String theory is the idea that the universe is not composed of essentially dimensionless point particles but of tiny "strings" that, like guitar strings, can vibrate at different rates - and these different rates of vibration are what appear as the fundamental particles (electrons, quarks, and so on) that form matter as we know it.
The great attraction of string theory is that it successfully, indeed by its very nature, unites the forces operating on the smallest scale (the strong and electroweak forces, described by quantum theory) and that operating on the largest, universal scale (gravity, described by the General Theory of Relativity). It is, then, a so-called "theory of everything," a single set of equations that describe the very structure of the universe and all the forces operating in it.
The mathematics involved are incredibly complex as are the mental gymnastics required to even attempt to conceive of the universe it describes, one of 11 dimensions (10 spatial, one time). Nonetheless, its advocates insist that it's on the verge of an ultimate description of the very nature of space and time, telling us finally to what question "42" is the answer.
What drives its detractors nuts is that it's been on that verge for 20 years now with no sign it's gotten any closer or that it can make a prediction which can be tested experimentally.
Part of the problem is that the equations of string theory do not give a single answer; rather, there are a truly huge number of answers, each one describing a potential universe. And most scientists hate the idea that there is nothing special about our universe. Not out of ego, but out of probabilities: If all possible universes are equally likely but only a tiny fraction of them have conditions that would allow for the ultimate development of life, how in blazes did it come to be that the one that happened turned out to be one of that tiny fraction? Scientists want reasons for things and while "dumb luck" is possible, it's both very unlikely and very unsatisfying as an answer. So most cosmologists believe there is something about the laws of nature which required a universe like or at least similar to ours to emerge from the Big Bang.
(There are ways around that conundrum: Several hypotheses involve multiple universes existing either sequentially or simultaneously; indeed, one version of quantum mechanics, known as the "many worlds" version, postulates that new universes are being created constantly. But again, it's hard to suggest an experimental test.)
Still, the tantalizing possibility of an ultimate answer, an answer which may actually point to a deeper structure, something even more fundamental than time and space, is enough to keep people working for all their professional lives on something they know may not be tested in their lifetimes. There are possibilities that in the next few years a few projects in the works could provide some initial tests of the theory's predictions, but that will not resolve the debate: Those tests, involving new satellite-based detectors and a new supercollider won't be definitive. But they can strengthen or weaken the case, so if they all point in one direction or the other, we may have a fair indication of if we're on to something or not.
The New York Times for December 7 has a nice, long article on the state of string theory. If you find it interesting, I'd highly recommend a book called The Elegant Universe by Brian Greene.
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