This past December, Jim Weatherall and I wrote "A Geometric Theory of Everything" for Scientific American, describing progress on unified geometric theories of gravitation and the Standard Model of particle physics. My personal contribution to this progress, a developing model called E8 Theory, was introduced three years ago in a paper titled "An Exceptionally Simple Theory of Everything." Almost immediately after this paper appeared, physicists and the interested public began a lengthy process of considering and discussing this new theory's merits and faults.
Not surprisingly, the initial response was largely critical, with most commenters encountering some unfamiliar mathematical structures in the paper and responding with appropriate skepticism. Much of this criticism was productive, helping me and others to develop the theory, while some was apparently motivated by physics politics rather than the search for a deeper understanding. Over the years, the many productive points of criticism have either been resolved favorably, answered by further development of the theory, or remain as open problems. Below, in an effort to keep the record straight, I describe the salient points of criticism and how they have played out:
1. Some physicists were initially mystified by the inclusion of both bosons and fermions in a single superconnection field -- formally adding fields of different types and units, seemingly in violation of basic principles, as described here. However, others pointed out that this sort of formal addition was not so unusual (coming as it does from the well established "BRST" model in quantum field theory, with references noted in the original paper), and is not problematic since the separate parts of the superconnection do not mix. This kind of superconnection was then discussed more extensively and constructively by mathematicians.
2. The most vocal objection to E8 Theory was inspired by the dramatic apparent violation of the Coleman-Mandula theorem, which prohibits the unification of gravity and Standard Model forces in spacetime. This is one of the greatest no-go theorems in particle physics and had prevented work on such unification for decades; but further consideration uncovered an important loophole, which is described in our article and more thoroughly in a published paper by a colleague. Even if E8 Theory accomplishes nothing else, it has brought attention to this loophole, providing a new understanding of cosmology as the symmetry breaking of a unified gauge-gravity theory.
3. Several people pointed out that the dynamics of the theory described in the paper, matching those of gravity and the Standard Model, were not invariant under the full E8 symmetry. This was an important problem, because when describing a unified theory one needs to describe how the full symmetry dynamically breaks to produce the less symmetric universe we see around us. Such a description was quickly provided by others and expanded upon.
4. In what has turned out to be the most widespread and destructive criticism, some physicists were misled to believe that the structure of gravity and the Standard Model (including one generation of fermions with parity-violating interactions) does not embed in the structure of the E8 Lie group. This criticism was first made and widely disseminated by Jacques Distler and Skip Garibaldi. It gained more public attention on the blog of cosmologist Sean Carroll, who wrote that "[Distler] shows that you can't even embed one generation [in E8]." Distler's colleagues also wrote a letter to the editor of Scientific American decrying the lack of parity violation. This fact would seem very damning for E8 Theory, but it is simply not true. The structure of gravity and the Standard Model along with one generation of fermions (including their parity-violating interactions) does fit in E8, as I described explicitly in a recent paper. In their misleading argument, Distler and Garibaldi make unnecessary assumptions about how the embedding needs to happen, and then prove it can't happen that way -- a "straw man" argument.
5. Early on, it was pointed out that the theory does not accommodate all three generations of fermions in an obvious way, or describe their masses. This problem was identified in the original paper, with a potential solution coming from triality. As of one year ago I was extremely discouraged by this puzzle, but with some insights into triality gained at the recent conference in Banff I now think it may work. E8 gauge transformations related to triality might mix and describe three generations of fermions, but it is very tricky. This issue remains the most significant problem, and until it is solved the theory is not complete and cannot be considered much more than a speculative proposal. Without fully describing how the three generations of fermions work, the theory and all predictions from it remain tenuous.
6. When one embeds gravity, the Standard Model forces, and the 64 particle states of one generation of fermions inside E8, there are many particles left over. Among these "extra" particles are "mirror fermions" -- partners to the fermions with all opposite charges (including opposite spins, making these different than antiparticles). Critics contend that these mirror fermions are bad, making the theory "nonchiral," and that the existence of physical mirror fermions has almost been ruled out by experiment. However, I see these extra particle states in E8 as providing a potential solution to the problem of the missing second and third generation fermions, since triality transformations can relate the 64 fermions of one generation to two other blocks of 64 in E8, including the mirror fermions.
7. There is not yet a consistent quantized description of E8 Theory. Although this is true, and remains an open problem, the formulation of the theory is compatible with the usual methods of quantum field theory. As E8 Theory develops, I expect renormalization and other quantum field theory or loop quantum gravity calculations will be carried out successfully. The lack of a fixed background spacetime does, however, make this difficult -- a known problem with quantizing gravitational theories.
8. Old-school scientists have dismissed E8 Theory for not being peer reviewed and published. Personally, I am not climbing an academic ladder and I enjoy an open exchange of ideas, so I did not feel the need to submit my original 2007 paper to a traditional journal, although I was invited to do so. Most physicists today rely on openly posted electronic preprints rather than journals. However, two E8 Theory papers have now been peer reviewed and gone to publication without difficulty. One paper, describing 90% of the theory, including the full E8 invariant dynamics, was written with coauthors Lee Smolin and Simone Speziale and published in a peer-reviewed journal. Another paper, "An explicit embedding of gravity and the standard model in E8," which counters Distler and Garibaldi's argument, was recently peer reviewed and accepted for publication in a conference proceedings.
All in all, despite an abundance of media hype and a mixed reaction from the physics community, I think things have gone well with the development of E8 Theory since its debut. Nevertheless, there are outstanding problems, and this is a young theory -- far from complete. For me, the inviolable mathematical truth that the entire structure of gravity, the Standard Model forces, and a generation of fermions (including parity-violating interactions) is part of the structure of E8 is extremely compelling, and is telling us something important about the universe. It was a pleasure to be able to describe this structure for Scientific American readers in our article. The mathematical fact of this embedding will not go away, and it may, as I believe, prove important, or it may, as Distler et al. believe, be an insignificant coincidence. Regardless of what anyone believes, in physics, it is only nature's opinion that ultimately matters.
Even as E8 Theory remains a contentious topic among physicists, it has brought to light many interesting structures and possibilities in particle physics, and revitalized the use of weight diagrams for exploring some of this beautiful structure. In writing our article for Scientific American my coauthor and I, as well as the ever-helpful editors, were very careful to ensure its accuracy. I would be very surprised if critics were to find fault in the article's veracity -- although I am not surprised if some are unhappy with its existence.
Elementary particle fields of gravity and the Standard Model embedded in the structure of the E8 Lie group.