PASADENA—The theory is so obscure there's not a Wikipedia page about it yet. It might be impossible to formulate mathematically. One theoretical physicist calls it the Emperor Palpatine of theories, even more powerful and inscrutable than the Darth Vader theory that he and others have been studying intensively. And yet it has a purity and elegance that makes them think it captures the deep essence of the natural world. "It’s this sort of ur-theory," says Nima Arkani-Hamed of the Institute for Advanced Study.
I learned about this strange theoretical brainstorm yesterday while attending a conference at Caltech that has drawn the most intimidatingly brilliant group of people ever assembled in one room. I considered myself lucky when I could understand just the title slide of their presentations. They have come to celebrate the 35th anniversary of the aforementioned Darth Vader theory, known formally as "N=4 supersymmetric Yang-Mills (SYM) theory". The dark-lord comparison might lead you to believe the theory is irredeemably evil, but in fact theorists consider it their most sublime creation.
The official name requires some unpacking. Supersymmetry is the idea that spacetime, in addition to its usual dimensions of space and time, has an entirely different type of dimension—a quantum dimension, whose coordinates are not ordinary real numbers but a whole new class of number that can be thought of as the square roots of zero. (Yes, that's allowed. This is quantum physics, after all.) You can’t visualize them, let alone see them, but you can perceive them indirectly: when you rotate an object from an ordinary dimension into a quantum dimension, the object changes what might have seemed to be its essential character. A particle of force becomes a particle of matter, and vice versa. Thus supersymmetry shows that "force" and "matter" are not essential categories, but the same thing viewed differently.
Supersymmetry comes in degrees. The type being sought at the Large Hadron Collider is a minimal version, denoted by N=1, which relates one class of force particle to one class of matter particle. N=4 SYM goes the whole hog: it interrelates all force and matter particles—all, that is, except for those associated with the force of gravity. The term "Yang-Mills" connotes that the theory is a souped-up version of the weak and strong nuclear forces. For gravity, you'd go to N=8.
The high degree of symmetry enormously simplifies the workings of N=4 SYM. The theory does have the disadvantage that it does not and cannot describe the real world, but it is a theoretical physicists’ version of C. elegans, having a purity that makes it a convenient test-bed for conceptual experimentation. Over the past several years, Arkani-Hamed and his colleagues have been trying to reformulate N=4 SYM in a way that makes no reference to space and time, in the hopes it will help them grasp how space and time might emerge from some deeper ingredients.
But now it seems that there is a still greater theory: the Emperor theory, known as (2,0) theory based on the amount and type of supersymmetry it possesses. After his talk, Arkani-Hamed sat down to tell me more about it. It actually goes back to the 1990s and the ferment within string theory back then, although it languished until fairly recently. The unnerving thing about the theory is that physicists think it exists even though they've never written it down and are not even sure they can. In this, the Emperor resembles that other creation of the mid-1990s: M-theory, a theory whose existence seems to be implicit in string theory, even though physicists hem and haw when you ask what exactly it is. Both M-theory and the Emperor theory are physics versions of an inchoate feeling you struggle to verbalize.
For something that is as incorporeal as a dead Jedi master, theorists claim to know a lot about the Emperor theory. It resides in five spatial dimensions rather than three. It can be thought of as a collection of the building blocks of M-theory. It is a theory not of strings but of quantum fields, similar in spirit to electrical and magnetic fields. In fact, it provides a true unification of electricity and magnetism, beyond even that envisioned in classical physics: these two phenomena are just different shadows of (2,0) theory projected from five into three spatial dimensions.
Perhaps most intriguingly, (2,0) theory is irreducibly quantum. "It’s the first instance known of a purely quantum-mechanical theory," Arkani-Hamed says. In fact, the theory reveals a heretofore unsuspected connection between the quantum nature of matter and the structure of spacetime. One may entail the other, bucking the conventional wisdom that they are contradictory, on account of spooky action at a distance.
To judge from how those brilliant people are still at a loss for words, let alone equations, I suspect it will be years before (2,0) theory is the subject of a Scientific American article, let alone a New Yorker cartoon. In the meantime, may all the forces of nature be with them.