# Unified field theory

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Field theory in physics that aims to unify the fundamental forces and particles

"Unified theory" redirects here. For the band, see [Unified Theory (band)](/source/Unified_Theory_(band)).

Not to be confused with [Grand Unified Theory](/source/Grand_Unified_Theory).

In [physics](/source/Physics), a **unified field theory** (**UFT**) is a type of [field theory](/source/Field_theory_(physics)) that allows all [fundamental forces](/source/Fundamental_forces) of nature, including gravity, and all [elementary particles](/source/Elementary_particle) to be written in terms of a single physical [field](/source/Field_(physics)).[1] According to [quantum field theory](/source/Quantum_field_theory), particles are themselves the quanta of fields. Different fields in physics include [vector fields](/source/Vector_field) such as the [electromagnetic field](/source/Electromagnetic_field), [spinor fields](/source/Spinor_field) whose quanta are [fermionic](/source/Fermion) particles such as [electrons](/source/Electron), and [tensor fields](/source/Tensor_field) such as the [metric tensor field](/source/Metric_tensor_(general_relativity)) that describes the shape of [spacetime](/source/Spacetime) and gives rise to gravitation in [general relativity](/source/General_relativity). Unified field theories attempt to organize these fields into a single mathematical structure.

For over a century, the unified field theory has remained an open line of research. The term was coined by [Albert Einstein](/source/Albert_Einstein), who attempted to unify his [general theory of relativity](/source/General_relativity) with [electromagnetism](/source/Electromagnetism) since the 1920s.[2] Einstein attempted to create a [classical unified field theory](/source/Classical_unified_field_theories). Among other difficulties, this required a new explanation of particles as singularities or [solitons](/source/Soliton) instead of field quanta. Later attempts to unify general relativity with other forces incorporate quantum mechanics. The concept of a "[Theory of Everything](/source/Theory_of_Everything)"[3] or [Grand Unified Theory](/source/Grand_Unified_Theory)[4] are closely related to unified field theory. A theory of everything attempts to create a complete picture of all events in nature. Grand Unified Theories do not attempt to include the gravitational force and can therefore operate entirely within quantum field theory. The goal of a unified field theory has led to significant progress in [theoretical physics](/source/Theoretical_physics).[5]

## Introduction

Unified field theory attempts to give a single elegant description of the following fields:[*[dubious](https://en.wikipedia.org/wiki/Wikipedia:Accuracy_dispute#Disputed_statement) – [discuss](https://en.wikipedia.org/wiki/Talk:Unified_field_theory#Dubious)*]

### Forces

All four of the known fundamental forces are mediated by fields. In the [Standard Model](/source/Standard_Model) of particle physics, three of these result from the exchange of [gauge bosons](/source/Gauge_boson). These are:

- [Strong interaction](/source/Strong_interaction): the interaction responsible for holding [quarks](/source/Quark) together to form [hadrons](/source/Hadron), and holding [neutrons](/source/Neutron) and also [protons](/source/Proton) together to form [atomic nuclei](/source/Atomic_nucleus). The exchange particle that mediates this force is the [gluon](/source/Gluon).

- [Electromagnetic interaction](/source/Electromagnetic_interaction): the familiar interaction that acts on electrically charged particles. The [photon](/source/Photon) is the exchange particle for this force.

- [Weak interaction](/source/Weak_interaction): a short-range interaction responsible for some forms of [radioactivity](/source/Radioactivity), that acts on [electrons](/source/Electron), [neutrinos](/source/Neutrino), and quarks. It is mediated by the [W and Z bosons](/source/W_and_Z_bosons).

[General relativity](/source/General_relativity) likewise describes gravitation as the result of the metric tensor field, which describes the shape of [spacetime](/source/Spacetime):

- [Gravitational interaction](/source/Gravitational_interaction): a long-range attractive interaction that acts on *all* particles. In hypothetical quantum versions of GR, the postulated exchange particle has been named the [graviton](/source/Graviton).

### Matter

In the Standard Model, the "matter" particles (electrons, quarks, neutrinos, etc) are described as the quanta of [spinor](/source/Spinor) fields. Gauge boson fields also have quanta, such as [photons](/source/Photon) for the electromagnetic field.

### Higgs

The Standard Model has a unique fundamental [scalar field](/source/Scalar_field), the [Higgs field](/source/Higgs_field), the quanta of which are called [Higgs bosons](/source/Higgs_boson).

## History

### Classic theory

The first successful [classical unified field theory](/source/Classical_unified_field_theories) was developed by [James Clerk Maxwell](/source/James_Clerk_Maxwell). In 1820, [Hans Christian Ørsted](/source/Hans_Christian_%C3%98rsted) discovered that [electric currents](/source/Electric_current) exerted forces on [magnets](/source/Magnet), while in 1831, [Michael Faraday](/source/Michael_Faraday) made the observation that time-varying [magnetic fields](/source/Magnetic_field) could induce electric currents. Until then, electricity and magnetism had been thought of as unrelated phenomena. In 1864, Maxwell published his famous paper on [a dynamical theory of the electromagnetic field](/source/A_Dynamical_Theory_of_the_Electromagnetic_Field). This was the first example of a theory that was able to encompass previously separate field theories (namely electricity and magnetism) to provide a unifying theory of electromagnetism. By 1905, [Albert Einstein](/source/Albert_Einstein) had used the constancy of the [speed-of-light](/source/Speed-of-light) in Maxwell's theory to unify our notions of space and time into an entity we now call [spacetime](/source/Spacetime). In 1915, he expanded this theory of [special relativity](/source/Special_relativity) to a description of gravity, [general relativity](/source/General_relativity), using a field to describe the curving geometry of four-dimensional (4D) spacetime.

In the years following the creation of the general theory, a large number of physicists and mathematicians enthusiastically participated in the attempt to unify the then-known fundamental interactions.[6] Given later developments in this domain, of particular interest are the theories of [Hermann Weyl](/source/Hermann_Weyl) of 1919, who introduced the concept of an (electromagnetic) [gauge field](/source/Gauge_theory) in a classical field theory[7] and, two years later, that of [Theodor Kaluza](/source/Theodor_Kaluza), who extended General Relativity to [five dimensions](/source/Five-dimensional_space).[8] Continuing in this latter direction, Oscar Klein proposed in 1926 that the fourth spatial dimension be [curled up](/source/Compactification_(physics)) into a small, unobserved circle. In [Kaluza–Klein theory](/source/Kaluza%E2%80%93Klein_theory), the gravitational curvature of the extra spatial direction behaves as an additional force similar to electromagnetism. These and other models of electromagnetism and gravity were pursued by Albert Einstein in his attempts at a [classical unified field theory](/source/Classical_unified_field_theories). By 1930 Einstein had already considered the Einstein-Maxwell–Dirac System [Dongen]. This system is (heuristically) the super-classical [Varadarajan] limit of (the not mathematically well-defined) [quantum electrodynamics](/source/Quantum_electrodynamics). One can extend this system to include the weak and strong nuclear forces to get the Einstein–Yang-Mills–Dirac System. The French physicist [Marie-Antoinette Tonnelat](/source/Marie-Antoinette_Tonnelat) published a paper in the early 1940s on the standard commutation relations for the quantized spin-2 field, in an attempt to unify general relativity with quantum mechanics. She continued this work in collaboration with [Erwin Schrödinger](/source/Erwin_Schr%C3%B6dinger) after [World War II](/source/World_War_II). In the 1960s [Mendel Sachs](/source/Mendel_Sachs) proposed a generally covariant field theory that did not require recourse to renormalization or perturbation theory. In 1965, Tonnelat published a book on the state of research on unified field theories.

### Modern progress

In 1963, American physicist [Sheldon Glashow](/source/Sheldon_Glashow) proposed that the [weak nuclear force](/source/Weak_nuclear_force), electricity, and magnetism could arise from a partially unified [electroweak theory](/source/Electroweak_theory). In 1967, Pakistani [Abdus Salam](/source/Abdus_Salam) and American [Steven Weinberg](/source/Steven_Weinberg) independently revised Glashow's theory by having the masses for the [W particle](/source/W_particle) and [Z particle](/source/Z_particle) arise through [spontaneous symmetry breaking](/source/Spontaneous_symmetry_breaking) with the [Higgs mechanism](/source/Higgs_mechanism). This unified theory modelled the [electroweak interaction](/source/Electroweak_interaction) as a force mediated by four particles: the photon for the electromagnetic aspect, a neutral Z particle, and two charged W particles for the weak aspect. As a result of the spontaneous symmetry breaking, the weak force becomes short-range and the W and Z bosons acquire masses of 80.4 and 91.2 GeV/c2, respectively. Their theory was first given experimental support by the discovery of weak neutral currents in 1973. In 1983, the Z and W bosons were first produced at [CERN](/source/CERN) by [Carlo Rubbia](/source/Carlo_Rubbia)'s team. For their insights, Glashow, Salam, and Weinberg were awarded the [Nobel Prize in Physics](/source/Nobel_Prize_in_Physics) in 1979. Carlo Rubbia and [Simon van der Meer](/source/Simon_van_der_Meer) received the Prize in 1984.

After [Gerardus 't Hooft](/source/Gerardus_'t_Hooft) showed the Glashow–Weinberg–Salam electroweak interactions to be mathematically consistent, the electroweak theory became a template for further attempts at unifying forces. In 1974, Sheldon Glashow and [Howard Georgi](/source/Howard_Georgi) proposed unifying the strong and electroweak interactions into the [Georgi–Glashow model](/source/Georgi%E2%80%93Glashow_model), the first [Grand Unified Theory](/source/Grand_Unified_Theory), which would have observable effects for energies much above 100 GeV.

Since then there have been numerous proposals for Grand Unified Theories involving larger and larger unifying groups. While these theories are self-consistent, no proposal produced a solution to outstanding issues in cosmology, like the [baryon asymmetry](/source/Baryon_asymmetry) problem or the missing mass now attributed to [dark matter](/source/Dark_matter). Experimental tests of such theories requires an energy scale well beyond the reach of current [accelerators](/source/Particle_accelerator) so no empirical evidence outside of cosmology can guide theory.[9]: 310

Grand Unified Theories make predictions for the relative strengths of the strong, weak, and electromagnetic forces, and in 1991 [LEP](/source/Large_Electron-Positron_Collider) determined that [supersymmetric](/source/Minimal_Supersymmetric_Standard_Model) theories have the correct ratio of couplings for a Georgi–Glashow Grand Unified Theory.[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*] Many Grand Unified Theories (but not [Pati–Salam](/source/Pati%E2%80%93Salam)) predict that [the proton can decay](/source/Proton_decay), and if this were to be seen, details of the decay products could give hints at more aspects of the Grand Unified Theory. It is at present unknown if the proton can decay, although experiments have determined a lower bound of 1035 years for its lifetime.[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*]

### Current status

Theoretical physicists have not yet formulated a widely accepted, consistent theory that combines [general relativity](/source/General_relativity) and [quantum mechanics](/source/Quantum_mechanics) to form a [theory of everything](/source/Theory_of_everything). Trying to combine the [graviton](/source/Graviton) with the strong and electroweak interactions leads to fundamental difficulties and the resulting theory is not [renormalizable](/source/Renormalization). The incompatibility of the two theories remains an outstanding problem in the field of physics.

## See also

- [Sheldon Glashow](/source/Sheldon_Glashow)

- [Unification of theories in physics](/source/Unification_of_theories_in_physics)

- [Grand Unified Theory](/source/Grand_Unified_Theory)

- [Theory of everything](/source/Theory_of_everything)

## References

1. **[^](#cite_ref-1)** ["Unified field theory | Einstein's Theory of Relativity | Britannica"](https://www.britannica.com/science/unified-field-theory). *www.britannica.com*. Retrieved 2024-10-10.

1. **[^](#cite_ref-2)** ["How the search for a unified theory stumped Einstein to his dying day"](https://phys.org/news/2015-11-theory-stumped-einstein-dying-day.html). *phys.org*.

1. **[^](#cite_ref-Hawking2006_3-0)** Stephen W. Hawking (28 February 2006). *The Theory of Everything: The Origin and Fate of the Universe*. Phoenix Books; Special Anniv. [ISBN](/source/ISBN_(identifier)) [978-1-59777-508-3](https://en.wikipedia.org/wiki/Special:BookSources/978-1-59777-508-3).

1. **[^](#cite_ref-4)** Ross, G. (1984). *Grand Unified Theories*. [Westview Press](/source/Westview_Press). [ISBN](/source/ISBN_(identifier)) [978-0-8053-6968-7](https://en.wikipedia.org/wiki/Special:BookSources/978-0-8053-6968-7).

1. **[^](#cite_ref-5)** Goenner, Hubert F. M. (2004-12-01). ["On the History of Unified Field Theories"](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5256024). *Living Reviews in Relativity*. **7** (1) 2. [Bibcode](/source/Bibcode_(identifier)):[2004LRR.....7....2G](https://ui.adsabs.harvard.edu/abs/2004LRR.....7....2G). [doi](/source/Doi_(identifier)):[10.12942/lrr-2004-2](https://doi.org/10.12942%2Flrr-2004-2). [ISSN](/source/ISSN_(identifier)) [1433-8351](https://search.worldcat.org/issn/1433-8351). [PMC](/source/PMC_(identifier)) [5256024](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5256024). [PMID](/source/PMID_(identifier)) [28179864](https://pubmed.ncbi.nlm.nih.gov/28179864).

1. **[^](#cite_ref-6)** See [Catherine Goldstein](/source/Catherine_Goldstein) & Jim Ritter (2003) "The varieties of unity: sounding unified theories 1920-1930" in A. Ashtekar, et al. (eds.), *Revisiting the Foundations of Relativistic Physics*, Dordrecht, Kluwer, p. 93-149; Vladimir Vizgin (1994), *Unified Field Theories in the First Third of the 20th Century*, Basel, Birkhäuser; Hubert Goenner [On the History of Unified Field Theories](http://relativity.livingreviews.org/Articles/lrr-2004-2/) [Archived](https://web.archive.org/web/20110805194546/http://relativity.livingreviews.org/Articles/lrr-2004-2/) 2011-08-05 at the [Wayback Machine](/source/Wayback_Machine).

1. **[^](#cite_ref-7)** Erhard Scholtz (ed) (2001), *Hermann Weyl's* Raum - Zeit- Materie *and a General Introduction to His Scientific Work*, Basel, Birkhäuser.

1. **[^](#cite_ref-8)** Daniela Wuensch (2003), "The fifth dimension: Theodor Kaluza's ground-breaking idea", *Annalen der Physik*, vol. 12, p. 519–542.

1. **[^](#cite_ref-9)** Cao, Tian Yu (October 3, 2019). [*Conceptual Developments of 20th Century Field Theories*](https://www.cambridge.org/core/product/identifier/9781108566926/type/book) (2 ed.). Cambridge University Press. [doi](/source/Doi_(identifier)):[10.1017/9781108566926](https://doi.org/10.1017%2F9781108566926). [ISBN](/source/ISBN_(identifier)) [978-1-108-56692-6](https://en.wikipedia.org/wiki/Special:BookSources/978-1-108-56692-6).

## Further reading

- Jeroen van Dongen *Einstein's Unification*, [Cambridge University Press](/source/Cambridge_University_Press) (July 26, 2010)

- Varadarajan, V.S. *Supersymmetry for Mathematicians: An Introduction (Courant Lecture Notes)*, [American Mathematical Society](/source/American_Mathematical_Society) (July 2004)

- Ernan McMullin (2002). ["The Origins of the Field Concept in Physics"](http://physics.gmu.edu/~rubinp/courses/416/pip_fields.pdf) (PDF). *Phys. Perspect*. **4** (1): 13–39. [Bibcode](/source/Bibcode_(identifier)):[2002PhP.....4...13M](https://ui.adsabs.harvard.edu/abs/2002PhP.....4...13M). [doi](/source/Doi_(identifier)):[10.1007/s00016-002-8357-5](https://doi.org/10.1007%2Fs00016-002-8357-5). [S2CID](/source/S2CID_(identifier)) [27691986](https://api.semanticscholar.org/CorpusID:27691986).

## External links

Wikiquote has quotations related to ***[Unified field theory](https://en.wikiquote.org/wiki/Special:Search/Unified_field_theory)***.

- [On the History of Unified Field Theories](https://web.archive.org/web/20110805194546/http://relativity.livingreviews.org/Articles/lrr-2004-2/), by Hubert F. M. Goenner

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