The goal of creating a unified field theory was (and to some extent, still is) most closely identified in the public mind with the name of Albert Einstein. However, Einstein was by no means the only researcher to attempt such unification in the first half of the twentieth century. Unification of gravitation and electromagnetism was an actively pursued by several physicists and mathematicians in the years between the two world wars. Albert Einstein photographed by Oren J. Turner in 1947. ...

Most scientists, but not Einstein, eventually abandoned classical theories. Current research on unified field theories focuses on the problem of creating quantum gravity and unifying such a theory with the other fundamental theories in physics, which are quantum theories. (Some programs, most notably string theory, attempt to solve both of these problems at once.) Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ...

This article describes various attempts to unify gravity and electromagnetism into a single classical, relativistic field theory, especially work by Einstein and his contemporaries, and the considerable influence of this work in spurring the purely mathematical development of differential geometry. It has been suggested that gravitation be merged into this article or section. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, which exerts a force on those particles that possess the property of electric charge, and is in turn affected by the presence and motion of such particles. ... Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ... Field theory (mathematics), the theory of the algebraic concept of field. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ...

For a survey of classical relativistic field theories of gravitation (which have been motivated by various theoretical concerns other than unification), see Classical theories of gravitation. For a survey of current work toward creating a quantum theory of gravitation, see quantum gravity. In theoretical physics, the current Gold Standard Theory of Gravitation is the general theory of relativity. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ...

Overview

The early attempts at creating a unified field theory began with the geometry of general relativity, and attempted to incorporate electromagnetic fields into a generalized geometry. Despite popular misconceptions, Einstein was not alone in his attempts to unify electromagnetism and gravity. Weyl, Eddington, Kaluza and Bach also worked on various attempts to unify these interactions. These scientists pursued four different avenues of generalization: generalizing geometry, dynamics, number field, and the addition of an extra spatial dimension. These avenues were explored both separately and together. Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician. ... Eddington is the name of several places United States of America Eddington, Maine Eddington, Pennsylvania United Kingdom Eddington, Berkshire Eddington, Kent Edington, Somerset Edington, Wiltshire Also see: Arthur Eddington, an important astrophysicist This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same... Theodor Franz Eduard Kaluza Born: 9 Nov 1885 in Ratibor, Germany (now Raciborz, Poland) Died: 19 Jan 1954 in Göttingen, Germany Theodor Kaluzas father was Max Kaluza. ...

Early Work

The first attempts to provide a unified theory were contributed by G. Mie, in 1912, and Reichenbacher, in 1916. However, these theories were incorrect, as they did not correctly incorporate general relativity - in the former case, because general relativity had yet to be formulated, and in the latter due to an appararent lack of understanding. These efforts, along with those of Forster, involved making the metric tensor, which had been symmetric and real, into an asymmetric and/or complex tensor, and also attempted to create a field theory for matter as well. Forster is a common name which can refer to. ...

Differential Geometry and Field Theory

From 1918 until 1923, there were three distinct approaches to field theory. The gauge theory of Weyl, Kaluza's five-dimensional theory and Eddington's development of affine geometry. Einstein corresponded with these researchers, and collaborated with Kaluza, but was not yet fully involved in the unification. 1918 (MCMXVIII) was a common year starting on Tuesday of the Gregorian calendar (see link for calendar) or a common year starting on Wednesday of the Julian calendar. ... 1923 (MCMXXIII) was a common year starting on Monday (link will take you to calendar). ... Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician. ... Theodor Franz Eduard Kaluza Born: 9 Nov 1885 in Ratibor, Germany (now Raciborz, Poland) Died: 19 Jan 1954 in Göttingen, Germany Theodor Kaluzas father was Max Kaluza. ... In geometry, affine geometry occupies a place intermediate between Euclidean geometry and projective geometry. ... Theodor Franz Eduard Kaluza Born: 9 Nov 1885 in Ratibor, Germany (now Raciborz, Poland) Died: 19 Jan 1954 in Göttingen, Germany Theodor Kaluzas father was Max Kaluza. ...

Weyl's Infinitesimal Geometry

In order to include electromagnetism into the geometry of general relativity, Hermann Weyl worked to generalize the Riemannian geometry upon which general relativity is based. His idea was to create a more general infinitesimal geometry. This geometry generalized Riemannian geometry in that there was a vector field, Q, in addition to the metric, g, which together gave rise to both the electromagnetic and gravitational fields. This theory was mathematically sound, albeit complicated, resulting in difficult and high order field equations. The critical mathematical ingredients in this theory - the Langrangians, and curvature tensor - were worked out by Weyl and colleagues. Then Weyl carried out an extensive correspondence with Einstein and others as to its physical validity, and the theory was ultimately found to be physically unreasonable. Hermann Weyl Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician. ...

Kaluza's Fifth Dimension

Kaluza's approach to unification was to embed space-time into a five-dimensional cylindrical world; one of four space dimensions and one of time. Unlike Weyl's approach, Riemannian geometry was maintained, and the extra dimension allowed for the incorporation of the electromagnetic field vector into the geometry. Unfortunately, despite the relative mathematical elegance of this approach, in collaboration with Einstein, and Einstein's aide Grommer, it was determined that this theory did not admit a non-singular, static, spherically symmetric solution. Although, this theory influenced Einstein's later work and was further developed later by Klein, in an attempt to incorporate relativity into quantum theory, in what is now know as Kaluza-Klein theory. In physics, Kaluza-Klein theory (or KK theory, for short) is a model which sought to unify the two fundamental forces of gravitation and electromagnetism. ...

Eddington's Affine Geometry

Einstein's Geometric Approaches

hey

Later Work

After the 1930's, fewer and fewer scientists worked on classical unification, due to the continual development of quantum theory, and the difficulties encountered in developing a quantum theory of gravity. Einstein continued to work on a theory to incorporate electromagnetism, but he became increasingly isolated in his research over a unified field theory of gravity and electromagnetism until his death. Despite the publicity of this work, due to Einstein's celebrity status, it was a series of unsuccessful attempts. Even now with four fundamental forces, gravity remains the one force whose unification proves problematic.

References

• Gönner, Hubert F. M.. On the History of Unified Field Theories. Living Reviews in Relativity. URL accessed on August 10, 2005.
• Reichenbächer, E. (1917). Grundzüge zu einer Theorie der Elektrizität und der Gravitation. Ann. Phys. 52: 134-173.
• Mie, G. (1912). Grundlagen einer Theorie der Materie. Ann. Phys. 37: 511-534.