In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, a unified field theory (UFT) is a type of
field theory that allows all that is usually thought of as
fundamental forces
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electrom ...
and
elementary particle
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, an ...
s to be written in terms of a pair of physical and virtual fields. According to the modern discoveries in physics, forces are not transmitted directly between interacting objects but instead are described and interrupted by intermediary entities called
field
Field may refer to:
Expanses of open ground
* Field (agriculture), an area of land used for agricultural purposes
* Airfield, an aerodrome that lacks the infrastructure of an airport
* Battlefield
* Lawn, an area of mowed grass
* Meadow, a grass ...
s.
Classically, however, a duality of the fields is combined into a single physical field. For over a century, unified field theory has remained an open line of research and the term was coined by
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
, who attempted to unify his
general theory of relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
with
electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
. The "
Theory of Everything
A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all asp ...
"
and
Grand Unified Theory
A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this ...
are closely related to unified field theory, but differ by not requiring the basis of nature to be fields, and often by attempting to explain physical
constants of nature
In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used.
For example, if one c ...
. Earlier attempts based on classical physics are described in the article on
classical unified field theories
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. Classical unified field theories are at ...
.
The goal of a unified field theory has led to a great deal of progress for future
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
, and progress continues.
Introduction to the Great Theory
Forces
![Standard Model of Elementary Particles + Gravity](https://upload.wikimedia.org/wikipedia/commons/b/b7/Standard_Model_of_Elementary_Particles_%2B_Gravity.svg)
All four of the known fundamental forces are mediated by fields, which in the
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions - excluding gravity) in the universe and classifying a ...
of particle physics result from the exchange of
gauge boson
In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge ...
s. Specifically, the four fundamental interactions to be unified are:
*
Strong interaction
The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the n ...
: the interaction responsible for holding
quark
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...
s together to form
hadron
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ele ...
s, and holding
neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
s and also
proton
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s together to form
atomic nuclei
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron ...
. The exchange particle that mediates this force is the
gluon
A gluon ( ) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles. Gluons bind q ...
.
*
Electromagnetic interaction
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
: the familiar interaction that acts on electrically charged particles. The
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
is the exchange particle for this force.
*
Weak interaction
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, ...
: a short-range interaction responsible for some forms of
radioactivity, that acts on
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
s,
neutrino
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
s, and quarks. It is mediated by the
W and Z bosons
In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , and ...
.
*
Gravitational interaction
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
: a long-range attractive interaction that acts on ''all'' particles. The postulated exchange particle has been named the
graviton
In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathem ...
.
Modern unified field theory attempts to bring these four forces and matter together into a single framework.
History
Classic theory
The first successful
classical unified field theory was developed by
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
. In 1820,
Hans Christian Ørsted
Hans Christian Ørsted ( , ; often rendered Oersted in English; 14 August 17779 March 1851) was a Danish physicist and chemist who discovered that electric currents create magnetic fields, which was the first connection found between electricity ...
discovered that
electric current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
s exerted forces on
magnet
A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, ...
s, while in 1831,
Michael Faraday
Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
made the observation that time-varying
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
s 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
"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. ''(Paper read at a meeting of the Royal Society on 8 December 1864).'' In the paper, Maxwell derives an electromagnetic wav ...
. 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
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
had used the constancy of the speed of light in Maxwell's theory to unify our notions of space and time into an entity we now call
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
and in 1915 he expanded this theory of
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
to a description of gravity,
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, using a field to describe the curving geometry of four-dimensional 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. In view of later developments in this domain, of particular interest are the theories of
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...
of 1919, who introduced the concept of an (electromagnetic)
gauge field
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups) ...
in a classical field theory and, two years later, that of
Theodor Kaluza
Theodor Franz Eduard Kaluza (; 9 November 1885 – 19 January 1954) was a German mathematician and physicist known for the Kaluza–Klein theory, involving field equations in five-dimensional space-time. His idea that fundamental forces can be ...
, who extended General Relativity to
five dimensions.
[Daniela Wuensch (2003), "The fifth dimension: Theodor Kaluza's ground-breaking idea", ''Annalen der Physik'', vol. 12, p. 519–542.] Continuing in this latter direction, Oscar Klein proposed in 1926 that the fourth spatial dimension be
curled up into a small, unobserved circle. In
Kaluza–Klein 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. By 1930 Einstein had already considered the Einstein-Maxwell–Dirac System
ongen This system is (heuristically) the super-classical
aradarajanlimit of (the not mathematically well-defined)
quantum electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
. 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 published a paper in the early 1940s on the standard commutation relations for the quantized spin-2 field. She continued this work in collaboration with
Erwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theory ...
after
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
. In the 1960s
Mendel Sachs
Mendel Sachs (; April 13, 1927 – May 5, 2012) was an American theoretical physicist. His scientific work includes the proposal of a unified field theory that brings together the weak force, strong force, electromagnetism, and gravity.
Biography ...
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
Sheldon Lee Glashow (, ; born December 5, 1932) is a Nobel Prize-winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University and Eugene Higgins Professor of Physics, Emeritus, at Harvard U ...
proposed that the
weak nuclear force
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, ...
, electricity, and magnetism could arise from a partially unified
electroweak theory
In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...
. In 1967, Pakistani
Abdus Salam
Mohammad Abdus Salam Salam adopted the forename "Mohammad" in 1974 in response to the anti-Ahmadiyya decrees in Pakistan, similarly he grew his beard. (; ; 29 January 192621 November 1996) was a Punjabi Pakistani theoretical physicist and a ...
and American
Steven Weinberg
Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interactio ...
independently revised Glashow's theory by having the masses for the
W particle and
Z particle arise through
spontaneous symmetry breaking
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the ...
with the
Higgs mechanism
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other bein ...
. This unified theory modeled the
electroweak interaction
In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...
as a force mediated by four particles: the photon for the electromagnetic aspect, and 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 , 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
The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in a northwestern suburb of Gene ...
by
Carlo Rubbia
Carlo Rubbia (born 31 March 1934) is an Italian particle physicist and inventor who shared the Nobel Prize in Physics in 1984 with Simon van der Meer for work leading to the discovery of the W and Z particles at CERN.
Early life and education
...
's team. For their insights, Glashow, Salam, and Weinberg were awarded the
Nobel Prize in Physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
in 1979. Carlo Rubbia and
Simon van der Meer
Simon van der Meer (24 November 19254 March 2011) was a Dutch Accelerator physics, particle accelerator physicist who shared the Nobel Prize in Physics in 1984 with Carlo Rubbia for contributions to the CERN project which led to the discovery o ...
received the Prize in 1984.
After
Gerardus 't Hooft
Gerardus (Gerard) 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating the ...
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
Howard Mason Georgi III (born January 6, 1947) is an American theoretical physicist and the Mallinckrodt Professor of Physics and Harvard College Professor at Harvard University. He is also Director of Undergraduate Studies in Physics. He was Co-M ...
proposed unifying the strong and electroweak interactions into the
Georgi–Glashow model
In particle physics, the Georgi–Glashow model is a particular grand unified theory (GUT) proposed by Howard Georgi and Sheldon Glashow in 1974. In this model the standard model gauge groups SU(3) × SU(2) × U(1) are combined into a single ...
, the first
Grand Unified Theory
A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this ...
, which would have observable effects for energies much above 100 GeV.
Since then there have been several proposals for Grand Unified Theories, e.g. the
Pati–Salam model
In physics, the Pati–Salam model is a Grand Unified Theory (GUT) proposed in 1974 by Abdus Salam and Jogesh Pati. Like other GUTs, its goal is to explain the seeming arbitrariness and complexity of the Standard Model in terms of a simpler, more f ...
, although none is currently universally accepted. A major problem for experimental tests of such theories is the energy scale involved, which is well beyond the reach of current
accelerators. Grand Unified Theories make predictions for the relative strengths of the strong, weak, and electromagnetic forces, and in 1991
LEP determined that
supersymmetric
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
theories have the correct ratio of couplings for a Georgi–Glashow Grand Unified Theory.
Many Grand Unified Theories (but not Pati–Salam) predict that
the proton can 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 10
35 years for its lifetime.
Current status
Theoretical physicists have not yet formulated a widely accepted, consistent theory that combines
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
and
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
to form a
theory of everything
A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all asp ...
. Trying to combine the
graviton
In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathem ...
with the strong and electroweak interactions leads to fundamental difficulties and the resulting theory is not
renormalizable
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similarity, self-similar geometric structures, that are used to treat infinity, infinities arising in calculated ...
. The incompatibility of the two theories remains an outstanding problem in the field of physics.
See also
*
Sheldon Glashow
Sheldon Lee Glashow (, ; born December 5, 1932) is a Nobel Prize-winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University and Eugene Higgins Professor of Physics, Emeritus, at Harvard U ...
References
Further reading
*Jeroen van Dongen ''Einstein's Unification'',
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press
A university press is an academic publishing hou ...
(July 26, 2010)
*Varadarajan, V.S. ''Supersymmetry for Mathematicians: An Introduction (Courant Lecture Notes)'',
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
(July 2004)
External links
On the History of Unified Field Theories by Hubert F. M. Goenner
{{DEFAULTSORT:Unified Field Theory
Particle physics
Theories of gravity
Unsolved problems in physics