Is mathematical pattern the theory of everything?
10:00 15 November 2007
NewScientist.com news service
Zeeya Merali
GARRETT LISI is an unlikely individual to be staking a claim for a theory of everything. He has no university affiliation and spends most of the year surfing in Hawaii. In winter, he heads to the mountains near Lake Tahoe, California, to teach snowboarding. Until recently, physics was not much more than a hobby.
That hasn't stopped some leading physicists sitting up and taking notice after Lisi made his theory public on the physics pre-print archive this week (
www.arxiv.org/abs/0711.0770). By analysing the most elegant and intricate pattern known to mathematics, Lisi has uncovered a relationship underlying all the universe's particles and forces, including gravity - or so he hopes. Lee Smolin at the Perimeter Institute for Theoretical Physics (PI) in Waterloo, Ontario, Canada, describes Lisi's work as "fabulous". "It is one of the most compelling unification models I've seen in many, many years," he says.
That's some achievement, as physicists have been trying to find a uniform framework for the fundamental forces and particles ever since they developed the standard model more than 30 years ago. The standard model successfully weaves together three of the four fundamental forces of nature: the electromagnetic force; the strong force, which binds quarks together in atomic nuclei; and the weak force, which controls radioactive decay. The problem has been that gravity has so far refused to join the party.
Most attempts to bring gravity into the picture have been based on string theory, which proposes that particles are ultimately composed of minuscule strings. Lisi has never been a fan of string theory and says that it's because of pressure to step into line that he abandoned academia after his PhD. "I've never been much of a follower, so I walked off to search for my own theory," he says. Last year, he won a research grant from the charitably funded Foundational Questions Institute to pursue his ideas.
He had been tinkering with "weird" equations for years and getting nowhere, but six months ago he stumbled on a research paper analysing E8 - a complex, eight-dimensional mathematical pattern with 248 points. He noticed that some of the equations describing its structure matched his own. "The moment this happened my brain exploded with the implications and the beauty of the thing," says Lisi. "I thought: 'Holy crap, that's it!'"
What Lisi had realised was that if he could find a way to place the various elementary particles and forces on E8's 248 points, it might explain, for example, how the forces make particles decay, as seen in particle accelerators.
Lisi is not the first person to associate particles with the points of symmetric patterns. In the 1950s, Murray Gell-Mann and colleagues correctly predicted the existence of the "omega-minus" particle after mapping known particles onto the points of a symmetrical mathematical structure called SU(3). This exposed a blank slot, where the new particle fitted.
Before tackling the daunting E8, Lisi examined a smaller cousin, a hexagonal pattern called G2, to see if it would explain how the strong nuclear force works. According to the standard model, forces are carried by particles: for example, the strong force is carried by gluons. Every quark has a quantum property called its "colour charge" - red, green or blue - which denotes how the quarks are affected by gluons. Lisi labelled points on G2 with quarks and anti-quarks of each colour, and with various gluons, and found that he could reproduce the way that quarks are known to change colour when they interact with gluons, using nothing more than high-school geometry (see Graphic).
Turning to the geometry of the next simplest pattern in the family, Lisi found he was able to explain the interactions between neutrinos and electrons by using the star-like F4. The standard model already successfully describes the electroweak force, uniting the electromagnetic and the weak forces. Lisi added gravity into the mix by including two force-carrying particles called "e-phi" and "omega", to the F4 diagram - creating a "gravi-electroweak" force.
Finally, he filled in most of the 248 points of the E8 pattern, using various "identities" of the 40 known particles and forces. For example, some particles can have quantum spin values that are either up or down, and each of these identities would sit on a different point. He filled the remaining 20 gaps with notional particles, for example those that some physicists predict to be associated with gravity.
With the points on the E8 pattern occupied, he could rotate it using computer simulations and so project it down in various ways to two dimensions. By rotating it a certain way, he found that he could recreate the earlier basic patterns describing the quark-gluon relationship and his gravi-electroweak force.
As he rotated the shape further, he found even more intriguing patterns. For example, in one configuration, you can see the gravi-electroweak interaction pattern surrounded by quarks and anti-quarks congregated into their individually "coloured" groups (visit
www.newscientist.com/article/dn12891 to watch an animation of the pattern's rotation). What's more, these quarks cluster into families of three, with almost identical properties but different masses. Physicists have long puzzled over why elementary particles appear to belong to such families, but this arises naturally from the geometry of E8, he says.
So far, all the interactions predicted by the complex geometrical relationships inside E8 match with observations in the real world. "As far as I have been able to tell, it's a perfect match of tens of thousands of interactions," says Lisi. "How cool is that?"
Lisi is specially pleased that his model is "without strings, extra space-time dimensions or other weird inventions that there's no evidence for", which bedevil string theory. The maths is simpler, too, which he says makes it even more compelling. Compared with string theory, "this uses baby mathematics," he says.
Other physicists are impressed. "Some incredibly beautiful stuff falls out of Lisi's theory," says David Ritz Finkelstein at the Georgia Institute of Technology in Atlanta. "I think that this must be more than coincidence and he really is touching on something profound."
The question of why our universe should be controlled by the E8 structure is not one that Lisi tackles. "I think the universe is pure geometry - basically, a beautiful shape twisting around and dancing over space-time," says Lisi. "Since E8 is perhaps the most beautiful structure in mathematics, it is very satisfying that nature appears to have chosen this geometry." Finkelstein, however, plans to investigate whether space-time could be described as a quilt woven together from E8 patches.
Sabine Hossenfelder, also at PI, argues that Lisi's idea could be complementary to string theory, rather than a radical alternative. She points out that string theorists already use E8 to describe a pattern of extra-dimensional space called the Calabi-Yau manifold, which they propose exists alongside the three dimensions that we see. "Is this a coincidence?" she asks.
The crucial test of Lisi's work will come only when he has made testable predictions. Lisi himself accepts this, saying that although his theory is beautiful to him, "nature may disagree". To fill E8 entirely will require more than 20 new particles not envisaged by the standard model. Lisi is now calculating the masses that these particles should have, in the hope that they may be spotted when the Large Hadron Collider - being built at CERN, near Geneva in Switzerland - starts up next year.
"This is an all-or-nothing kind of theory - it's either going to be exactly right, or spectacularly wrong," says Lisi. "I'm the first to admit this is a long shot. But it ain't over till the LHC sings."
Dude, I have this rad theory in my GUT
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Is mathematical pattern the theory of everything?
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