The generalized theory of gravitation was an attempt to unify gravity and electromagnetism. This work is most closely identified with Albert Einstein. He was, however, neither the first nor only scientist to attempt such unification. Rather, he was the most famous and diligent researcher. Unification theory was an active endeavor prior to World War II, however, most scientists, save for Einstein, abandoned classic theories, and worked on quantum gravity and grand unified theories of the other forces. Full unified field theories have been problematic due to the difficulty in reconciling the classical description of gravity with the quantum description of the other fundamental forces. Despite this lack of success, the early efforts by Einstein and others to develop a general geometric framework for gravity and electromagnetism, was influential in spurring developments in differential geometry. Gravitation is the tendency of masses to move toward each other. ... Electromagnetism is the physics of electromagnetic fields: a field, encompassing all of space, comprised of electrical and magnetic fields. ... Albert Einstein, by Yousuf Karsh Albert Einstein (March 14, 1879 – April 18, 1955) was a German theoretical physicist who is widely regarded as the greatest scientist of the 20th century. ... Gravitation is the tendency of masses to move toward each other. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ...

Overview

The early attempts in creating a unified field theory started 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 persued 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...

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 was a common year starting on Tuesday (see link for calendar). ... 1923 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. ... In geometry, affine geometry occupies a place intermediate between Euclidean geometry and projective geometry. ...

Weyl's Infintesimal Geometry

In order to include electromagnetism into the geometry of general relativity, Weyl worked to generalize the Riemannian geometry upon which general relativity is based. His idea was to create a more general infinitesmal geometry. This geometry generalized Riemannian geometry, such that there was a vector field, Q, in addition to the metric, g, which gave rise to the electromagnetic field, as well as gravity. This theory was mathematically complete,albeit complex, resulting in difficult and high order field equations. The critical mathematical details: the Langrangians, and curvature tensor were worked out by Weyl and colleagues. After working out the mathematics of his theory, Weyl carried out an extensive correspondence with Einstein, and others, as to its physically validity, and the theory ultimately was found to be not physically reasonable. Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician. ... 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 time dimension. Unlike Weyl's approach, Riemannin 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, statical, spherically symmetric solution. Although, this theory influenced Einstion'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.

Eddington's Affine Geometry

Einstein's Geometric Approaches

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 encounted in developing a quantum theory of gravity. Einstein continued to work on a theory to incorporate 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

• Mie, G., “Grundlagen einer Theorie der Materie”, Ann. Phys., 37, 511-534, (1912)
• Reichenbächer, E., “Grundzüge zu einer Theorie der Elektrizität und der Gravitation”, Ann. Phys., 52, 134-173, (1917).
• On the History of Unified Field Theories]