Segal spent much time and effort on a quadratic cosmological redshift that he claimed was implicit in the physics of the Conformal Group. Segal's redshift was described by Bertram Kostant, who had Segal as advisor for his 1954 Chicago Ph.D., in another of the obituaries in the Notices of the AMS 46 (June/July 1999) 659-668.:

"... One particular nilpotent element, in the representation of SU(2,2) associated with solutions of Maxwell's equations, defines the standard operator to determine the frequencies of light waves.

[John Baez, who had Segal as advisor for his 1986 MIT Ph.D., says: "... That's the generator of Minkowski time translations. ... If you use the Minkowski Hamiltonian everywhere (there's one for each observer) you don't get the redshift. ... ".]

But Irving focused on another element with a nonnegative spectrum, an element that was elliptic and not nilpotent, but closely related ... This elliptic element has beautiful mathematical properties, like generating an invariant cone. ... This elliptic element is at the heart of Segal's cosmological theory.

[John Baez says: "... That's the generator of Einstein time translations. ... if you use the Einstein Hamiltonian everywhere you don't get the redshift. ... ".]

What he is saying is that it is the elliptic element that should be used to determine the energy of an electromangnetic wave, and not the nilpotent element.

[John Baez says: "... But if we do that *everywhere*, we simply get physics on the Einstein universe R x S^3 - no redshift. ... ".]

The redshift ... is accounted for by the difference between the elliptic and nilpotent element - negligible locally, but significant at great distances. ...".

[John Baez says: "... Aha: this is the tricky part. How is it "accounted for by the difference" between these elements, exactly? ... ".]

I. E. Segal, H. P. Jakobsen, B. Oersted, S. M. Paneitz, and B. Speh, in their article Covariant chronogeometry and extreme distances: Elementary particles (Proc. Nat. Acad. Sci. USA 78 (1981) 5261-5265, at page 5261), say: "... the energy of a photon in ...[ Conformal Unispace ]... splits Lorentz-covariantly into a local and delocalized part. The local part is represented by the conventional energy operator in ...[ Minkowski space-time ]... , which can be regarded as a submanifold of ...[ Conformal Unispace ]... ; the delocalized part drives, essentially as an interaction hamiltonian, a redshift in very good agreement with objective observations on galaxies and quasars. ...".

John Baez says: "... Segal used to say the dynamics of distant stars was governed by the Einstein Hamiltonian but we saw them from the Minkowski viewpoint. However, he never clarified how this should actually work. ...".

In my opinion, it might work like this:

•Our base-line experimental data for spectral lines comes from local (Earth-based or Solar-Earth) experiments all of which lie that a region representable by Minkowski space-time;

•Our long-distance astronomical spectral line observations come from experiments that extend beyond our local region representable by Minkowski space-time, so that the relevant regions of our long-distance astronomical spectral line observations must be represented by Conformal Unispace. Such Conformal Unispace measurements of spectral lines will, as Segal, Jakobsen, Oersted, Paneitz, and Speh say, give "... a redshift in very good agreement with objective observations on galaxies and quasars ...".

Bertram Kostant said, in his Segal obituary article:

"... I have it from a highly reliable but unnamed source that there is a growing group of cosmologists who have come to believe that the correct understanding of the redshift is some sort of fusion of the Doppler effect and Irving's theory. So it is not impossible that Irving could turn out to be correct after all. ...".