The Elegant Universe - Brian Greene [107]
As had been the case with Kaluza's original attempt, various versions of higher-dimensional supergravity looked quite promising at first. The new equations resulting from the extra dimensions were strikingly reminiscent of those used in the description of electromagnetism, and the strong and the weak forces. But detailed scrutiny showed that the old conundrums persisted. Most importantly, the pernicious short-distance quantum undulations of space were lessened by supersymmetry, but not sufficiently to yield a sensible theory. Physicists also found it difficult to find a single, sensible, higher-dimensional theory incorporating all features of forces and matter.7
It gradually became clear that bits and pieces of a unified theory were surfacing, but that a crucial element capable of tying them all together in a quantum-mechanically consistent manner was missing. In 1984 this missing piece—string theory—dramatically entered the story and took center stage.
More Dimensions and String Theory
By now you should be convinced that our universe may have additional curled-up spatial dimensions; certainly, so long as they are small enough, nothing rules them out. But extra dimensions may strike you as an artifice. Our inability to probe distances smaller than a billionth of a billionth of a meter permits not only extra tiny dimensions but all manner of whimsical possibilities as well—even a microscopic civilization populated by even tinier green people. While the former certainly seems more rationally motivated than the latter, the act of postulating either of these experimentally untested—and, at present, untestable—possibilities might seem equally arbitrary.
Such was the case until string theory. Here is a theory that resolves the central dilemma confronting contemporary physics—the incompatibility between quantum mechanics and general relativity—and that unifies our understanding of all of nature's fundamental material constituents and forces. But to accomplish these feats, it turns out that string theory requires that the universe have extra space dimensions.
Here's why. One of the main insights of quantum mechanics is that our predictive power is fundamentally limited to asserting that such-and-such outcome will occur with such-and-such probability. Although Einstein felt that this was a distasteful feature of our modern understanding, and you may agree, it certainly appears to be fact. Let's accept it. Now, we all know that probabilities are always numbers between 0 and 1—equivalently, when expressed as percentages, probabilities are numbers between 0 and 100. Physicists have found that a key signal that a quantum-mechanical theory has gone haywire is that particular calculations yield "probabilities" that are not within this acceptable range. For instance, we mentioned earlier that a sign of the grinding incompatibility between general relativity and quantum mechanics in a point-particle framework is that calculations result in infinite probabilities. As we have discussed, string theory cures these infinities. But what we have not as yet mentioned is that a residual, somewhat more subtle problem still remains. In the early days of string theory physicists found that certain calculations yielded negative probabilities, which are also outside of the acceptable range. So, at first sight, string theory appeared to be awash in its own quantum-mechanical hot water.
With stubborn determination, physicists sought and found the cause of this unacceptable feature. The explanation begins with a simple observation. If a string is constrained to lie on a two-dimensional surface—such as the surface of a table or a garden hose—the number of independent directions in which it can vibrate is reduced to two: the left-right and back-forth dimensions along the surface. Any vibrational pattern that remains on the surface involves some combination of vibrations in these