Turning the clock back by half a century could be the key to solving one of science’s biggest puzzles: how to bring together gravity and particle physics. At least that is the hope of researchers advocating a back-to-basics approach in the search for a unified theory of physics.
In July mathematicians and physicists met at the Banff International Research Station in Alberta, Canada, to discuss a return to the golden age of particle physics. They were harking back to the 1960s, when physicist Murray Gell-Mann realized that elementary particles could be grouped according to their masses, charges and other properties, falling into patterns that matched complex symmetrical mathematical structures known as Lie (“lee”) groups. The power of this correspondence was cemented when Gell-Mann mapped known particles to the Lie group SU(3), exposing a vacant position indicating that a new particle, the soon to be discovered “Omega-minus,” must exist.
During the next few decades, the strategy helped scientists to develop the Standard Model of particle physics, which uses a combination of three Lie groups to weave together all known elementary particles and three fundamental forces: electromagnetism; the strong force, which holds atomic nuclei together; and the weak force, which governs radioactivity. It seemed like it would only be a matter of time before physicists found an overarching Lie group that could house everything, including gravity. But such attempts came unstuck because they predicted phenomena not yet seen in nature, such as the decay of protons, says physicist Roberto Percacci of the International School for Advanced Studies in Trieste, Italy.
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The approach fell out of favor in the 1980s, as other candidate unification ideas, such as string theory, became more popular. But inspired by history, Percacci developed a model with Fabrizio Nesti of the University of Ferrara in Italy and presented it at the meeting. In the model, gravity is contained within a large Lie group, called SO(11,3), alongside electrons, quarks, neutrinos and their cousins, collectively known as fermions. Although the model cannot yet explain the behavior of photons or other force-carrying particles, Percacci believes it is an important first step.
One fan of Percacci’s work is A. Garrett Lisi, an independent researcher with a Ph.D. in physics from the University of California, San Diego. Lisi hit the headlines in 2007 with his own attempt to embed a “theory of everything” in the most complex and elegant Lie group, called E8. Percacci’s work, Lisi says, “provides a nice unification of gravity and the Standard Model.”
Lisi’s ideas revived mathematicians’ interest in this historical approach to physics, which led to the Banff meeting, says Gregg J. Zuckerman, an expert on E8 at Yale University. Lisi’s attempt, he adds, “represents a more general ideal about returning to Lie groups as a way to unify gravity with the Standard Model.”
Others are taking this ideal forward in different ways. Rather than thinking of Lie groups as boxes that can hold forces and particles, mathematician Tevian Dray and physicist Corinne Manogue of Oregon State University are tearing them apart and examining one of their mathematical building blocks—an eight-dimensional number system called octonions. (Everyday real numbers are one-dimensional, whereas complex numbers, which have both real and imaginary parts, are two-dimensional.)
Many mathematicians shy away from octonions because they do not obey all the standard laws of algebra, Dray observes, so the order in which you perform mathematical operations can give you different answers. Dray and Manogue have turned this seemingly unpalatable asymmetry to their advantage to describe the biased properties of some particles. For instance, octonions naturally reproduce neutrinos’ puzzling “left-handedness”—that is, their intrinsic quantum “spin” is always oriented in one sense relative to their motion.
Octonions also seem tailor-made for performing calculations in 10 dimensions, Dray explains, making them potentially useful for string theorists, who posit that our universe contains six extra compact dimensions. String theorists have not been able to pinpoint one unique mechanism that describes how these extra dimensions collapse down, but Dray and Manogue have found that choosing one particular octonion to concentrate on performs this feat simply and automatically.
“We are starting to get glimmers of the properties that a final theory must have,” says Dray, who emphasizes that much work remains to be done to obtain a fully working octonion model. What is encouraging, he adds, is that many researchers are getting tantalizing hints, using differing approaches, that Lie groups are the right path to take. These hints are strong enough to stimulate mathematicians, such as Jeffrey Adams of the University of Maryland, to lend their expertise to physicists pursuing the Lie group approach. “I’d be disappointed if there’s not something like this that works,” Adams says.
Not everyone shares this optimism. Skip Garibaldi, a mathematician at Emory University, says that E8-inspired nostalgia is misguided. Working with physicist Jacques Distler of the University of Texas at Austin, Garibaldi has shown that Lisi’s theory predicts the existence of unwanted particles, whose interactions are the mirror image of regular fermions. Such particles would most likely have already exerted a noticeable effect on known particles, Garibaldi argues. “There is no way to shove gravity inside E8 without also predicting something that has nearly been ruled out by experiment,” he says.
Lisi, who posted the latest version of his theory on the Internet in June and presented it at the meeting, concedes that mirror fermions are an issue but adds that E8 theory is a work in progress and that mirror fermions could have evaded notice if they are heavier than commonly thought. They could even show up in the Large Hadron Collider, he says.
It is too early to judge whether the back-to-basics program will ultimately pay off, Zuckerman remarks. But he undoubtedly speaks for many when he says, “I can tell you that the literature is very exciting to me.”