# Unified Field Theory

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## unified field theory

[′yü·nə‚fīd ′fēld ‚thē·ə·rē]## Unified Field Theory

a physical theory whose aim is a unified description of all elementary particles (or, at least, of groups of particles) and the derivation of the properties of these particles, of the laws of their motion, and of their interconversions on the basis of certain universal laws describing a single “primary material,” the various states of which correspond to various particles.

The first example of a unified field theory was the attempt by H. A. Lorentz to explain the total inertia of the electron (that is, derive the value of its mass) on the basis of classical electrodynamics. The electron itself was considered, in this case, to be a concentration in the electromagnetic field such that the laws governing its motion must, in the final analysis, be reduced to the laws describing this field. The consistent development of this program proved to be impossible, but the attempt itself to “reconcile” the discrete (the electron was regarded as a material particle) and the continuous (electromagnetic field), namely, the attempt to provide a unified description of different fundamental types of matter, was resumed much later as well.

The development of quantum concepts showed that the problem is not one of “reconciling” particles and fields and the discrete and the continuous. Any “particle” or “field” has a dual nature, combining in itself the properties of particles as well as the properties of waves. However, in this case, each type of “wave-particle” has its individual properties and specific laws of motion. These laws for electrons differ from those, for example, for neutrinos or photons. The discovery of each new “elementary particle” is regarded in modern theory as the discovery of a new type of matter. As new particles (and since all particles also have wave properties, it is possible to say new types of fields) were discovered, it became increasingly necessary to understand why there were so many (more than 200 at present), to explain the properties of these particles, and to decipher, finally, the meaning of the word “elementary” as applied to particles. Once again, but on a higher level, attempts were made at a unified description of matter.

A great stimulating role in this respect was played by Einstein’s general theory of relativity. Both the laws of gravitation and the equations of motion of the attracting masses are derived in this theory from general laws that determine the gravitational field. The general theory of relativity relates gravitation to the geometric properties of space-time. Some works attempted a broader “geometrization” of the theory, that is, such hypotheses relating to geometry were introduced that would make it possible to include electromagnetic fields in the analysis, as well as incorporate quantum effects. Such a “geometric” approach is very attractive but substantial advances in this direction have not yet proved possible.

A completely new approach, which may be called a model approach, originated with the studies of L. de Broglie on the neutrino theory of light. These studies assume that photons, which are quanta of light, are pairs of coalesced neutrinos (hence the term “coalescence theory”). A neutrino does not have an electric charge, its rest mass is zero, and its spin is ½ (in units of Planck’s constant ħ). Coalescing, two neutrinos may form a neutral particle of zero mass and spin 1, that is, with the characteristics of a photon.

The neutrino theory of light, even though it has its shortcomings, was the first theory in the series of models of compound particles. Among these theories are the model of E. Fermi and Yang Chen Ning, which examines the π-meson as a bound state of a nucleon and an antinucleon, and the model of Shoichi Sakata (Japan), M. A. Markov, and L. B. Okun’, in which all strongly interacting particles were constructed from three fundamental particles. A-widely accepted model in recent years is the quark model, first proposed by M. Gell-Mann and G. Zweig in 1964. According to this model, all strongly interacting particles (mesons, baryons, resonances) consist of special “subparticles”—three types of quarks—with fractional electric charges as well as of the corresponding antiparticles (antiquarks). This model, which proved to be very fruitful for the systematics of elementary particles and explained a number of fine effects related to the particle masses and their magnetic moments, as well as some other experimental observations, sharply reduces the number of candidates for the designation of “truly elementary” particles, and, hence, in a way solves the problem of a unified description of matter. However, the theory is still far from the necessary clarity, and experimental answers are still required to a series of cardinal questions. It is sufficient to say that quarks have not been observed in the free state, and it is not unlikely that this is impossible in principle. In this case, the quark model will lose its significance as the component model.

Even before the formulation of the quark model, W. Heisenberg (1957) began developing a theory in which the basis is represented by a universal unified field, described by quantities designated as spinors in mathematics. For this reason, the theory received the name the unified nonlinear spinorial theory. In contrast to the above-mentioned coalescence theory, this fundamental field, which describes “matter as a whole,” is not connected directly with any real particle. The second essential distinction of the primary equation of Heisenberg’s theory is nonlinearity, reflecting the interaction of the fundamental field with itself. This is expressed mathematically by the appearance of members in the equation of motion that are proportional not to the quantity itself describing the field but to a power of this quantity different from zero. As in the general theory of relativity, this non-linearity makes it possible to derive the equations of motion of real particles from the basic equation. The same equation must also yield the values of the masses, electric charges, spins, and other particle characteristics.

The mathematical investigation of Heisenberg’s equation is a difficult task that has thus far been solved only in a fairly crude approximation. Moreover, the self-consistency of the procedure for eliminating infinities in Heisenberg’s theory has not yet been proved. At the same time, the quantitative results obtained in this theory appear to be encouraging, and the general program of nonlinear unified field theory still looks promising.

Thus, a unified field theory has not yet been constructed. However, the inseparable relationship between all particles, the universal interconvertibility of particles, and the increasingly more clear evidence of the unity of matter all make it mandatory to search for transitions from the contemporary quantum field theory, which is limited to ascertaining the diversity of forms of matter, to a unified theory, which is designed to explain this diversity.

### REFERENCES

*Nelineinaia kvantovaiia teoriia polia: Sb. statei.*Moscow, 1959.

Heisenberg, W.

*Vvedenie v edinuiu polevuiu teoriiu elementarnykh chastits.*Moscow, 1968. (Translated from English.)

Einstein, A.

*Sobr. nauchnykh trudov*, vols. 1–2. Moscow, 1965–66.

V. I. GRIGOR’EV