A fundamental goal of physics is to describe and understand all the forces appearing in nature. All the phenomena occurring in the universe can be traced to the action of just four fundamental forces or interactions, namely, the gravitational, electromagnetic, strong, and weak interactions. This classification, although it greatly simplifies the picture of different interactions, does not provide real understanding of the nature of the different forces. Recent theoretical work suggests the existence of an M-theory, which would unify and explain all the interactions in a natural way.

#### Elementary particles

Since the time of the ancient Greeks, matter was treated as being composed of indivisible atoms. About 1900, it was shown that atoms are built from smaller units, electrons and nuclei. The atomic nucleus was soon shown to consist of still smaller units, protons and neutrons. Electrons, protons, and neutrons were called (not quite properly) elementary particles. Since 1930, many new elementary particles have been discovered. Elementary particles are assumed to be structureless, pointlike objects characterized by mass, electric charge, spin, and other quantum numbers. Any particle with mass is a source of the gravitational field, and when it carries an electric charge it creates its own electromagnetic field.

The electromagnetic field, weak interaction, and strong interaction are quantum in nature; that is, such interactions are transmitted by the exchange of special particles called quanta. A photon, which is a massless, spin-1, electrically neutral particle, moving with the speed of light, is a quantum of the electromagnetic field. The strong and weak interactions are transmitted by massive quanta. Despite many efforts, physicists have not been able to formulate a consistent quantum theory of gravity. It is believed, however, that gravitational interactions are transmitted by a massless, spin-2 particle, called the graviton.

The range of an interaction is inversely proportional to the mass of its quantum. Thus, the gravitational and electromagnetic interactions, transmitted by massless quanta, are of infinite range, while the strong and weak interactions, transmitted by massive quanta, are short range.

#### Renormalization

Promptly after quantum mechanics was discovered, physicists started to describe and calculate interactions between charged particles. It soon became clear that such calculations led to infinite results and that the main reason for this unexpected and unrealistic outcome was the assumption that elementary particles are pointlike. A very complicated procedure called renormalization was devised to extract finite results from these infinite expressions. It was surprising that the finite results obtained in such a way were in very good agreement with observations. Quantum electrodynamics, the quantum theory describing interactions between charged particles, is the most successful theory created so far. It is not considered, however, a complete theory because it is supplemented by a set of rules necessary to obtain finite results. For many years, quantum electrodynamics was used as a model of a quantum theory describing interactions between elementary particles.

#### Gauge theories

In 1954, using classical electromagnetic theory as a model, C. N. Yang and R. L. Mills constructed a classical gauge theory allowing in its simplest versions two or three different electric and magnetic fields. Quantum versions of gauge theories were soon applied to describe the weak and strong interactions. However, like quantum electrodynamics, the quantum gauge theories lead to infinite results, and to obtain finite results it is necessary to properly manipulate infinite terms. In 1971, G. t'Hooft showed that there exists a consistent set of rules leading to finite results in quantum gauge theories.

#### Quarks

Meanwhile, in 1963, M. Gell-Mann and independently G. Zweig, by unraveling a hidden symmetry between elementary particles, postulated that protons and neutrons, among other elementary particles, are not truly elementary but are composed of smaller units, which were named quarks. To explain the observed properties of elementary particles, six different types of quarks are needed. The existence of all six quarks has been observationally confirmed.

#### Standard model

In the late 1960s, the weak and electromagnetic interactions were unified into a new type of interaction, now called the electroweak interaction. This unification means that at sufficiently high energies of the interacting particles it is not possible to distinguish between the weak and electromagnetic interactions. The theory describing interactions between quarks and their strange properties was combined with the electroweak theory, which in the meantime was successfully tested observationally, into the standard model of elementary particles. So far, the standard model has survived all the observational tests that have been carried out, but because it contains several parameters that must be specified by fitting observational data, it is not considered a fundamental model. The standard model, for example, does not include the gravitational interaction.

#### String theory

Meanwhile, a new, radically different approach slowly emerged. The first point of departure was the assumption that elementary particles are not pointlike objects but one-dimensional extended strings. A string could be open, like a piece of thread, or closed, like a rubber band. The typical length of a string is only about 10^{−35} m. To test this length scale, it is necessary to reach very high energies. Different states of vibration of a string correspond to different elementary particles.

In 1984, M. Green and J. Schwarz discovered that a consistent quantum theory of interacting strings can exist only in a spacetime with either 10 or 26 dimensions. To obtain the 4-dimensional physical space that is observed, it is necessary to assume that the additional 6 or 22 dimensions are compactified or “wrapped around” at a very small scale, comparable to the size of a string and therefore unobservable at low energy. There was great interest when the low-energy limit of string theory was shown to very closely resemble the standard model. New versions of string theory were soon proposed which, at the low-energy limit, resembled the standard model even more closely. Each of these theories contained massless spin-2 particles, that is, gravitons, and in the low-energy limit also reproduced the classical theory of general relativity. However, the great excitement of the mid-1980s faded when it proved impossible to derive observationally tested predictions from string theory.

So far, five different string theories containing general relativity in an appropriate limit have been proposed. The type I string theory allows open and closed strings, while other string theories are based on closed strings only. To this list, string theorists also added the 11-dimensional supergravity theory.

#### String duality

During the last few years, it has been shown that the six theories are interrelated. This surprising result is connected with a recently discovered duality relating different string theories. This duality was discovered when E. Witten and then others realized that one string theory at a strong-coupling limit is equivalent to another string theory at a weak-coupling limit. It was therefore possible to perform calculations at the strong-coupling limit. For example, in 10-dimensional Minkowski spacetime, the strong-coupling limit of the type I string theory is equivalent to the weakly coupled SO(32) heterotic string. The five string theories and the 11-dimensional supergravity theory are different weak-coupling limits of a more general, yet to be discovered, M-theory. The M-theory is now the prime candidate for the theory of everything, unifying all interactions that appear in nature.

#### D-branes and black holes

Very little is known about the M-theory. Probably, the M-theory resides in an 11-dimensional spacetime. If so, there is an interesting possibility that strings are actually 2-dimensional membranes.

J. Polchinski showed that duality between different string theories requires existence not only of strings but also of higher-dimensional objects, named D-branes (short for D-dimensional membranes). D-branes are a kind of topological defect, similar to dislocations in crystals, with the distinctive property that the end points of strings can be attached to them. D-branes carry charges and vibrate, move in spacetime, and interact with strings and other D-branes.

By using string theory and D-branes, it was possible to solve one of the mysteries of black holes. Black holes form at end points of evolution of sufficiently massive stars. The central core of such a star is unable to counterbalance its own gravitational attraction and collapses to form a black hole; the energy released during the collapse causes a dramatic expulsion of the outer layers of the star (a supernova explosion). S. Hawking showed that, if quantum processes are taken into account, black holes radiate energy in the same way as a black body whose temperature is inversely proportional to the mass of the black hole. The black hole can be characterized by a temperature, and hence by an entropy, which is proportional to its surface area. For a standard system, the entropy is proportional to the logarithm of the number of quantum microstates of the system. Recently, several groups of researchers were able to calculate the number of quantum microstates for a class of black holes and confirm that the entropy of a black hole is indeed described by the formula given by quantum-statistical mechanics. This result indicates that black holes behave as standard quantum-mechanical systems, and that the process of formation of a black hole, contrary to Hawking's assertion, is not connected with loss of information.

The recent developments in string theory have revived prospects for formulating the theory of everything. However, since the M-theory has not been discovered yet, the present situation is similar to the early development of quantum mechanics when N. Bohr formulated the basic rules for finding energy levels in an atom.