"Surfer dude stuns physicists with theory of everything.” So ran a Daily Telegraph headline last November. The story circulated and quickly achieved widespread notoriety (even my dentist asked me about it). The physics blogosphere carried long threads of comments attacking and defending the theory and then attacking the tone of the discussion. The shouting and acrimony have died down, and the mainstream physics community remains largely unconvinced that the theory can stay afloat. In the words of Marcus du Sautoy, a University of Oxford mathematician writing in the Telegraph in late January: “Unfortunately, the consensus, after investigation, is that it is impossible to use E8 in the way Lisi was hoping and produce a consistent model that reflects reality.” Not everyone, of course, agrees.
A. Garrett Lisi, the surfer dude in question, came up with his theory while dividing his time among surfing, snowboarding and speculating about physics. He has a Ph.D. in physics from the University of California, San Diego, but has held no academic affiliation since then. He presented his ideas at conferences and invited seminars months before the media furor. From the start, he has been quick to comment that the chances of his theory being correct are very small, but he considers string theory (the approach most favored by physicists) to be even less likely.
Taken at face value, the theory sounds like an incredible discovery. It is based on a remarkable mathematical structure called E8. With 248 dimensions, E8 is the largest, most complicated and most beautiful of five idiosyncratic objects known as the exceptional simple Lie groups. (The title of Lisi’s paper, “An Exceptionally Simple Theory of Everything,” is first and foremost a pun.) And although E8 has a vast number of dimensions, the physical universe described by the theory could have only the four dimensions we are familiar with and not the 10 or 11 of string theory.
E8 has come up before in physics, most notably in string theory, but Lisi’s theory harkens back more to the early 1960s, when physicist Murray Gell-Mann noted that the zoo of subatomic particles then known could be organized into patterns that corresponded to features of another (and far more elementary) Lie group, SU(3). One of the patterns was missing a particle, and Gell-Mann predicted that a particle with certain properties should exist to fill that spot. Experimentalists soon discovered just such a particle.
Today the Standard Model of particle physics organizes all the known elementary particles into these patterns (or “representations”), but it takes a combination of three Lie groups to account for how the particles can interact via three fundamental forces (electromagnetism and the strong and weak nuclear forces). Lisi’s insight was that he could place all these particles onto a representation of E8 with only a small number of spots left empty. This process is not just a matter of putting particles in nice-looking patterns in some arbitrary fashion; several properties, such as the electric charges of the particles, have to match up exactly with the relevant quantities in the representation. Furthermore, the patterns include particles that produce the four fundamental forces—including gravity. Hence the optimistic use of “theory of everything” in the title of Lisi’s paper.
Closer examination, however, revealed a few Jurassic-size flies in the ointment. For instance, the theory combines the matter particles and the force-carrying particles, referred to in the trade as fermions and bosons, in a way that at first appears fundamentally inconsistent. Various “supersymmetric” theories (including superstring theory) do combine fermions and bosons as well—but only with a detailed mathematical underpinning that E8 does not provide. One way of stating the problem is that if the new theory really describes bosons and fermions, then the structure it places them in cannot possibly be a Lie group at all.[break]
Lisi argues that he is using a “mathematical trick” from what is called BRST theory, an established formalism used in string theory and quantum field theory, in which some bosons and fermions play the opposite of their usual roles (and are called “ghosts”). But in ordinary BRST theory, ghosts never manifest as detectable, physical particles, so it is unclear how they could do so consistently in the E8 theory.
Perhaps the longest public debate on the merits of Lisi’s theory took place primarily between Jacques Distler of the University of Texas at Austin and Lee Smolin of the Perimeter Institute for Theoretical Physics in Ontario, the latter of whom had been widely quoted in the media with unqualified praise for the theory. (Smolin says he was quoted out of context.) Smolin had also quickly written a paper suggesting ways to correct certain flaws in the E8 proposal. For the particles in the E8 theory to represent the known particles properly, the combination of smaller groups used to form the Standard Model must be embedded inside E8 in just the right way. Distler had demonstrated in his blog that this is a mathematical impossibility. So far as he was concerned, the theory was dead and not worth trying to resuscitate. Yet argument raged on over details of Distler’s proof and ultimately ended with neither side conceding. Lisi, incidentally, played very little part in these disputes.
Today the theory is being largely but not entirely ignored. Lisi, naturally, continues to work on it, as does Smolin. Lisi says that even if what Distler claims is true, it would only be true for the variant of E8 (“real E8”) originally used in his paper and that another variant (“complex E8”) would certainly work. Smolin argues that the press coverage gave the false impression that Lisi’s proposal was a finished work. “In reality,” he says, “almost every new theoretical proposal is first presented in a way that is flawed and incomplete, with open issues that need to be filled in.... While Lisi’s proposal has exciting aspects, this is the case with it as well.”