'Most beautiful' math structure appears in lab for first time

A complex form of mathematical symmetry linked to string theory has been glimpsed in the real world for the first time, in laboratory experiments on exotic crystals.

Mathematicians discovered a complex 248-dimensional symmetry called E8 in the late 1800s. The dimensions in the structure are not necessarily spatial, like the three dimensions we live in, but they correspond to mathematical degrees of freedom, where each dimension represents a different variable.

In the 1970s, the symmetrical form turned up in calculations related to string theory, a candidate for the "theory of everything" that might explain all the forces in the universe. But string theory still awaits experimental proof.

The structure is also the basis for another proposed theory of everything advanced in 2007 by surfer-physicist Garrett Lisi, who refers to E8 as "perhaps the most beautiful structure in mathematics".

Now, physicists have detected the signature of E8 in a very different realm – experiments on super-chilled crystals.

Up or down

Radu Coldea of the University of Oxford and his colleagues chilled a crystal made of cobalt and niobium to 0.04 °C above absolute zero. Atoms in the crystal are arranged in long, parallel chains. Because of a quantum property called spin, electrons attached to the atom chains act like tiny bar magnets, each of which can only point up or down.

Strange things occurred when the experimenters applied a powerful 5.5-Tesla magnetic field perpendicular to the direction of these electron "magnets". Patterns appeared spontaneously in the electron spins in the chains – in a simplified example with three electrons, the spins could read up-up-down or down-up-down, among other possibilities. Each distinct pattern has a different energy associated with it.

The ratio of these different energy levels showed that the electron spins were ordering themselves according to mathematical relationships in E8 symmetry.

Complex symmetry

Alexander Zamolodchikov, currently at Rutgers University in Piscataway, New Jersey, pointed out in 1989 that the theoretically predicted energies of such systems match expectations from E8 symmetry.

But the underlying reason why is still mysterious. Robert Konik of Brookhaven National Laboratory in Upton, New York, who was not involved in the experiment, says the fact that such a simple system – essentially consisting of one-dimensional chains of magnets – should display such complex symmetry is surprising.

"Just sort of looking at the system, you wouldn't necessarily expect it to occur," he told New Scientist. It is "remarkable" to see this rather exotic piece of mathematics appear in the real world, he adds.

No link

Although E8 does show up in string theory calculations, observing the symmetry in magnetic crystal experiments does not provide any evidence for string theory itself, Konik says.

"The fact that you see this particular symmetry in this spin chain doesn't say anything about string theory per se," he says. "The existence of this symmetry in a sense is sort of separate from any [particular] physical phenomenon."

For the same reason, the experiments also provide no backing for Lisi's proposed theory of everything, which is based on E8, he adds.

Journal reference: Science (DOI: 10.1126/science.1180085)

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