Einstein's Unified Field Theory Research Articles

Nonsingular particle solutions in variations on Einstein's nonsymmetric unified field theory

The Einstein-Kur\ifmmode \mbox{\c{s}}\else \c{s}\fi{}uno$\stackrel{\mathrm{\ifmmode \check{}\else \v{}\fi{}}}{\mathrm{g}}$lu nonsymmetric field theory has a distributed particle solution for the spherically symmetric time-independent case where ${g}_{23}\ensuremath{\ne}0$. The mass of the particle is derived from the field energy when the integration constants are chosen to avoid singularities. Linearization of the equations yields the Klein-Gordon equation for the charge density. The field functions are similar to a solution previously found for Bonnor's modification of the nonsymmetric theory.

Symmetries in a unified gauge theory with torsion

We consider aGL4×Un generalization of the Bonnor-Moffat-Boal formulation of Einstein unified field theory. Choosing a suitable form of the curvature tensor and introducing a phenomenological electric-current density, we show that charge conjugation corresponds to complex conjugation of the nonsymmetric unified fields. Making use of the complex tetrads underlying the fundamental Hermitian tensor field, we show that the gauge-covariant Dirac equation is obtained by minimal replacement of the Christoffel affinity of GR, with the generalized torsion containing connection. Finally, we consider spontaneous breaking of theUn gauge symmetry. The formalism splits into a vector sector and a tensor sector, the rotation angles\(\theta _W \) and\(\theta _G \) diagonalizing the vector and tensor mass matrices being related by\(\theta _G = \theta _W + \frac{1}{2}\pi \). TheUn components of the torsion vector describe the vector bosons mediating the electromagnetic and weak interactions, while theUn components of the symmetric part of the fundamental tensor describe the graviton and aSUn multiplet of tensor mesons.

Erratum: Charged particles in Einstein's unified field theory

Erratum: Charged particles in Einstein's unified field theory

Paths of spinning particles in general relativity as geodesics of an Einstein connection

This paper deals with the Papapetrou-Pirani equations of motion for a spinning test particle in general relativity. The motion of the center of mass can be represented by the geodesic equation of an affine connection that is the sum of the Christoffel connection and a tensor that depends on the Riemann-Christoffel curvature tensor, the mass of the particle, its 4-velocity, and its spin tensor. The connection is not unique, and here it is chosen to satisfy one of the basic geometrical principles of Einstein's unified field theory: The symmetric part of the fundamental tensor of the geometry is specified to be the metric tensor of general relativity. The special case of conformally flat space-times is discussed.

Charged particles in Einstein's unified field theory

The structure of charged particles in Einstein's unified field theory---the theory of the nonsymmetric field---is analyzed. A charged particle is represented through a time-independent spherically symmetric solution to the field equations. Using this idealization, it is shown that the structure of a charged particle is completely determined by the field equations, the condition that the symmetric part of the field be flat at infinity, and the requirement that the particle interact with other charged particles over laboratory distances via the conventional electromagnetic interaction. The structure of a charged particle is described in detail, and the limitations of the idealization of spherical symmetry are discussed. The nonconventional electromagnetic interaction over astronomical distances and its possible empirical consequences are examined.

An extension of the nonsymmetric unified field theory

The field equations, in the new formulation of Einstein's unified field theory, are extended from the present vacuum form to the general case in which sources are present. In this generalization the contracted torsion tensor corresponds to the electromagnetic four-potential. By this correspondence, Einsteinsλ-gauge transformation becomes identical to the ordinary electromagnetic gauge symmetry. The generalized Bianchi identities are found and used to discuss deviations from the Einstein-Lorentz equations of motion.

Electric and magnetic charge in Einstein's unified field theory

Electric and magnetic charge in Einstein's unified field theory

On a New Solution of Einstein's Unified Field Theory

(Received April. 19; 1971) A new set of exact solutions to Einstein's Unified Field Theory has ·been found; It has the property that the symmetric part of the connection vanishes globally in some system of coordinates and that arbitrary initial values of 'the basic tensor (/f.k can be specified' ·at any given point (complete integrability). The components of the fundamental tensor are poly­ nomials of degree. :::;:;2 in the coordinate system under consideration. For the. case of a con­ stant electromagnetic current of length zero, these solutions yieid a result different from the General Theory of Relativity.

On Treder's Interpretation of Einstein's Unified Field Theory

Einstein's Unified Theory1>-a> seems to be a very natural and plausible generaliza­ tion of the General Theory of Relativity. As compared to the latter, it has six new degrees of freedom which may be associated with the electromagnetic field. Indeed, if the antisymmetric 'part of the metric g,k is connected with the dual of the field tensor ftk

External field of a localized charge in unified field theory

The possibility of the existence of localized charged distribution giving rise to a special axially symmetric electrostatic field has been explored in Einstein's unified field theory [2]. The field equations have been studied in two particular cases. In one case the field equations have a solution representing flat space-time along with an electrostatic field which is constant in the direction of the axis of symmetry. For the other case the solution is non-existent.

Paths of charges in general relativity as geodesics of Einstein's non-Riemannian geometry

The equation of motion of charged incoherent matter, and hence of a test charge, in general relativity can be written as the geodesic equation of an affine connection. Here, the connection is chosen to satisfy a condition which has the form of one of the basic geometrical principles of Einstein's unified field theory. The symmetric part of the fundamental tensor of the geometry is chosen to be the metric tensor of general relativity; equations to be satisfied by the skew part, involving the electromagnetic field, are obtained. An alternative condition on the affinity is also considered.

Non existence of spherically symmetric solution representing vacuum electrostatic field

Spherically symmetric solution representing the external field of a localized charge does not exist in Einstein's unified field theory.

A Sequel to “A Contribution to Einstein's Unified-Field Theory” by J. Pizzo and J. Kronsbein

A Sequel to “A Contribution to Einstein's Unified-Field Theory” by J. Pizzo and J. Kronsbein

The Development of Unified Field Theories: Einstein's Unified Field Theory . M. A. Tonnelat. Translated from the French edition (Paris, 1955) by Richard Akerib. Gordon and Breach, New York, 1966. 198 pp., illus. $10.

The Development of Unified Field Theories: <i>Einstein's Unified Field Theory</i> . M. A. Tonnelat. Translated from the French edition (Paris, 1955) by Richard Akerib. Gordon and Breach, New York, 1966. 198 pp., illus. $10.

Unified Gravitational and Electromagnetic Waves

Starting with a very general form of the nonsymmetric tensor 9ik expressed in a coordinate· system suitably chosen to obtain wave solutions, a scheme is developed to derive rigorous. solutions of the field equations of Einstein which describe the flow of unified gravitational and electromagnetic radiation. Several such solutions are derived giving waves with two dimensional symmetry. It is found that solutions describing gravitational and electromagnetic waves obtained in the general theory of relativity with the help of an energy momentum tensor, can be derived in exactly the same form from the geometrical theory of the unified law of inertia enunciated by Hlavaty. § i. Introduction The geometrical structure of Einstein's unified field theory has been presented' by Hlavaty 1 > in a well ordered form. But the physical structure of the theory is not properly understood as yet. In spite of numerous efforts, mathematical solu­ tions of the field equations are yet to be found which will gain recognized physical_ interpretation. The only known solutions of the equations with a plausible physical interpretation are (1) the spherically symmetric static solutions worked out by Papapetrou 2 > Wyman, 3 > Bonner 4 > ; and (2) the plane wave solutions of Hlavaty/> Takeno. 5 > The spherically symmetric solution has failed to give a simple model of either a point charge or a point mass particle (distinct from Schwarz-· schild's model of general relativity). An effort was made to generalize the spherically symmetric solutions of Papapetrou, for the case of a nonstatic radiating mass. But it was found that though spherically symmetric gravitational field of a radiating star can be describ­ ed by the field equations of general relativity, no such solutions are permitted in the scheme of the unified field theory (Vaidya 6 )). In the present paper an attempt is made to obtain general 'solutions of the second type giving propagation of gravitational and electromagnetic waves in the scheme of the unified field theory. Throughout the paper we shall use the notations, of Hlavaty. 1 >

On a Solution of Field Equations in Einstein's Unified Field Theory, II

The title in CONTENTS on back cover, Vol. 16, No. 6, is to be replaced by the correct one, mentioned above.

On a Solution of Field Equations in Einstein's Unified Field Theory, II

On a Solution of Field Equations in Einstein's Unified Field Theory, II

On a Solution of Field Equations in Einstein's Unified Field Theory, I

On a Solution of Field Equations in Einstein's Unified Field Theory, I

A New Static Spherically Symmetric Solution of Einstein's Unified Field Theory

A New Static Spherically Symmetric Solution of Einstein's Unified Field Theory

The Equations of Motion in Einstein's New Unified Field Theory

It is shown that the field equations of Einstein's latest unified field theory do not lead to the Lorentz equations of motion for charged particles in an electromagnetic field, if these particles are considered to be singularities of the field. To a fourth-order approximation, the motion of such particles is not influenced by the electromagnetic field, no matter how much charge is placed on the particles.