# Section 3: String Theory

Almost by accident in the mid 1970s, theorists realized that they could obtain a quantum gravity theory by postulating that the fundamental building blocks of nature are not point particles, a traditional notion that goes back at least as far as the ancient Greeks, but instead are tiny strands of string. These strings are not simply a smaller version of, say, our shoelaces. Rather, they are geometrical objects that represent a fundamentally different way of thinking about matter. This family of theories grew out of the physics of the strong interactions. In these theories, two quarks interacting strongly are connected by a stream of carriers of the strong force, which forms a "flux tube." The potential energy between the two quarks, therefore, grows linearly with the distance between the quarks. See the math

Figure 6: As quarks are pulled apart, eventually new quarks appear.

We choose to call the proportionality constant that turns the distance between the strongly interacting particles into a quantity with the units of energy "Tstring" because it has the dimensions of mass per unit length as one would expect for a string's tension. In fact, one can think of the object formed by the ﬂux tube of strong force carriers being exchanged between the two quarks as being an effective string, with tension Tstring.

One of the mysteries of strong interactions is that the basic charged objects—the quarks—are never seen in isolation. The string picture explains this confinement: If one tries to pull the quarks farther and farther apart, the growing energy of the flux tube eventually favors the creation of another quark/anti-quark pair in the middle of the existing quark pair; the string breaks, and is replaced by two new flux tubes connecting the two new pairs of quarks. For this reason and others, string descriptions of the strong interactions became popular in the late 1960s. Eventually, as we saw in Unit 2, quantum chromodynamics (QCD) emerged as a more complete description of the strong force. However, along the way, physicists discovered some fascinating aspects of the theories obtained by treating the strings not as effective tubes of flux, but as fundamental quantum objects in their own right.

Perhaps the most striking observation was the fact that any theory in which the basic objects are strings will inevitably contain a particle with all the right properties to serve as a graviton, the basic force carrier of the gravitational force. While this is an unwanted nuisance in an attempt to describe strong interaction physics, it is a compelling hint that quantum string theories may be related to quantum gravity.

Figure 7: Gravitons arise naturally in string theory, leading to Feynman diagrams like the one on the right.

In 1984, Michael Green of Queen Mary, University of London and John Schwarz of the California Institute of Technology discovered the first fully consistent quantum string theories that were both free of catastrophic instabilities of the vacuum and capable in principle of incorporating the known fundamental forces. These theories automatically produce quantum gravity and force carriers for interactions that are qualitatively (and in some special cases even quantitatively) similar to the forces like electromagnetism and the strong and weak nuclear forces. However, this line of research had one unexpected consequence: These theories are most naturally formulated in a 10-dimensional spacetime.

We will come back to the challenges and opportunities offered by a theory of extra spacetime dimensions in later sections. For now, however, let us examine how and why a theory based on strings instead of point particles can help with the problems of quantum gravity. We will start by explaining how strings resolve the problems of Einstein's theory with high-energy scattering. In the next section, we discuss how strings modify our notions of geometry at short distances.

## Strings at high energy

In the previous section, we learned that for particles colliding at very high energies, the sum of the probabilities for all the possible outcomes of the collision calculated using the techniques of Unit 2 is greater than 100 percent, which is clearly impossible. Remarkably, introducing an extended object whose fundamental length scale is not so different from the Planck length, ~ 10-32 centimeters, seems to solve this basic problem in quantum gravity. The essential point is that in high-energy scattering processes, the size of a string grows with its energy.

Figure 8: String collisions are softer than particle collisions.