Rummaging for a Final Theory: Can a 1960s Approach Unify Gravity with the Rest of Physics?

To unify the four forces of nature, physicists are turning to Lie groups, an approach famously resurrected in 2007 by a surfer-dude theorist

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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.

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.

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