String Theory, Extra Dimensions, and the Nature of Ultimate Laws

Key Insight

String theories, while offering a promising route to unification, introduce a significant challenge by requiring space-time to have 10 or 26 dimensions, instead of the observed four. This discrepancy is addressed by the hypothesis that the additional dimensions are 'curled up' into an extremely small space, approximately 10^-17 inches, rendering them undetectable at macroscopic scales. This phenomenon is analogous to observing a straw from a distance, where it appears one-dimensional, but upon closer inspection, its two-dimensional surface becomes evident. This explanation, however, implies that these extra dimensions are far too minuscule for practical applications like space travel. A key unresolved question is why, in the very early universe, one time dimension and three spatial dimensions flattened out, while the others remained tightly curled.

The 'anthropic principle' provides a possible rationale for the observed four dimensions, suggesting that life, as we understand it, necessitates a specific dimensional configuration. In a two-dimensional space, complex biological organisms would face insurmountable obstacles, such as the inability to pass each other or a digestive tract dividing the creature into two. Conversely, more than three spatial dimensions introduce severe physical instabilities: the gravitational force would diminish much more rapidly with distance (e.g., dropping to 1/8 for a doubled distance in four dimensions, compared to 1/4 in three), leading to unstable planetary orbits where planets would either spiral into or away from their suns. Stars themselves would be unstable, unable to balance pressure against gravity, either collapsing into black holes or falling apart. Similarly, atomic structures would be impossible, as electrical forces would cause electrons to either escape or spiral into the nucleus. Therefore, the existence of intelligent beings is contingent upon the universe possessing precisely one time and three spatial dimensions that are not curled up.

String theory initially faced problems with the existence of at least four different versions and millions of ways to curl up the extra dimensions, preventing a unique solution. However, the discovery of 'dualities' around 1994 demonstrated that various string theories and curling configurations could lead to identical results in four dimensions. Furthermore, the emergence of 'p-branes'—objects occupying higher-dimensional volumes (e.g., a particle as a 0-brane, a string as a 1-brane, up to 9-branes)—suggests a 'democracy' among supergravity, string, and p-brane theories, implying they are different approximations of a more fundamental, overarching theory valid in different situations. This overarching theory might not be a single formulation, but rather a collection of overlapping formulations, akin to multiple maps needed to describe a complex surface, each valid in its own region but consistent where they overlap. While there are infinite sequences of more refined theories, gravity, particularly at the Planck energy (10^19 GeV), provides a natural limit, as particles reaching this energy would form black holes and effectively cut themselves off from the rest of the universe, implying an ultimate theory exists. Such a theory, if consistent and matching observations, would revolutionize common understanding of the universe, making its laws accessible to a wider populace, though prediction limitations due to the uncertainty principle and the inherent complexity of solving equations for real-world scenarios would still remain.