Unified field theory

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In physics, a unified field theory (UFT) is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a pair of physical and virtual fields. According to modern discoveries in physics, forces are not transmitted directly between interacting objects but instead are described and interpreted by intermediary entities called fields. [1]

Contents

However, a duality of the fields is combined into a single physical field. [2] For over a century, unified field theory has remained an open line of research. The term was coined by Albert Einstein, [3] who attempted to unify his general theory of relativity with electromagnetism. The "Theory of Everything" [4] and Grand Unified Theory [5] 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. Earlier attempts based on classical physics are described in the article on classical unified field theories.

The goal of a unified field theory has led to a great deal of progress for future theoretical physics, and progress continues. [6]

Introduction

Forces

The Standard Model of elementary particles + hypothetical Graviton Standard Model of Elementary Particles + Gravity.svg
The Standard Model of elementary particles + hypothetical Graviton

All four of the known fundamental forces are mediated by fields, which in the Standard Model of particle physics result from the exchange of gauge bosons. Specifically, the four fundamental interactions to be unified are:

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. In 1820, Hans Christian Ørsted discovered that electric currents exerted forces on magnets, while in 1831, Michael Faraday made the observation that time-varying magnetic fields 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. 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 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 1915, he expanded this theory of special relativity to a description of gravity, 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. [7] Given later developments in this domain, of particular interest are the theories of Hermann Weyl of 1919, who introduced the concept of an (electromagnetic) gauge field in a classical field theory [8] and, two years later, that of Theodor Kaluza, who extended General Relativity to five dimensions. [9] 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 [Dongen]. This system is (heuristically) the super-classical [Varadarajan] limit of (the not mathematically well-defined) 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 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 after World War II. In the 1960s 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 proposed that the weak nuclear force, electricity, and magnetism could arise from a partially unified electroweak theory. In 1967, Pakistani Abdus Salam and American Steven Weinberg independently revised Glashow's theory by having the masses for the W particle and Z particle arise through spontaneous symmetry breaking with the Higgs mechanism. This unified theory modelled the 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 by Carlo Rubbia's team. For their insights, Glashow, Salam, and Weinberg were awarded the Nobel Prize in Physics in 1979. Carlo Rubbia and Simon van der Meer received the Prize in 1984.

After 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 proposed unifying the strong and electroweak interactions into the Georgi–Glashow model, the first Grand Unified Theory, 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, 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 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 1035 years for its lifetime.

Current status

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

See also

Related Research Articles

<span class="mw-page-title-main">Electromagnetism</span> Fundamental interaction between charged particles

In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, which are distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles. Electric forces cause an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs between charged particles in relative motion. These two forces are described in terms of electromagnetic fields. Macroscopic charged objects are described in terms of Coulomb's law for electricity and Ampère's force law for magnetism; the Lorentz force describes microscopic charged particles.

<span class="mw-page-title-main">Electroweak interaction</span> Unified description of electromagnetism and the weak interaction

In particle physics, the electroweak interaction or electroweak force is the unified description of two of the fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV, they would merge into a single force. Thus, if the temperature is high enough – approximately 1015 K – then the electromagnetic force and weak force merge into a combined electroweak force.

In physics, the fundamental interactions or fundamental forces are interactions in nature that appear not to be reducible to more basic interactions. There are four fundamental interactions known to exist:

<span class="mw-page-title-main">Elementary particle</span> Subatomic particle having no known substructure

In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number: electrons and other leptons, quarks, and the fundamental bosons. Subatomic particles such as protons or neutrons, which contain two or more elementary particles, are known as composite particles.

<span class="mw-page-title-main">Grand Unified Theory</span> Comprehensive physical model

Grand Unified Theory (GUT) is any model in particle physics that merges the electromagnetic, weak, and strong forces into a single force at high energies. Although this unified force has not been directly observed, many GUT models theorize its existence. If the unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct.

<span class="mw-page-title-main">Theory of everything</span> Hypothetical physical concept

A theory of everything (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 aspects of the universe. Finding a theory of everything is one of the major unsolved problems in physics.

<span class="mw-page-title-main">Weak interaction</span> Interaction between subatomic particles and one of the four known fundamental interactions

In nuclear physics and particle physics, the weak interaction, also called the weak force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It is the mechanism of interaction between subatomic particles that is responsible for the radioactive decay of atoms: The weak interaction participates in nuclear fission and nuclear fusion. The theory describing its behaviour and effects is sometimes called quantum flavordynamics (QFD); however, the term QFD is rarely used, because the weak force is better understood by electroweak theory (EWT).

<span class="mw-page-title-main">Standard Model</span> Theory of forces and subatomic particles

The Standard Model of particle physics is the theory describing three of the four known fundamental forces in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.

<span class="mw-page-title-main">Steven Weinberg</span> American theoretical physicist (1933–2021)

Steven Weinberg 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 interaction between elementary particles.

<span class="mw-page-title-main">W and Z bosons</span> Bosons that mediate the weak interaction

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
W+
,
W
, and
Z0
. The
W±
 bosons have either a positive or negative electric charge of 1 elementary charge and are each other's antiparticles. The
Z0
 boson is electrically neutral and is its own antiparticle. The three particles each have a spin of 1. The
W±
 bosons have a magnetic moment, but the
Z0
has none. All three of these particles are very short-lived, with a half-life of about 3×10−25 s. Their experimental discovery was pivotal in establishing what is now called the Standard Model of particle physics.

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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 attempts to create a unified field theory based on classical physics. In particular, unification of gravitation and electromagnetism was actively pursued by several physicists and mathematicians in the years between the two World Wars. This work spurred the purely mathematical development of differential geometry.

A classical field theory is a physical theory that predicts how one or more fields in physics interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically intended to describe electromagnetism and gravitation, two of the fundamental forces of nature.

<span class="mw-page-title-main">History of quantum field theory</span>

In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major advances in the theory were made in the 1940s and 1950s, leading to the introduction of renormalized quantum electrodynamics (QED). The field theory behind QED was so accurate and successful in predictions that efforts were made to apply the same basic concepts for the other forces of nature. Beginning in 1954, the parallel was found by way of gauge theory, leading by the late 1970s, to quantum field models of strong nuclear force and weak nuclear force, united in the modern Standard Model of particle physics.

<span class="mw-page-title-main">Five-dimensional space</span> Geometric space with five dimensions

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<span class="mw-page-title-main">History of subatomic physics</span> Chronological listing of experiments and discoveries

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Complex spacetime is a mathematical framework that combines the concepts of complex numbers and spacetime in physics. In this framework, the usual real-valued coordinates of spacetime are replaced with complex-valued coordinates. This allows for the inclusion of imaginary components in the description of spacetime, which can have interesting implications in certain areas of physics, such as quantum field theory and string theory.

<span class="mw-page-title-main">History of classical field theory</span>

In the history of physics, the concept of fields had its origins in the 18th century in a mathematical formulation of Newton's law of universal gravitation, but it was seen as deficient as it implied action at a distance. In 1852, Michael Faraday treated the magnetic field as a physical object, reasoning about lines of force. James Clerk Maxwell used Faraday's conceptualisation to help formulate his unification of electricity and magnetism in his field theory of electromagnetism.

Unification of theories about observable fundamental phenomena of nature is one of the primary goals of physics. The two great unifications to date are Isaac Newton’s unification of gravity and astronomy, and James Clerk Maxwell’s unification of electromagnetism; the latter has been further unified with the concept of electroweak interaction. This process of "unifying" forces continues today, with the ultimate goal of finding a theory of everything.

References

  1. "Unified field theory | Einstein's Theory of Relativity | Britannica". www.britannica.com. Retrieved 2024-10-10.
  2. Ernan McMullin (2002). "The Origins of the Field Concept in Physics" (PDF). Phys. Perspect. 4 (1): 13–39. Bibcode:2002PhP.....4...13M. doi:10.1007/s00016-002-8357-5. S2CID   27691986.
  3. "How the search for a unified theory stumped Einstein to his dying day". phys.org.
  4. Stephen W. Hawking (28 February 2006). The Theory of Everything: The Origin and Fate of the Universe. Phoenix Books; Special Anniv. ISBN   978-1-59777-508-3.
  5. Ross, G. (1984). Grand Unified Theories. Westview Press. ISBN   978-0-8053-6968-7.
  6. Goenner, Hubert F. M. (2004-12-01). "On the History of Unified Field Theories". Living Reviews in Relativity. 7 (1): 2. Bibcode:2004LRR.....7....2G. doi: 10.12942/lrr-2004-2 . ISSN   1433-8351. PMC   5256024 . PMID   28179864.
  7. See 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 Archived 2011-08-05 at the Wayback Machine .
  8. Erhard Scholtz (ed) (2001), Hermann Weyl's Raum - Zeit- Materie and a General Introduction to His Scientific Work, Basel, Birkhäuser.
  9. Daniela Wuensch (2003), "The fifth dimension: Theodor Kaluza's ground-breaking idea", Annalen der Physik, vol. 12, p. 519–542.

Further reading