In the 20th century, two theoretical frameworks emerged for formulating the laws of physics. The first is
Albert Einstein's
general theory of relativity, a theory that explains the force of
gravity and the structure of
spacetime at the macro-level. The other is
quantum mechanics, a completely different formulation, which uses known
probability principles to describe physical phenomena at the micro-level. By the late 1970s, these two frameworks had proven to be sufficient to explain most of the observed features of the
universe, from
elementary particles to
atoms to the evolution of stars and the universe as a whole.
[1]
In spite of these successes, there are still many problems that remain to be solved. One of the deepest problems in modern physics is the problem of
quantum gravity.
[1] The general theory of relativity is formulated within the framework of
classical physics, whereas the other
fundamental forces are described within the framework of quantum mechanics. A quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics, but difficulties arise when one attempts to apply the usual prescriptions of quantum theory to the force of gravity.
[2] In addition to the problem of developing a consistent theory of quantum gravity, there are many other fundamental problems in the physics of
atomic nuclei,
black holes, and the early universe.
[a]
String theory is a
theoretical framework that attempts to address these questions and many others. The starting point for string theory is the idea that the
point-like particles of
particle physics can also be modeled as one-dimensional objects called
strings. String theory describes how strings propagate through space and interact with each other. In a given version of string theory, there is only one kind of string, which may look like a small loop or segment of ordinary string, and it can vibrate in different ways. On distance scales larger than the string scale, a string will look just like an ordinary particle, with its
mass,
charge, and other properties determined by the vibrational state of the string. In this way, all of the different elementary particles may be viewed as
vibrating strings. In string theory, one of the vibrational states of the string gives rise to the
graviton, a quantum mechanical particle that carries gravitational force. Thus string theory is a theory of quantum gravity.
[3]
One of the main developments of the past several decades in string theory was the discovery of certain 'dualities', mathematical transformations that identify one physical theory with another. Physicists studying string theory have discovered a number of these dualities between different versions of string theory, and this has led to the conjecture that all consistent versions of string theory are subsumed in a single framework known as
M-theory.
[4]
Studies of string theory have also yielded a number of results on the nature of black holes and the gravitational interaction. There are certain paradoxes that arise when one attempts to understand the quantum aspects of black holes, and work on string theory has attempted to clarify these issues. In late 1997 this line of work culminated in the discovery of the
anti-de Sitter/conformal field theory correspondence or AdS/CFT.
[5] This is a theoretical result which relates string theory to other physical theories which are better understood theoretically. The AdS/CFT correspondence has implications for the study of black holes and quantum gravity, and it has been applied to other subjects, including
nuclear[6] and
condensed matter physics.
[7][8]
Since string theory incorporates all of the fundamental interactions, including gravity, many physicists hope that it will eventually be developed to the point where it fully describes our universe, making it a
theory of everything. One of the goals of current research in string theory is to find a solution of the theory that reproduces the observed spectrum of elementary particles, with a small
cosmological constant, containing
dark matter and a plausible mechanism for
cosmic inflation. While there has been progress toward these goals, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of details.
[9]
One of the challenges of string theory is that the full theory does not have a satisfactory definition in all circumstances. The scattering of strings is most straightforwardly defined using the techniques of
perturbation theory, but it is not known in general how to define string theory
nonperturbatively.
[10] It is also not clear whether there is any principle by which string theory selects its
vacuum state, the physical state that determines the properties of our universe.
[11] These problems have led some in the community to criticize these approaches to the unification of physics and question the value of continued research on these problems.
[12]
Strings
Main article:
String (physics)
Interaction in the quantum world:
worldlines of point-like
particles or a
worldsheet swept up by closed
strings in string theory.
The application of quantum mechanics to physical objects such as the
electromagnetic field, which are extended in space and time, is known as
quantum field theory. In particle physics, quantum field theories form the basis for our understanding of elementary particles, which are modeled as excitations in the fundamental fields.
[13]
In quantum field theory, one typically computes the probabilities of various physical events using the techniques of
perturbation theory. Developed by
Richard Feynman and others in the first half of the twentieth century, perturbative quantum field theory uses special diagrams called
Feynman diagrams to organize computations. One imagines that these diagrams depict the paths of point-like particles and their interactions.
[13]
The starting point for string theory is the idea that the point-like particles of quantum field theory can also be modeled as one-dimensional objects called strings.
[14] The interaction of strings is most straightforwardly defined by generalizing the perturbation theory used in ordinary quantum field theory. At the level of Feynman diagrams, this means replacing the one-dimensional diagram representing the path of a point particle by a two-dimensional (2D) surface representing the motion of a string.
[15] Unlike in quantum field theory, string theory does not have a full non-perturbative definition, so many of the theoretical questions that physicists would like to answer remain out of reach.
[16]
In theories of particle physics based on string theory, the characteristic length scale of strings is assumed to be on the order of the
Planck length, or 10−35 meters, the scale at which the effects of quantum gravity are believed to become significant.
[15] On much larger length scales, such as the scales visible in physics laboratories, such objects would be indistinguishable from zero-dimensional point particles, and the vibrational state of the string would determine the type of particle. One of the vibrational states of a string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force.
[3]
The original version of string theory was
bosonic string theory, but this version described only
bosons, a class of particles which transmit forces between the matter particles, or
fermions. Bosonic string theory was eventually superseded by theories called
superstring theories. These theories describe both bosons and fermions, and they incorporate a theoretical idea called
supersymmetry. In theories with supersymmetry, each boson has a counterpart which is a fermion, and vice versa.
[17]
There are several versions of superstring theory:
type I,
type IIA,
type IIB, and two flavors of
heterotic string theory (
SO(32) and
E8×E8). The different theories allow different types of strings, and the particles that arise at low energies exhibit different
symmetries. For example, the type I theory in