Unified field theory

A unified field theory is a field theory that describes all forces and particles in terms of a field.

The term was coined by Albert Einstein, who attempted himself to unify his general theory of relativity with electromagnetism. The concepts of 'Theory of Everything' and 'Grand Unified Theory' are related to the idea of a unified field theory. They differ in that they do not require the basis of nature to be fields. 

Progress continues, to this day, on the goal of achieving a unified field theory.

Background: Four forces

Strong nuclear force - the gluon, described by quantum chromodynamics (1973) binds quarks into hadron particles.

Weak nuclear force - responsible for radioactivity as mediated by the W and Z boson.

Electromagnetism - Einstein first theorized that light was quantized in 1905. This quanta of light is the photon and it described by QED or quantum electrodynamics. 

Gravity - Isaac Newton tells us that there is an attractive force between two bodies that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Albert Einstein, starting in 1907 and culminating in 1915, gives us his general theory of relativity. It is general while his 1905 theory is special, since, special relativity only applies in situations where gravitation, acceleration and the curvature of spacetime can be completely ignored. Einstein proposed that the metric tensor of Bernhard Riemann (1854) was able to accurately describe the curvature of a spacetime manifold. A hypothetical force mediating particle for gravity would be the graviton (no mass and spin-2). It would be massless since the range of gravity is infinite and it would be spin-2 since the source of gravitation is the stress-energy tensor, thus it is a hypothetical tensor boson. 

History: In classic theory

The first classical unified field theory was given to us by James Clerk Maxwell. It was his 1864 paper on a dynamical theory of the electromagnetic field. This is the first example of a unification of previously existing field theories, namely, electricity and magnetism. This provided a unified theory of electromagnetism. 

By 1905, Albert Einstein had unified space and time into the single interwoven continuum of spacetime. By 1915, with the publishing of the general theory, spacetime and gravity were both described, using a field of curved geometry of 4-dimensional spacetime. 

Herman Weyl in 1919 introduced the concept of an electromagnetic gauge field in a classical field theory. 

Theodor Kaluza in 1921 extended general relativity to 5 dimensions to include the Maxwell equations in a 5D metric with 15 components. (10 for the Einstein spacetime, 4 for the electromagnetic vector potential and 1 for a scalar field.)

By 1930, Einstein had considered the Einstein-Maxwell-Dirac system, the superclassical limit of quantum electrodynamics. One can extend this system to include the weak and strong nuclear forces to acquire the Einstein-Yang-Mills-Dirac system. 

Electroweak interaction

In 1963, Sheldon Glashow proposed that the Weak nuclear force, electricity and magnetism could arise from a partially unified electroweak theory. 

In 1967, Abdus Salam and Steven Weinberg, revise Glashow's proposal independently, that the masses of the W and Z boson should arise from spontaneous symmetry breaking with the Higgs mechanism. 

In 1983, the W and Z were produced at CERN by Carlo Rubbia's team.

Glashow, Salam and Weinberg recieved the Nobel Prize in 1979 while Rubbia did in 1984. 

The Glashow-Weinberg-Salam model was shown to be mathematically consistent by Gerard t'Hooft and was furthermore seen as a template for future theories of unification of particle interactions. 

Grand unified theories

In 1974, Sheldon Glashow and Howard Georgi proposed the Georgi-Glashow model, which attempted to unify the electroweak interaction with the strong force. This was the first GUT or Grand Unified Theory. 

There have been several other proposed GUTs, such as the Pati-Salam model, yet none have been universally accepted at the present. 

Current status of a ToE

There is, at the present, not a universally accepted ToE or Theory of Everything, which would be a unified understanding of all matter and forces, gravity, electromagnetism and strong and weak nuclear forces. This theory would be a consistent combination of the two pillars of modern physics: general relativity and quantum mechanics. There are fundamental difficulties if we attempt to incorporate a graviton into the theory of the photon, gluon, W and Z boson. The theory is not renormalizable, that is, meaningless infinities arise.

The incompatibility between general relativity and quantum mechanics remains an outstanding difficulty in physics.