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Scientific Method / Science & Exploration

Setting the record straight: no simple theory of everything

New work shows that the remarkably simple theory of everything hidden inside …

A bit over two years ago, news sources and science blogs lit up when a pre-print paper from Dr. A. Garrett Lisi came to light that proposed a novel theory of everything—one theory that accurately describes all four of the universes fundamental forces. Current theories have demonstrated that three of the four fundamental forces and their associated particles can all be obtained from different symmetry operations (think rotations and reflections) of an algebraic group called a Lie group The pre-print, hosted by the on-line repository arXiv, proposed that, within the complicated symmetry group E8, all four forces of nature could be described and united.

The hype that ensued ensured that a search for the term "surfer physicist" now leads to press stories about Lisi's ideas, and spawned an entire Wikipedia entry for the paper alone. As an engineer who specializes in theoretical work, it seemed to me to be a case of "give me enough parameters and I can fit a horse." Our in-Orbiting Headquarters physicist, Dr. Chris Lee, described it as solid, but noted it had some serious shortcomings.

In the intervening years, the paper—to the best of my knowledge and research ability—has not made it through peer-review to publication. A new paper, set to be published in an upcoming edition of Communications in Mathematical Physics, formally addresses the idea, and not only finds that Lisi's specific theory falls short, but that no theory based on the E8 symmetry group can possibly be a "Theory of Everything."

The new paper, which is also freely available as a preprint through the arXiv, is highly technical and lays out its case as a proof to a mathematical problem that attempts to define the criteria for a valid theory of everything. The authors begin by laying out three key criteria that a pair of subgroups on a Lie group must have in order to be a 'Theory of Everything.' The first is a trivial, yet purely mathematical, restriction that must hold true between the chosen sub-groups. The second is that the model cannot contain any "'exotic' higher-order spin particles." The final issue is that the gauge theory employed in our group must be chiral—a limitation dictated by the existing Standard Model.

In the original work by Lisi, it was proposed that the 248 dimensions of E8 corresponded to specific particles, either bosons or fermions—over 20 of which had yet to be discovered. The authors of the paper state that, in private communications, Dr. Lisi has backed off on this specific claim, and now states that only a subset of these dimensions represent actual particles. This modified version of the theory has yet to be publicly presented. 

Going with the original version, one has to ask whether there is the correct amount of space within the potential subgroups to explain what we already know about. Math tells us that all the fermions—particles with half-integer spin—must come from what is known as the (-1)-eigenspace of the Lie group. Physics and math tell us that, in order to describe the known fermions, the subgroup of interest must have 180 dimensions.

Unfortunately, the (-1)-eigenspace on E8 (where the fermions must exist) has either 112 or 128 dimensions—too few to account for the known fermions. This goes directly against the claims made in Lisi's original work, and is not compatible with known spin theory and three generations of matter as described by the Standard model. The authors do point out that this result is not incompatible with a 1- or 2-generation Standard Model (as opposed to the accepted 3-generational Standard Model) being embedded in a real form of E8.

The authors go on, in a purely mathematical fashion, to prove that any "Theory of Everything" is not capable of meeting all three criteria in any real representation of E8, or even in a complex representation of E8. They show that any set of subspaces that meet the first criteria and either the second criteria or a relaxed version of it, will necessarily fail to meet the third.

When asked, Prof. Garibaldi, co-author of the paper and expert in exceptional Lie groups, stated that he felt an obligation to help set the record straight. "A lot of mystery surrounds the Lie groups, but the facts about them should not be distorted," he said. "These are natural objects that are central to mathematics, so it's important to have a correct understanding of them." 

He went on to describe the work in easy to understand terms, and elegantly showed how disputes in science are handled. "You can think of E8 as a room, and the four subgroups related to the four fundamental forces of nature as furniture, let's say chairs," Garibaldi explained. "It's pretty easy to see that the room is big enough that you can put all four of the chairs inside it. The problem with the 'theory of everything' is that the way it arranges the chairs in the room makes them non-functional."

(An example of this being that one chair is inverted and stacked atop another chair—it's there, but it isn't useful for sitting.) 

"I'm tired of answering questions about the 'theory of everything,'" Garibaldi said. "I'm glad that I will now be able to point to a peer-reviewed scientific article that clearly rebuts this theory. I feel that there are so many great stories in science, there's no reason to puff up something that doesn't work."

Communications in Mathematical Physics, 2010. DOI: Upcoming.  arXiv pre-print arXiv:0905.2658v3

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