Unified Field Theory Of Gravitation Research Articles

Einstein's Washington Manuscript on Unified Field Theory*.

In this note, we point attention to and briefly discuss a curious manuscript of Einstein, composed in 1938 and entitled “Unified Field Theory,” the only such writing, published or unpublished, carrying this title without any further specification. Apparently never intended for publication, the manuscript sheds light both on Einstein′s modus operandi as well as on the public role of Einstein′s later work on a unified field theory of gravitation and electromagnetism.

The R.I. Pimenov unified gravitation and electromagnetism field theory as semi-Riemannian geometry

More then forty years ago R.I. Pimenov introduced a new geometry -- semi-Riemannian one -- as a set of geometrical objects consistent with a fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to which the physically different quantities (meter, second, coulomb etc.) are geometrically modelled as space coordinates that are not superposed by automorphisms. As there is only one type of coordinates in Riemannian geometry and only three types of coordinates in pseudo-Riemannian one, a multiple fibered semi-Riemannian geometry is the most appropriate one for the treatment of more then three different physical quantities as unified geometrical field theory. Semi-Euclidean geometry $^{3}R_5^4$ with 1-dimensional fiber $x^5$ and 4-dimensional Minkowski space-time as a base is naturally interpreted as classical electrodynamics. Semi-Riemannian geometry $^{3}V_5^4$ with the general relativity pseudo-Riemannian space-time $^{3}V^4,$ and 1-dimensional fiber $x^5,$ responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike Kaluza-Klein theories, where the 5-th coordinate appears in nondegenerate Riemannian or pseudo-Riemannian geometry, the theory based on semi-Riemannian geometry is free from defects of the former. In particular, scalar field does not arise. PACS: 04.50.Cd, 02.40.-k, 11.10.Kk

An Assessment of Evans’ Unified Field Theory I

Evans attempted to develop a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for a theory that implements some of the ideas that have been (imprecisely) indicated by Evans and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation, together with Evans' unified field theory, collapses to an ordinary Einstein equation.

An Assessment of Evans’ Unified Field Theory II

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans' theory and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation, together with Evans' unified field theory, collapses to an ordinary Einstein equation.

Field equations in teleparallel space–time: Einstein's Fernparallelismus approach toward unified field theory

A historical account of Einstein's Fernparallelismus approach toward a unified field theory of gravitation and electromagnetism is given. In this theory, a space–time characterized by a curvature-free connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field, is investigated. The approach was pursued by Einstein in a number of publications that appeared in the period from summer 1928 until spring 1931. In the historical analysis special attention is given to the question of how Einstein tried to find field equations for the tetrads. We claim that it was the failure to find and justify a uniquely determined set of acceptable field equations that eventually led to Einstein's abandoning this approach. We comment on some historical and systematic similarities between the Fernparallelismus episode and the Entwurf theory, i.e., the precursor theory of general relativity pursued by Einstein in the years 1912–1915.

The fifth dimension: Theodor Kaluza's ground-breaking idea

Theodor Kaluza (1885–1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions. Despite Einstein's great interest in Kaluza's theory, 50 years elapsed before it contributed toward a paradigm shift in modern theoretical physics. The biography of this still unknown scientist is briefly presented along with an outline of his work in physics. A short history of the theories of unification and the dimensionality of space-time is followed by a discussion of the significance of Kaluza's five-dimensional unified theory in modern physics from the point of view of superstring and M-theory.

The fifth dimension: Theodor Kaluza's ground‐breaking idea

AbstractTheodor Kaluza (1885–1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions. Despite Einstein's great interest in Kaluza's theory, 50 years elapsed before it contributed toward a paradigm shift in modern theoretical physics. The biography of this still unknown scientist is briefly presented along with an outline of his work in physics. A short history of the theories of unification and the dimensionality of space‐time is followed by a discussion of the significance of Kaluza's five‐dimensional unified theory in modern physics from the point of view of superstring and M‐theory.

Nonsymmetric unified theory of gravitation, electromagnetism and Yang–Mills field

The recently studied new variation of Einstein's metric nonsymmetric unified field theory of gravitation and electromagnetism is enlarged to include the Yang–Mills field theory. It is shown that the antisymmetric part of the metric tensor, now a 2 × 2 matrix, can be made to describe both a field obeying Maxwell's equations and a field obeying Yang–Mills's field equations in the flat space linear approximation, thereby making its identification with the sum of a generalized electromagnetic and isotopic field strength tensors a possibly consistent procedure. The theory is shown to be free of unphysical ghost-negative energy radiative modes even when expanded on a curved Riemannian background. The Einstein–Maxwell–Yang–Mills theory is contained in the first approximation of the field equations on a curved general relativity background.

Nonsymmetric unified field theory. II. Phenomenological aspects

The nonsymmetric unified field theory of gravitation and electromagnetism developed in a previous paper in vacuum is here supplemented by introducing the sources. The sources of the field, the matter energy-momentum tensor and the electromagnetic current, are introduced explicitly into the Lagrangian providing a close contact with elementary particle physics concepts in the linear approximation of the theory and an explicit form for the conservation laws. The theory is shown to be free of ghost-negative energy particles and tachyons as well. The equations of motion of test charged particles are established through the invariance of the interaction Lagrangian.

A non-dualistic unified field theory of gravitation, electromagnetism and spin

The wisdom of classicalunified field theories in the conceptual framework of Weyl, Eddington, Einstein and Schrodinger has often been doubted and in particular there does not appear to be any empirical reason why the Einstein-Maxwell (E-M) theory needs to be geometrized. The crux of the matter is, however not whether the E-M theory is aesthetically satisfactory but whether it answers all the modern questions within the classical context. In particular, the E-M theory does not provide a classical platform from which the Dirac equation can be derived in the way Schrodinger's equation is derived from classical mechanics via the energy equation and the Correspondence Principle. The present paper presents a non-dualistic unified field theory (UFT) in the said conceptual framework as propounded by M. A. Tonnelat. By allowing the metric formds2=gμνdxvxv and the non-degenerate two-formF=(1/2> l)ϕμνdxv∧dxvto enter symmetrically into the theory we obtain a UFT which contains Einstein's General Relativity and the Born-Infeld electrodynamics as special cases. Above all, it is shown that the Dirac equation describing the electron in an “external” gravito-electromagnetic field can be derived from the non-dualistic Einstein equation by a simple factorization if the Correspondence Principle is assumed.

Local conserved currents in unified field theory

In this paper we develop the existing unified field theory of gravitation and electromagnetism based on the connection between electric charge and homotopically invariant structures in the matter field. We find an infinite class of conserved currents which are local functions of the metric and matter field.

Unified Yang-Mills theory of gravitation and electromagnetism

The group properties of a new unified field theory of gravitation and electromagnetism are studied within a Yang-Mills scheme using a complex tetrad formalism.

Toward a unified field theory of gravitation and strong interactions

The chiralSU(3) quark model is shown to be a consequence of general relativity for Petrov type Id space-times, in much the same way that the Dirac equation is a consequence of special relativity.

Physical consequences of a solution of the nonsymmetric unified field theory

The physical consequences and possible tests of our solution of the nonsymmetric unified field theory of gravitation and electromagnetism are discussed. It is found in general that a universal constant $k$ introduced in the unification of the theory shows itself as a fourth-order effect in the propagation of light near a charged body. Further, it is shown that magnetic monopoles are not an allowed solution of the theory.

A unified field theory of gravitation and electromagnetism

The field equations of the theory are obtained by applying the usual variational principle to a scalar density action function constructed from a symmetrical metric tensor and a symmetrical affine connexion. The equations involve a four-dimensional curl which is identified as the electromagnetic field tensor. By rewriting the field equations it is shown that the theory is equivalent to a simple modification of the Born-Infeld theory. The modification is sufficient to destroy the symmetry between magnetostatics and electrostatics and prevents the existence of solutions corresponding to magnetic poles. Two different formulations of the theory are found, one involving electromagnetic potentials and the other involving only the electromagnetic field. Some aspects of the static spherically symmetric solution are discussed and the field equations are examined in a weak field approximation.

Sur les tenseurs symétriques et antisymétriques d'ordre deux, fonctions d'un tenseur asymétrique d'ordre deux

We give the maximum number of distinct symmetric quadratic tensors just as the maximum number of distinct skew-symmetric quadratic tensors that can be built up with the aid of the components of a real asymmetric quadratic tensor only. We show that these numbers are effectively attained in the case of the four-dimensional spaces of the unified field theory of gravitation and electromagnetism.

A unified field theory of gravitation and electromagnetism

A unified field theory of gravitation and electromagnetism is developed from the metrical properties of a non-Riemannian spacetime structureS4. The equations of the geodesics inS4 are non-minimal curves in a Riemannian spaceR4 and are identical with the relativistic equations of motion of a test particle moving in a gravitational and electromagnetic field. The Gaussian curvature of the geodesic surfaces is discussed and the scalar which arises is used to form a Lagrangian, from which the field equations are derived. These field equations are the usual Einstein gravitational equations and Maxwell electromagnetic equations, together with interaction terms, and imply equations of motion which are consistent with those obtained from the geodesic equations. The affine properties of the non-Riemannian space are briefly discussed.

Solution with Axial Symmetry of Einstein's Equations of Teleparallelism

In a recent paper Dr G. C. McVittie discussed the solution with axial symmetry of Einstein's new field-equations in his Unified Field Theory of Gravitation and Electricity. Owing to an error in his calculation of the field equations, Dr McVittie did not obtain the general solution, which we discuss in the present paper.

Solution with Axial Symmetry of Einstein's Equations of Teleparallelism

Einstein has recently adopted a new set of field-equations in his Unified Field-Theory of Gravitation and Electricity, the so-called theory of parallelism at a distance or Teleparallelism, and has given a solution of these equations with spherical symmetry, corresponding to the field of a charged mass-particle. In the present paper we discuss the solution of these equations with axial symmetry, which corresponds to a statical field whose field-variables depend on a single coordinate only, viz. the coordinate which is measured along the axis of symmetry.