I should warn the reader that all that follows is a personal interpretation from a curious person that is attempting to learn new subjects. Your corrections are welcome.

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As I have previously mentioned, Garrett Lisi’s work sounds extremely interesting, and any reasonable person expects that it finds its way to a serious critical analysis before far reaching conclusions and speculations take over. There are many issues that need further work. This is what Garrett explicitly have said several times.

Lisi’s paper got attention: a relatively heavy media hype (considering perhaps the title of the paper and the fact that Lisi is not in the academia, and enjoys a different lifestyle) and inumerous discussions all over the blogosphere. Now that things appear to have calmed down (although we can still hear some fresh echoes of “Lisi’s wave”), a new paper by Smolin, citing Lisi’s work, appeared in the scene.

From a first reading of Smolin’s paper, the most interesting aspect of it (as I see it) appears to be the introduction of an extension of the Plebanski action that accepts any large group structure (containing the local Lorentz group), showing that, with a symmetry breaking mechanism, the resulting dynamics is that of a unified Einstein-Yang-Mills, plus corrections. Smolin suggests his framework could be used for building up the dynamical sector of Lisi’s proposal (by applying the group E8 in the proposed extended action), a part of Lisi’s work that has not been worked out satisfactorily. According to Smolin, it would give “a fully gauge invariant action, which has solutions which spontaneously break the symmetry and give, when expanded around, the bosonic part of Lisi’s action, plus corrections”.

Smolin also suggests techniques from LQG, more specifically, the notion of “disordered locality”, as an alternative for the description of fermions and scalars to that used by Lisi (BRST extension of the connection). That part of the paper is not sufficiently clear to me, but while I try to figure it out, I would gladly accept a clarification.

Although Smolin recognises that there are open issues in Lisi’s work, specially whether the three generations of quarks and leptons are realized in the proposed structure of the E8 group, he boldly advances Lisi’s idea into aspects that as far as I was able to follow have not emerged from the whole body of discussions elsewhere. But I guess these ideas have been exchanged privately for some time (as inferred from the acknowledgement section of both Smolin and Lisi’s paper, as well as the mentioning by Lisi in his paper that the “quantum E8 theory follows the methods of quantum field theory and loop quantum gravity — though the details await future work”).

In any case, the main idea of Smolin’s paper seems to be independent of Lisi’s proposal. That is, suppose the E8 group ends up to be the wrong route. And instead one finds another group that realises the unification. Would not Smolin’s framework be consistent enough in order to allow the study of the resulting dynamics of the “correct” group, whatever it is?

So I think we have two separate issues here. One is the validity of Lisi’s proposal first of all. The other is how far Smolin’s work is dependent on it. As I mentioned, it does not appear to be completely dependent on it. He uses Lisi’s proposal as an example of application. But I may be wrong.

In any case, it is of fundamental importance to go through all the necessary details and assumptions systematically before reaching any conclusions.

On that regard, Jacques Distler has posted twice about Lisi’s work on his blog (here and here) where he argues the impossibility of getting all three fundamental particle generations through Lisi’s embedding into the E8 group. What calls the attention is Distler’s purely mathematical argumentation involving group theory representation only.

So it seems that we have reached a very first bottleneck on Lisi’s idea, in which there appears to be concrete technical (mathematical) issues that are absolutely necessary to be cleared up before continuing. Since it is a purely mathematical issue, it is indeed a point of tension that should be released before anything else. Otherwise the whole edifice of unification through E8 symmetry seems to face an early collapse.

This is unambiguous — as far as mathematics is: is Distler right or wrong?

Is Smolin’s results dependent on Lisi’s work?

If you would like to discuss specifics of the first question, please do it here. To the second question, you are invited to go here. These posts are for technical comments only. For general or more qualitative comments, you may use the present post.

As a final remark, I wonder whether those papers are being considered for refereed publication. I think that well moderated blogs can be a remarkable arena where scientific works can be widely discussed. But at the same time they do have a limited scope. Also, the peer review system has its problems; this is well known and acknowledged. It is not clear whether the authors will submit their papers to a journal. So what are we left with?

Not every member of the scientific community, whatever the field, is connected to the blogosphere. And even if they were connected, would it be acknowledged that blogs are the place where a consensus on the validity of a scientific work is to be met? Where should they be met anyway? We live the revolution of information and communication that the internet has brought, so there is a visible change in the scientific arena of discussions. Things are not as before.

In any case, Nature is the final judge. If you have a theory that can be cleary tested, then that is what is needed at the end of the day.

Except, of course, if you have got wrong mathematics to begin with.

Update: Garrett Lisi invites a technical discussion on his paper in this thread over at PF.