No Exceptionally Simple Theory of Everything inside the Enigmatic E8 

E8-inspired graph Courtesy of  J. G. Moxness, an emulation of a hand-drawn original by Peter McMullen

The “exceptionally simple theory of everything,” proposed by a physicist in 2007, does not hold water, says Emory mathematician Skip Garibaldi. Garibaldi did the math to disprove the theory, which involves a mysterious structure known as E8. The resulting paper, co-authored by physicist Jacques Distler of the University of Texas, will appear in an upcoming issue of Communications in Mathematical Physics.

In November of 2007, physicist Garret Lisi published an online paper entitled “An Exceptionally Simple Theory of Everything.” Although his paper was not peer-reviewed, and Lisi himself told the Daily Telegraph that the theory was still in development, and he gave a “low” likelihood to the prediction, the idea was widely reported in the media.

Garibaldi was among the skeptics when the theory hit the news. So was Distler, a particle physicist, who wrote about problems he saw with Lisi’s idea on his blog. Distler’s posting inspired Garibaldi to think about the issue more, eventually leading to their collaboration.

Lisi’s paper centered on the elegant mathematical structure known as E8, which also appears in string theory. First identified in 1887, E8 has 248 dimensions and cannot be seen, or even drawn, in its complete form.

The enigmatic E8 is the largest and most complicated of the five exceptional Lie groups, and contains four subgroups that are related to the four fundamental forces of nature:

• the electromagnetic force

• the strong force (which binds quarks)

• the weak force (which controls radioactive decay)

• the gravitational force

In a nutshell, Lisi proposed that E8 is the unifying force for all the forces of the universe.

“That would be great if it were true, because I love E8,” Garibaldi says. “But the problem is, it doesn’t work as he described it in his paper.”

As a leading expert on several of the exceptional Lie groups, Garibaldi felt an obligation to help set the record straight. Using linear algebra and proving theorems to translate the physics into math, Garibaldi and Distler not only showed that the formulas proposed in Lisi’s paper do not work, they also demonstrated the flaws in a whole class of related theories.

“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 explains. “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.”

He gives the example of one chair inverted and stacked atop another chair.

“I’m tired of answering questions about the ‘theory of everything,’” Garibaldi says. “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.”