Moving Beyond String Theory


By Mark Anderson|

Sep, 26, 2006

Ask any credentialed nerd what the ultimate theory of physics is, and chances are they'll reply, "string theory."

In string theory -- an idea that's been around since the late 1970s -- the universe is a 10-dimensional place, with six of those dimensions curled up inside themselves like a cat in front of a fireplace. All particles and forces are different resonances and vibrations of these 10-dimensional strings.

Strings are far from the only game in town. There are other, potentially equally promising approaches to unifying physics' two seemingly incompatible visions of the cosmos: general relativity and quantum mechanics.

This fall, Columbia University mathematician Peter Woit has published a critique of string theory (Not Even Wrong: The Failure of String Theory), pointing out that in more than three decades, string theory still has yet to make a single prediction that can be verified in the lab or through the lens of a telescope. If all scientific disciplines maintained such fluffy and forgiving standards, Woit argues, science would devolve into little more than medieval disputations about angels and heads of pins.

Lee Smolin of Canada's Perimeter Institute ( has taken the next step in his new book, The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next, outlining the most promising non-stringy paths to reconciliation between Einstein and the quantum.

Oxford University mathematical physicist Roger Penrose, author of The Road to Reality (,66751-0.html), invented a mathematical tool called "twistors."

Smolin and Penrose take a look at the diverging paths beyond string theory.

Twistor String Theory

This retooling of string theory uses Penrose's twistors, which reduce the number of dimensions in the theory to the familiar four -- three spatial dimensions plus time. Twistors are by definition four-dimensional objects that locate not a position in space and time but rather a network of possible causal relationships between space-time events. Depicting a particle such as an electron as occupying a definite x, y, z and t gives a false sense of definiteness: Space and time are fuzzy at quantum scales. But cause and effect are not, and cause and effect are effectively what twistor space maps.

"What's rather striking about this twistor string approach is that it really is four dimensions," said Penrose just after a conference on twistor string theory. "So my objections (about string theory's extra hidden dimensions) essentially evaporate."

Pros: The mathematical beauty of string theory remains mostly unassailed, while the universe gets its four dimensions. Actual predictions for future particle accelerator experiments may yet emerge.

Cons: It's still unclear what this "theory" is -- and it may just be a sidelight on the 10-dimensional theory that yields more solvable equations. The inventor of twistors himself said, "I need to see a clear theory which I might be able to use, but I didn't get that."

Loop Quantum Gravity

If string theory evaporated tomorrow, something called Loop Quantum Gravity (LQG) would probably be the odds-on favorite to take its place. LQG, and a related approach called Spin Foam theory, posits that Einstein's theories of space and time break down at very small scales (called the Planck scale, one-billion-billionth the size of an atomic nucleus) and in its place are entities described by another mathematical tool Penrose invented, called spin networks.

These graphs represent loops of field lines that, like string theory, become the fundamental building blocks of the universe. But unlike strings, no extra hidden dimensions are needed. The end result is that LQG predicts specific, quantifiable ways in which classical Einsteinian relativity would break down -- and could soon be observable in fine-tuned measurements of the Big Bang's microwave background or in observations by GLAST, a gamma-ray telescope scheduled to launch next year.

Pros: Smolin, one of the originators of LQG, makes an eloquent and persuasive case for the theory, which has been able to make bold new predictions. And it reduces to something resembling classical, Newtonian gravity at low-energy and long-distance limits.

Cons: No one has yet been able to get spacetime itself, the stuff Einstein made famous, to emerge from LQG's spin networks.

Causal Dynamical Triangulations

Here we encounter one of a couple ideas that, if its profile ever increases, will probably need a catchier title. CDT breaks down tiny units of volume and area -- the crucial stuff that makes up any spacetime -- into tiny tetrahedra, a little like a computer graphics chip renders complex surfaces by decomposing them into many itsy bitsy squares and triangles.

CDT can be seen, says Smolin, "as a very simplified form of Loop Quantum Gravity." And even if it is not The Ultimate Theory, CDT's practitioners have developed clever solutions and approximation methods that could be used for the real thing.

Pros: Classical spacetime, as described by Einstein, does emerge from CDT models.

Cons: It's not clear yet if falsifiable predictions can be made that would distinguish CDT from LQG or other theories.

Non-Commutative Geometry

Behind this clunky name lies a clever idea, developed by a French mathematician named Alain Connes. It recognizes that observable quantities of a particle such as position and momentum cannot both be precisely measured -- a quintessential aspect of quantum systems. Connes and his colleagues have outlined the spatial geometry that would produce this kind of "non-commutative" algebra. (Technically, a non-commutative operation is one in which AB does not equal BA.)

"Connes keeps one eye on what the physics tells us and the other eye on his mathematical notions, and tries to build from these a specific ... geometry which he claims goes more deeply into how physics and spacetime structure combine with one another," said Penrose.

Pros: An extremely useful mathematical toolkit that has turned up both in string theory and in LQG.

Cons: May just be another extremely useful mathematical tool -- along the lines of twistors and spin networks -- and not a physical theory unto itself.

No Ultimate Theory. Some holdouts maintain that the universe may simply have two sets of operators' manuals -- the Einsteinian for the massive and cosmic and the quantum mechanical for the tiny and energetic.

Of course, as Smolin points out in The Trouble With Physics, science is littered with present-day commonplaces that were once radical and courageous acts of unification: Copernicus said the Earth and the other planets were not two separate things but one. Giordano Bruno said the sun and the stars were not two separate things but one. Isaac Newton said the force that makes an apple fall from a tree is the same force that moves the planets through the heavens.

Skeptics of previous scientific grand unification efforts are often, though certainly not always, proved to have been lacking only in imagination.