matrices, along the lines of the approach to the superparticle presented in [@Schray]. This approach, which is briefly described in [@Other], demonstrates that the theory is invariant under a much bigger group than the Lorentz group, namely the exceptional group $E_6$ (actually, $E_7$, since only conformal transformations are involved). We therefore believe it may be possible to extend the theory so as to include quarks and color.

Finally, as noted in [@Dim], we have worked only in momentum space, and have discussed only free particles. Perhaps our most intriguing result is the observation that the introduction of position space would require a preferred complex unit in the Fourier transform. Similarly, a description of interactions based on minimal coupling would again involve a preferred complex unit. Therefore, it does not appear to be [*possible*]{} to use the formalism presented here to give a full, interacting, 10-dimensional theory in which all 10 spacetime dimensions are on an equal footing. We view this as 