Since the 19th century, some physicists, notably Albert Einstein, have attempted to develop a single theoretical framework that can account for all the fundamental forces of nature – a unified field theory.
[1][2] These scientists pursued several avenues of generalization, including extending the foundations of geometry and adding an extra spatial dimension.
Sir Arthur Stanley Eddington was a noted astronomer who became an enthusiastic and influential promoter of Einstein's general theory of relativity.
He was among the first to propose an extension of the gravitational theory based on the affine connection as the fundamental structure field rather than the metric tensor which was the original focus of general relativity.
Eddington emphasized what he considered to be epistemological considerations; for example, he thought that the cosmological constant version of the general-relativistic field equation expressed the property that the universe was "self-gauging".
, which represents matter/energy, was merely provisional, and that in a truly unified theory the source term would automatically arise as some aspect of the free-space field equations.
He also shared the hope that an improved fundamental theory would explain why the two elementary particles then known (proton and electron) have quite different masses.
The Dirac equation for the relativistic quantum electron caused Eddington to rethink his previous conviction that fundamental physical theory had to be based on tensors.
He subsequently devoted his efforts into development of a "Fundamental Theory" based largely on algebraic notions (which he called "E-frames").
These attempts initially concentrated on additional geometric notions such as vierbeins and "distant parallelism", but eventually centered around treating both the metric tensor and the affine connection as fundamental fields.
Einstein's proposed unified-field equations (fundamental laws of physics) were generally derived from a variational principle expressed in terms of the Riemann curvature tensor for the presumed space-time manifold.
The degree of abstraction, combined with a relative lack of good mathematical tools for analyzing nonlinear equation systems, make it hard to connect such theories with the physical phenomena that they might describe.
Einstein became increasingly isolated in his research on a generalized theory of gravitation, and most physicists consider his attempts ultimately unsuccessful.
Einstein pressed on with his attempts to theoretically unify gravity and electromagnetism, but he became increasingly isolated in this research, which he pursued until his death.