# Grand Unified Theory

# Grand Unified Theory

One of the major theoretical hurdles to a reachable synthesis of current theories of particles and force interactions is called grand unified theory (GUTs, and sometimes also called grand unification theory and grand unified field theory). Within theoretical physics, GUTs is the collective term for attempts to unify the fundamental forces within the universe: the strong and weak nuclear forces and electromagnetism. Thus, scientists researching GUTs are trying to reconcile the evolving principles of quantum theory with the principles of general relativity advanced by German-born American theoretical physicist Albert Einstein (1879-1955) over one century ago. The synthesis is made difficult because the unification of quantum mechanics (itself a unification of the laws of chemistry with atomic physics) with special relativity to form a complete quantum field theory consistent with observable data is itself not yet complete.

A grand unified theory of physics is not within the reach of present technology. There are also theoretical obstacles to formulating a grand unified theory.

A grand unified theory is a theory that will reconcile the electroweak force (the unified forces of electricity and magnetism) and the strong force (the force that binds quarks within the atomic nucleus together). A grand unified theory that could subsequently incorporate gravitational theory would, become the ultimate unified theory, often referred to by physicists as a theory of everything (TOE).

The technological barriers to a unified theory are a consequence of the tremendous energies required to verify the existence of the particles predicted by the theory. In essence, experimental physicists are called upon to recreate the conditions of the universe that existed during the first few millionths of a second of the big bang—when the universe was tremendously hot, dense, and therefore extremely energetic.

There are admittedly great difficulties and high amounts of inconsistency between quantum and relativity theory that may put such a theory of everything (TOE) far beyond the present grasp of scientists. Some scientists speculate, however, that although a TOE is beyond the reach, scientists may be within reach of a grand unified theory (GUT) that, excepting quantum gravity, will unite the remaining fundamental forces.

Quantum theory was principally developed by German physicist Maxwell Planck (1858–1947), Danish physicist Niels Bohr (1885–1962), Austrian physicist Erwin Schrödinger (1887–1961), English physicist P.A.M. Dirac (1902–1984) and German physicist Werner Heisenberg (1901–1976) during the first half of the twentieth century through the independent research on various parts of the theory. Quantum mechanics fully describes wave particle duality, and the phenomena of superposition in term of probabilities. Quantum field theory describes and encompasses virtual particles and renormalization.

In contrast, special relativity describes space-time geometry and the relativistic effects of different inertial reference frames (i.e., the relativity of describing motion) and general relativity describes the nature of gravity. General relativity fuses the dimensions of space and time. The motion of bodies under apparent gravitational force is explained by the assertion that, in the vicinity of mass, space-time curves. The more massive the body the greater is the curvature or force of gravity.

Avoiding the mathematical complexities, a fair simplification of the fundamental incompatibility between quantum theory and relativity theory may be found in the difference between the two theories with respect to the nature of the gravitational force. Quantum theory depicts a quantum field with a carrier particle for the gravitational force—that although not yet discovered—is termed a graviton. As a force carrier particle, the graviton is analogous to the photon that acts as the boson or carrier of the electromagnetism (i.e., light). In stark contrast, general relativity theory does away with the need for the graviton by depicting gravity as a consequence of the warping or bending of space-time by matter (or, more specifically, mass).

Although both quantum and relativity theories work extremely well in explaining the universe at the quantum and cosmic levels respectively, the theories themselves are fundamentally incompatible and hence the search for unification theories.

### KEY TERMS

**Electroweak force** —A unification of the fundamental forces of electromagnetism (that light is carried by quantum packets termed photons manifested by alternating fields of electricity and magnetism) and the weak force.

**Field theory** —A concept first advanced Scottish physicist James Clerk Maxwell (1831–1879) as part of his development of the theory of electromagnetism to explain the manifestation of force at a distance without an intervening medium to transmit the force. Einstein’s general relativity theory is also a field theory of gravity.

**Fundamental forces** —The forces of electromagnetism (light), weak force, strong force, and gravity. Aptly named, the strong force is the strongest force, but acts over only the distance of the atomic nucleus. In contrast, gravity is 1039 times weaker than the strong force and acts at infinite distances.

**Gravitational force** —A force dependent upon mass and the distance between objects. The English physicist and mathematician Sir Isaac Newton (1642–1727) set out the classical theory of gravity in his *Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy* ). According to classical theory, gravitational force, always attractive between two objects, increases directly and proportionately with mass of the objects but is inversely proportional to the square of the distance between the objects. According to general relativity, gravity results from the bending of fused space-time. According to modern quantum theory, gravity is postulated to be carried by a vector particle termed a graviton.

**Local gauge invariance** —In physics, a concept that asserts that all field equations ultimately contain symmetries in space and time. Gauge theories depend on difference in values as opposed to absolute values.

**Strong force (or Strong interactions)** —A force that binds quarks together to form protons and neutrons and hold protons and neutrons—and to hold together the electrically repelling positively charged protons within the atomic nucleus.

**Unified field theory** —In physics, a theory describing how a single set of particles and fields can become (or underlie) the observable fundamental forces of the electroweak force (electromagnetism and weak force unification) and the strong force.

**Virtual particles** —A particle that is emitted and then reabsorbed by particles involved in a force interaction (e.g., the exchange of virtual photons between charged particles in involved in electromagnetic force interactions).

**Weak force** —The force that causes transmutations of certain atomic particles. For example, weak force interactions in beta decay change neutrons and protons allowing carbon-14 to decay into nitrogen at a predictable rate useful in carbon-14 dating.

Such unifications are not trivial mathematical or rhetorical flourishes; they evidence an unswerving trail back towards the beginning of time and the creation of the universe in the big bang. What the electroweak unification reveals is that at higher levels of energy, (e.g., the energies associated with the big bang), the forces of electromagnetism and the weak force are really one in the same. It is only at the more modest present state of the universe, far cooler and less dense, that the forces take on the characteristic differences of electromagnetism and the weak force.

Experiments at high energy levels have revealed the existence of a number of new particles. According to modern field theory and the standard model, particles are manifestations of field and particles interact (exert forces) through fields. Accordingly, for every particle (e.g., quarks and leptons—one form of a lepton is the electron) there must be an associate field. Forces between particles result from the exchange of particles that are termed virtual particles. Electromagnetism depends upon the exchange of photons (QED theory). The weak force depends upon the exchange of W^{+}, W^{-}, and Z_{o} particles. Eight different forms of gluons are exchanged in a gluon field to produce the strong force. Regardless, the energy requirements required to identify the particles associated with a unified field required by a grand unified theory are greater than present technologies can achieve. Most mathematical calculations involving quantum fields indicate that unification of the fields may require 1,016 GeV. Some models allow the additional fusion of the gravitational force at 1,018 GeV.

The higher energies needed are not simply a question of investing more time and money in building larger accelerators. Using present technologies, the energy levels achievable by a particle accelerator are proportional to the size of the accelerator (specially the diameter of the accelerator). Alas, to archive the energy levels required to find the particles of a grand unified force would require an accelerator larger than the entire solar system.

Although a quantum explanation of gravity is not required by a grand unification theory that seeks only to reconcile electroweak and strong forces, it is important to acknowledge that the unification of force and particle theories embraced by the Standard model is not yet complete. Further, it may not be possible to rule out gravity and develop a unified theory of electroweak and strong forces that ignores gravity.

*See also* Atomic theory; Electromagnetic spectrum; Feynman diagrams; Gravity and gravitation; Particle detectors; Relativity, general; Standard model; Subatomic particles.

## Resources

### BOOKS

Falk, Dan. *Universe on a T-shirt: The Quest for the Theory of Everything*. New York: Arcade Publishing, 2004.

Greene, Brian. *The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory*. New York: W.W. Norton & Co., 2003.

Mohanatra, Rabindra Nath. *Unification and Supersymmetry: The Frontiers of Quark-Lepton Physics*. New York: Springer-Verlag, 2003.

Oyibo, G.A. *Grand Unified Theorem: Discovery of the Theory of Everything and the Fundamental Building Block of Quantum Theory*. New York: Nova Science Publishers, 2004.

### OTHER

Particle Data Group. Lawrence Berkeley National Laboratory. “The Particle Adventure: The Fundamentals of Matter and Force” <http://particleadventure.org/particleadventure/> (accessed October 11, 2006).

K. Lee Lerner

# Grand Unified Theory

# Grand unified theory

One of the major theoretical hurdles to a reachable synthesis of current theories of particles and **force** interactions into a grand unification theory (also known as Grand Unified Field Theory, Grand Unified Theory, or GUT) is the need to reconcile the evolving principles of quantum theory with the principles of general relativity advanced by German-American physicist Albert Einstein (1879-1955) nearly a century ago. The synthesis is made difficult because the unification of **quantum mechanics** (itself a unification of the laws of **chemistry** with atomic **physics** ) with special relativity to form a complete quantum field theory consistent with observable data is itself not yet complete.

A grand unified theory of physics is not within the reach of our present technology and there are also theoretical obstacles to formulating a Grand unified theory.

A grand unified theory is a theory that will reconcile the electroweak force (the unified forces of **electricity** and **magnetism** ) and the strong force (the force that binds **quarks** within the atomic nucleus together). A grand unified theory that could subsequently incorporate gravitational theory would, become the ultimate unified theory, often referred to by physicists as a "theory of everything" (TOE).

The technological barriers to a unified theory are a consequence of the tremendous energies required to verify the existence of the particles predicted by the theory. In essence, experimental physicists are called upon to recreate the conditions of the universe that existed during the first few millionths of a second of the Big bang - when the universe was tremendously hot, dense, and therefore energetic.

There are admittedly great difficulties and high **mountains** of inconsistency between quantum and relativity theory that may put such a "theory of everything" (TOE) far beyond our present grasp. Some scientists speculate that although a TOE is beyond our reach, we may be within reach of a grand unified theory (GUT) that, excepting quantum gravity, will unite the remaining fundamental forces.

Quantum theory was principally developed during the first half of the twentieth century through the independent **work** on various parts of the theory by German physicist Maxwell Planck (1858–1947), Danish physicist Niels Bohr (1885–1962), Austrian physicist Erwin Schrödinger (1887–1961), English physicist P.A.M. Dirac (1902–1984) and German physicist Werner Heisenberg (1901–1976). Quantum mechanics fully describes wave particle duality, and the phenomena of superposition in term of probabilities. Quantum field theory describes and encompasses **virtual particles** and renormalization.

In contrast, special relativity describes space-time **geometry** and the relativistic effects of different inertial reference frames (i.e., the relativity of describing **motion** ) and general relativity describes the nature of gravity. General relativity fuses the dimensions of **space** and **time** . The motion of bodies under apparent gravitational force is explained by the assertion that, in the vicinity of **mass** , space-time curves. The more massive the body the greater is the curvature or "force of gravity."

Avoiding the mathematical complexities, a fair simplification of the fundamental incompatibility between quantum theory and relativity theory may be found in the difference between the two theories with respect to the nature of the gravitational force. Quantum theory depicts a quantum field with a carrier particle for the gravitational force—that although not yet discovered—is termed a graviton. As a force carrier particle, the graviton is analogous to the **photon** that acts as the boson or carrie of the **electromagnetism** (i.e., **light** ). In stark contrast, general relativity theory does away with the need for the graviton by depicting gravity as a consequence of the warping or bending of space-time by **matter** (or, more specifically, mass).

Although both quantum and relativity theories work extremely well in explaining the universe at the quantum and cosmic levels respectively, the theories themselves are fundamentally incompatible and hence the search for unification theories.

Such unifications are not trivial mathematical or rhetorical flourishes; they evidence an unswerving trail back towards the beginning of time and the creation of the universe in the big bang. What the electroweak unification reveals is that at higher levels of **energy** , (e.g., the energies associated with the big bang), the forces of electromagnetism and the weak force are really one in the same. It is only at the more modest present state of the universe, far cooler and less dense, that the forces take on the characteristic differences of electromagnetism and the weak force.

Experiments at high energy levels have revealed the existence of a number of new particles. According to modern field theory and the **Standard model** , particles are manifestations of field and particles interact (exert forces) through fields. Accordingly, for every particle (e.g., quarks and leptons—one form of a lepton is the **electron** ) there must be an associate field. Forces between particles result from the exchange of particles that are termed virtual particles. Electromagnetism depends upon the exchange of photons (QED theory). The weak force depends upon the exchange of W+, W–, and Zo particles. Eight different forms of gluons are exchanged in a gluon field to produce the strong force. Regardless, the energy requirements required to identify the particles associated with a unified field required by a grand unified theory are greater than present technologies can achieve. Most mathematical calculations involving quantum fields indicate that unification of the fields may require 1016 GeV. Some models allow the additional fusion of the gravitational force at 1018 GeV.

The higher energies needed are not simply a question of investing more time and money in building larger **accelerators** . Using our present technologies, the energy levels achievable by a particle accelerator are proportional to the size of the accelerator (specially the diameter of the accelerator). Alas, to archive the energy levels required to find the particles of a grand unified force would require an accelerator larger than our entire **solar system** .

Although a quantum explanation of gravity is not required by a grand unification theory that seeks only to reconcile electroweak and strong forces, it is important to acknowledge that the unification of force and particle theories embraced by the Standard model is not yet complete. Further, it may not be possible to rule out gravity and develop a unified theory of electroweak and strong forces that ignores gravity.

See also Atomic theory; Electromagnetic spectrum; Feynman diagrams; Gravity and gravitation; Particle detectors; Relativity, general; Subatomic particles.

## Resources

### books

Feynman, Richard and Steven Weinberg *Elementary Particles and the Laws of Physics.* Cambridge, UK: Cambridge University Press, 1987.

Greene, Brian. *The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory.* New York: Vintage books, 2000.

Gribbin, John. *Q is for Quantum: An Encyclopedia of Particle Physics.* New York: The Free Press, 1998.

Hawking, Stephen. *The Illustrated Brief History of Time, Updated and Expanded.* New York: Bantam, 2001.

Klein, Etienne, et al. *The Quest for Unity: The Adventure of Physics.* Oxford, UK: Oxford University Press, 2000.

Mohapatra, Rabindra. *Unification and Supersymmetry.* Oxford, UK: Oxford University Press, 2002.

### periodicals

Weinberg, Steven. "A Unified Physics by 2050?" *Scientific American.* December, 1999.

### other

Particle Data Group. Lawrence Berkeley National Laboratory. "The Particle Adventure: The Fundamentals of Matter and Force" [cited February, 5, 2003]. <http://particleadventure.org/particleadventure/>.

K. Lee Lerner

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

**Electroweak force**—A unification of the fundamental forces of electromagnetism (that light is carried by quantum packets termed photons manifested by alternating fields of electricity and magnetism) and the weak force.

**Field theory**—A concept first advanced Scottish physicist James Clerk Maxwell (1831–1879) as part of his development of the theory of electromagnetism to explain the manifestation of force at a distance without an intervening medium to transmit the force. Einstein's general relativity theory is also a field theory of gravity.

**Fundamental forces**—The forces of electromagnetism (light), weak force, strong force, and gravity. Aptly named, the strong force is the strongest force, but acts over only the distance of the atomic nucleus. In contrast, gravity is 1039 times weaker than the strong force and acts at infinite distances.

**Gravitational force**—A force dependent upon mass and the distance between objects. The English physicist and mathematician Sir Isaac Newton (1642–1727) set out the classical theory of gravity in his

*Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)*. According to classical theory, gravitational force, always attractive between two objects, increases directly and proportionately with mass of the objects but is inversely proportional to the square of the distance between the objects. According to general relativity, gravity results from the bending of fused space-time. According to modern quantum theory, gravity is postulated to be carried by a vector particle termed a graviton.**Local gauge invariance**—In physics, a concept that asserts that all field equations ultimately contain symmetries in space and time. Gauge theories depend on difference in values as opposed to absolute values.

**Strong force (or Strong interactions)**—A force that binds quarks together to form protons and neutrons and hold protons and neutrons—and to hold together the electrically repelling positively charged protons within the atomic nucleus.

**Unified field theory**—In physics, a theory describing how a single set of particles and fields can become (or underlie) the observable fundamental forces of the electroweak force (electromagnetism and weak force unification) and the strong force.

**Virtual particles**—A particle that is emitted and then reabsorbed by particles involved in a force interaction (e.g., the exchange of virtual photons between charged particles in involved in electromagnetic force interactions).

**Weak force**—The force that causes transmutations of certain atomic particles. For example, weak force interactions in beta decay change neutrons and protons allowing Carbon-14 to decay into Nitrogen at a predictable rate useful in Carbon-14 dating.

# Grand Unified Theory

# Grand Unified Theory

A Grand Unified Theory (GUT) unifies, or interrelates in a single quantum field interaction, the three fundamental nongravitational forces: electromagnetism, the weak nuclear interaction, and the strong nuclear interaction. These three forces are each characterized by a *coupling constant,* which gives the strength of the interaction by a range over which the force acts (long-range like electro-magnetism, or short-range like the two nuclear forces), and by certain characteristic symmetries that are described by mathematical symmetry groups. A successful GUT would show how the three different coupling constants become identical at some very high energy, subsume the symmetries of the three individual interactions in a much larger symmetry group, and explain all of the masses, processes, couplings, decays, ranges, and other behaviors of all particles at lower energies—lower than the GUT unification energy. The current standard model of particle physics, though highly successful in other ways, does not do this. Further, there are strong indications that a more complete and adequate explanation, describing deep connections that have so far evaded our understanding, awaits a successful GUT model.

A GUT would express the fact that at the most fundamental level all nongravitational interactions, and all particles, quarks, electrons, and neutrinos, are intimately interrelated and, in fact, identical above the unification energy. Their difference at low energies is expressed in a GUT by saying that the symmetries characterizing the interactions at very high energies, rendering particles and forces identical or equivalent, are "spontaneously broken" below the unification energy. Such spontaneously broken symmetries are present in the underlying relationships characterizing the system, but are not expressed—are hidden—in a given equilibrium state of the system, such as that realized in the present state of the universe. Construction of a GUT theory is an essential step towards achieving total unification, which would also include gravity. Although promising and detailed progress has been made on a number of fronts, there was no adequate GUT as of 2002.

There are strong indications that all the basic physical interactions are intimately related and that they can be unified. In the mid nineteenth century, the Scottish physicist James Clerk Maxwell began realizing this intuition by unifying electrical and magnetic phenomena in his electromagnetic theory. In the 1970s, Sheldon Glashow, Stephen Weinberg, and Abdus Salam succeeded in developing an adequate electroweak theory, which describes how electromagnetism and the weak nuclear interaction are related, and how they are identical at temperatures above 1015 K (kelvin). This electroweak theory was confirmed in 1983 by the discovery of the W and Z massive bosons, which carry the electroweak force and which were predicted by the theory. A completely successful GUT would incorporate the strong nuclear interaction with this electroweak interaction in an analogous way at some higher temperature above 1027 K.

Part of the motivation for a GUT is the lack of explanation for many of the parameters and characteristics of the standard model, and of the universe itself. For example, there is no explanation for the baryon-anti-baryon asymmetry, which means that there is more matter in the universe than there is antimatter. There is also some positive experimental support for a GUT, including equality of the magnitude of the charges of the proton and the electron and the non-zero rest-mass of the neutrino. Furthermore, GUT candidates generically predict the decay of protons at some very slow rate, as well as the presence of monopoles and other topological defects, which are localized regions in which the vacuum energy is different from the rest of the universe (false vacuum). Observational limits on these phenomena are being used, and will continue to be used, to identify the most adequate GUT candidates.

From a cosmological point of view, the success of a GUT would mean that at some very early stage in the history of the universe—well before one second after the Big Bang, when the temperature of the universe was greater than 1027 K—the physics of the universe was characterized by just two interactions: gravity and the GUT interaction. The universe would have been much too hot for protons, neutrons, and electrons to exist, as they do at lower temperatures. As the universe expanded, it cooled. And, as it cooled below 1027 K, the GUT interaction split into the strong nuclear and the electroweak interactions. A short time later—still much less than one second after the Big Bang—when the temperature had plummeted below 1015 K, the electroweak interaction split further into the weak nuclear and the electromagnetic interactions. From that point on, the basic physics of the universe was the same as it is today, but devoid of the complex macroscopic and microscopic structures that developed much later.

## Implications for theology

There are no direct implications of GUT unification for religion and theology, but there are several important indirect influences. First, GUT unification, when it is finally achieved, will contribute to describing how everything in material reality is intimately interconnected in very basic ways. Those relationships constitute reality as it is and are an essential part of how God's continuing creative action is realized—through these "laws of nature." Second, a GUT characterizes a definite, very early stage in the evolution of the universe. A successful GUT will strengthen the already strong case for the evolution of the presently lumpy, cool, complex, and highly differentiated cosmos from a very hot, simple, homogeneous, and relatively undifferentiated primordial state, which was characterized by a much simpler physics. For the theistic thinker, a GUT represents one of the key ways in which God gradually brought into being the reality of which human beings are a part.

*See also* Field Theories

*Bibliography*

bailin, david, and love, alexander. "grand unified theory." in introduction to gauge field theory, rev. edition. bristol, uk, and philadelphia: institute of physics, 1993.

börner, gerhard. "grand unification schemes." in the early universe: facts and fiction, 3rd edition. berlin, heidelberg, and new york: springer-verlag, 1993.

collins, p. d. b.; martin, a. d.; and squires, e. j. "grand unified theories." in particle physics and cosmology. new york: wiley, 1989.

davies, paul. "the new physics: a synthesis." in the new physics, ed. paul davies. cambridge, uk: cambridge university press, 1989.

georgi, howard. "grand unified theories." in the new physics, ed. paul davies. cambridge, uk: cambridge university press, 1989.

guth, alan, and steinshardt, paul. "the inflationary universe." in the new physics, ed. paul davies. cambridge, uk: cambridge university press, 1989.

kaku, michio. "gauge field theories." in quantum unified theory: a modern introduction. new york and oxford: oxford university press, 1993.

william r. stoeger

# grand unified theory

**grand unified theory ( GUT)** Theory that would demonstrate that three of the four fundamental forces are actually different aspects of the same fundamental force. The weak nuclear force and electromagnetic force have been incorporated as the electroweak force, as demonstrated by particle accelerator experiments. In order to prove the GUT, the electroweak force must be unified with the strong nuclear force. If the gravitational force could be incorporated, then a unified field theory would be produced.

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