The Last Free City

A string theory is a physical model whose fundamental building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that were the basis of most earlier physics. For this reason, string theories are able to avoid problems associated with the presence of pointlike particles in a physical theory. Detailed study of string theories has revealed that they describe not just strings but other objects, variously including points, membranes, and higher-dimensional objects. As discussed below, it is important to realize that no string theory has yet made firm predictions that would allow it to be experimentally tested.

The term 'string theory' properly refers to both the 26-dimensional bosonic string theories and to the 10-dimensional superstring theories discovered by adding supersymmetry. Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name 'bosonic string theory'. In the 1990s, Edward Witten and others found strong evidence that the different superstring theories were different limits of an unknown 11-dimensional theory called M-theory. These discoveries sparked the Second Superstring Revolution.

Interest in string theory is driven largely by the hope that it will prove to be a theory of everything. It is one viable solution for quantum gravity, and in addition to gravity it can naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories also include fermions, the building blocks of matter. It is not yet known whether string theory is able to describe a universe with the precise collection of forces and matter that we observe, nor how much freedom to choose those details the theory will allow.

On a more concrete level, string theory has led to advances in the mathematics of knots, Calabi-Yau spaces and many other fields. Much exciting new mathematics in recent years has its origin in string theory. String theory has also led to much insight into supersymmetric gauge theories, a subject which includes possible extensions of the standard model.

Extra dimensions

One intriguing feature of string theory is that it predicts the number of dimensions which the Universe should possess. Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions "by hand".

Instead, string theory allows one to compute the number of spacetime dimensions from first principles. Technically, this happens because Lorentz invariance can only be satisfied in a certain number of dimensions. This is roughly like saying that if we measure the distance between two points, then rotate our observer by some angle and measure again, the observed distance only stays the same if the Universe has a particular number of dimensions.

The only problem is that when the calculation is done, the Universe's dimensionality is not four as one may expect (three axes of space and one of time), but twenty-six. More precisely, bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 dimensions.

However, these models appear to contradict observed phenomena. Physicists usually solve this problem in one of two different ways. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience. We achieve the 6-dimensional model's resolution with Calabi-Yau spaces. In 7 dimensions, they are termed G2 manifolds. Essentially these extra dimensions are "compactified" by causing them to loop back upon themselves.

A standard analogy for this is to consider multidimensional space as a garden hose. If we view the hose from a sufficient distance, it appears to have only one dimension, its length. This is akin to the 4 macroscopic dimensions we are accustomed to dealing with every day. If, however, one approaches the hose, one discovers that it contains a second dimension, its circumference. This "extra dimension" is only visible within a relatively close range to the hose, just as the extra dimensions of the Calabi-Yau space are only visible at extremely small distances, and thus are not easily detected.

(Of course, everyday garden hoses exist in three spatial dimensions, but for the purpose of the analogy, we neglect its thickness and consider only motion on the surface of the hose. A point on the hose's surface can be specified by two numbers, a distance along the hose and a distance along the circumference, just like how points on the Earth's surface can be uniquely specified by latitude and longitude. In either case, we say that the object has two spatial dimensions. Like the Earth, garden hoses have an interior, a region that requires an extra dimension; but a Calabi-Yau space has no interior.)

Another possibility is that we are stuck in a 3+1 dimensional subspace of the full universe, where the "3+1" reminds us that time is a different kind of dimension than space. Because it involves mathematical objects called D-branes, this is known as a braneworld theory.

In either case, gravity acting in the hidden dimensions produces other, non-gravitational, forces, such as electromagnetism. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility.

Problems

String theory, as with any current theory of quantum gravity, is unverifiable, and therefore it is also unfalsifiable. Human beings do not have the technology to observe strings (which are said to be roughly 10-35 meters across). Eventually, we may be able to observe strings in a meaningful way, or at least to gain substantial insight by observing cosmological phenomena which may elucidate string physics.

Another problem is that, like quantum field theory, much of string theory is still only formulated perturbatively (i.e., as a series of approximations rather than as an exact solution). Although nonperturbative techniques have progressed considerably—including conjectured complete definitions in space-times satisfying certain asymptotics—a full nonperturbative definition of the theory is still lacking.