The Elegant Universe - Brian Greene [148]
Our work and that of Witten show that physical characteristics such as the number of families of string vibrations and the types of particles within each family are unaffected by these processes. As the Calabi-Yau space evolves through a tear, what can be affected are the precise values of the masses of the individual particles—the energies of the possible patterns of string vibrations. Our papers showed that these masses will vary continuously in response to the changing geometrical form of the Calabi-Yau component of space, some going up while others go down. Of primary importance, though, is the fact that there is no catastrophic jump, spike, or any unusual feature of these varying masses as the tear actually occurs. From the point of view of physics, the moment of tearing has no distinguishing characteristics.
This point raises two issues. First, we have focused on tears in the spatial fabric that occur in the extra six-dimensional Calabi-Yau component of the universe. Can such tears also occur in the more familiar three extended spatial dimensions? The answer, almost certainly, is yes. After all, space is space—regardless of whether it is tightly curled up into a Calabi-Yau shape or is unfurled into the grand expanse of the universe we perceive on a clear, starry night. In fact, we have seen earlier that the familiar spatial dimensions might themselves actually be curled up into the form of a giant shape that curves back on itself, way on the other side of the universe, and that therefore even the distinction between which dimensions are curled up and which are unfurled is somewhat artificial. Although our and Witten's analyses did rely on special mathematical features of Calabi-Yau shapes, the result—that the fabric of space can tear—is certainly of wider applicability.
Second, could such a topology-changing tear happen today or tomorrow? Could it have happened in the past? Yes. Experimental measurements of elementary particle masses show their values to be quite stable over time. But if we head back to the earliest epochs following the big bang, even non-string-based theories invoke important periods during which elementary particle masses do change over time. These periods, from a string-theoretic perspective, could certainly have involved the topology-changing tears discussed in this chapter. Closer to the present, the observed stability of elementary particle masses implies that if the universe is currently undergoing a topology-changing spatial tear, it must be doing it exceedingly slowly—so slowly that its effect on elementary particle masses is smaller than our present experimental sensitivity. Remarkably, so long as this condition is met, the universe could currently be in the midst of a spatial rupture. If it were occurring slowly enough, we would not even know it was happening. This is one of those rare instances in physics in which the lack of a striking observable phenomenon is cause for great excitement. The absence of an observable calamitous consequence from such an exotic geometrical evolution is testament to how far beyond Einstein's expectations string theory has gone.
Chapter 12
Beyond Strings: In Search of M-Theory
In his long search for a unified theory, Einstein reflected on whether "God could have made the Universe in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all."1 With this remark, Einstein articulated the nascent form of a view that is currently shared by many physicists: If there is a final theory of nature, one of the most convincing arguments in support of its particular form would be that the theory couldn't be otherwise. The ultimate theory should take the form that it does because it is the unique explanatory framework capable of describing the universe without running up against any internal inconsistencies or logical absurdities. Such a theory would declare that things are the way they