Is a grand unified theory of the fundamental forces within the reach of physicists today

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Is a grand unified theory of the fundamental forces within the reach of physicists today?

Viewpoint: Yes, history, recent advances, and new technologies provide reasonable hope that a grand unified theory may be within reach.

Viewpoint: No, a grand unified theory of the fundamental forces is not within the reach of physicists today.

The belief that a small number of organizing principles underlies the immense variety of phenomena observed in the natural world has been a constant theme in the history of science. One of the first unification theories was introduced in the fifth century b.c. by Empedocles: a system of four elements—air, earth, fire, and water—with qualities of coldness or hotness and moistness or dryness. This system soon was supported by a geometrical model outlined in Plato's Timaeus (ca. 360 b.c.), and extended to the medical realm with Hippocrates' theory of the four humors. While the four-element theory bears little resemblance to the modern periodic table of chemical elements or its mathematical explanation in terms of quantum mechanics, it represents the same basic drive toward unification. It also provides an important lesson: unification theories, no matter how impressive, may be misleading.

The human tendency to perceive patterns in the data of experience is strong, and may have something to do with the high value placed on unifying theories in science. Ancient Europeans pondered the night sky and grouped stars into mythical figures. Astronomers still sometimes make use of this ancient system of constellations to locate objects. Other cultures found other figures. The tendency to find patterns in random data has been well documented in psychological studies.

The modern notions of force and the relationship between force and motion first were established in Isaac Newton's Philosophiae Naturalis Principia Mathematica (Mathematical principles of natural philosophy), published in 1687. Newton's three laws of motion and his force law for universal gravitation provided a single framework within which the motion of both terrestrial objects (footballs and cannonballs) and celestial objects (moons and planets) could be computed with unprecedented accuracy. Like the unification theories to follow, in addition to integrating two realms of phenomena previously thought to be governed by different laws, the Newtonian synthesis allowed predictions that were subsequently confirmed, including the occurrence of eclipses, cometary returns, and the existence of the planets Neptune and Pluto, which were discovered through their effect on the orbits of other planets.

The investigation of electric and magnetic effects in the nineteenth century led to a unified theory of the electromagnetic force in the set of equations developed by the Scottish physicist James Clerk Maxwell in 1864. Maxwell's equations allowed for solutions that described waves traveling through space at a speed determined by the basic constants of the electric and magnetic force laws; this speed is exactly the observed speed of light. Because the solutions were not restricted to any specific wavelength, Maxwell's equations stimulated the investigation of the entire electromagnetic spectrum from radio waves to gamma rays. Attempts to reconcile the wavelike character of light with Newtonian mechanics led to a belief in a "luminiferous aether" that permeated all space, but allowed the passage of material objects without resistance. A true unification did not occur until 1905, when Albert Einstein's special theory of relativity replaced the absolute notions of time and space underlying Newton's mechanics with postulates that allowed for different measurements by observers in motion with respect to each other. After Einstein's development of the special theory of relativity there was no need for the concept of an "aether."

Dmitry Mendeleyev's periodic table classifying the chemical elements was another impressive unification achieved in the nineteenth century. Like the syntheses of Newton and Maxwell, it made predictions, in this case of new chemical elements and their properties, that were soon confirmed. The discovery of the electron in 1897 by the English physicist Joseph John Thomson brought about the hope that the chemical properties of the elements could be explained from the structures of their atoms. Experimental studies of the atom's structure revealed that all of the positive charge in the atom was confined to a very tiny nucleus, with the negatively charged electrons distributed in space around it. Unfortunately, the known laws of electromagnetism and dynamics allowed no such arrangement of charges, moving or stationary, to be stable. Again the basic Newtonian mechanics had to be revised. The resulting quantum mechanics theory, which reached its definitive form around 1925, provided a workable picture of atomic structure and explained both chemical bonding and the characteristic optical spectra of the elements.

The quantum mechanical synthesis made it clear that, outside of the nucleus, only two fundamental forces were at work. One, the gravitational force, was extremely weak, but nonetheless was the only active force in the universe on the astronomical scale. The other, the electromagnetic force, was responsible for chemical bonding, tension and compression in materials, friction, and the contact force between material bodies.

The two twentieth-century modifications of Newtonian mechanics—special relativity and quantum mechanics—had yet to be reconciled with each other. A major step in this direction was the development of the equation for the behavior of electrons by the British physicist Paul Dirac in 1928, about the same time as the more general nonrelativistic quantum theory was taking form. Dirac's equation predicted the existence of strange "negative energy" states for the electron—states that in fact described the positron, the antiparticle to the electron discovered in the early 1930s in the cosmic ray experiments of the U.S. physicist Carl Anderson. The discovery that an electron and a positron could annihilate each other and convert their entire mass-energy into electromagnetic radiation—while sufficiently energetic quanta of electromagnetic energy could, under the right circumstances, create an electron-positron pair—called for the development of a comprehensive theory of electrons and positrons. This theory, now called quantum electrodynamics, provided a picture of the photon, or quantum of electromagnetic energy, as the carrier of the electromagnetic force. Charged particles attract or repel each other by the exchange of photons, and the photon itself in a sense carries the potential for pair creation with it.

The basic model of material particles exerting forces on each other through the exchange of particles also provided the key to understanding the short-range forces between nuclear particles. In 1935 the Japanese physicist Hideki Yukawa proposed a family of medium-weight particles, or mesons, that carried the strong but short-range nuclear force between protons and neutrons. Accelerator experiments eventually yielded direct evidence for the meson, as well as the existence of particles much heavier than the proton that decayed quickly into protons and mesons. Eventually enough particles were found in the proton-meson or baryon family that it was proposed that all of them were constructed from even more elementary particles—a family of quarks that exchanged particles called gluons as they interacted with each other.

A third fundamental force, the weak nuclear force that is responsible for beta decay, also proved amenable to the force-carrier interpretation, although the force-carrying particles, the W+, W-, and Z⁰bosons, were confirmed experimentally only in 1983. Since the electromagnetic, strong, and weak forces all appeared to work by the same mechanism, it was only natural for physicists to seek a further unification of these forces. A unified theory of the weak and electromagnetic forces was proposed by the U.S. physicist Sheldon Lee Glashow in 1961 and worked out in detail over the next decade. The unified electroweak theory required the existence of a new type of particle, the Higgs boson, which had not been found as of 2001. Several unified theories for the electroweak and strong forces have been put forward, and the interpretation of each of these within the force-carrier or standard model makes many physicists confident that a unified theory will be confirmed.

The stumbling block, then, to a true grand unified theory or "theory of everything" is the integration of the last fundamental force, gravity, with the standard model. While a force-carrying particle, the graviton, has been proposed, it has not been demonstrated to exist. Proposals that on theoretical grounds might be acceptable as a theory of everything (such as string theory) appear to require energies many orders of magnitude higher than can presently be confirmed. The question addressed in the following articles is whether a preponderance of evidence supporting such a grand unification theory can be gained by experiments that will be feasible over the next decade or two.

—DONALD R. FRANCESCHETTI

Viewpoint: Yes, history, recent advances, and new technologies provide reasonable hope that a grand unified theory may be within reach.

The ultimate step awaiting modern physicists is the unification of the theories that are part of the quantum-based "standard model," which encompasses electromagnetism, the weak force, and the strong force, with a quantum theory of gravity in a way that is consistent with the theory of general relativity. There are great difficulties and high mountains of inconsistency between quantum and relativity theory that may put a "theory of everything" far beyond our present grasp. However, physicists may soon be able to take an important step toward this ultimate goal by advancing a grand unified theory that, excepting quantum gravity, would unite the remaining fundamental forces. Although a theory of everything is tantalizingly beyond our present grasp, it may well be within the reach of the next few generations.

Advances in the last half of the twentieth century, particularly in the work of the Pakistani physicist Abdus Salam and the U.S. physicist Steven Weinberg, already have provided a base camp for the assault on a grand unified theory. Their work has united two of the fundamental forces—electromagnetism and the weak force—into electroweak theory.

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

Physics as a History of Unification

The history of physics, especially following the publication in 1687 of Isaac Newton's Philosophiae Naturalis Principia Mathematica (Mathematical principles of natural philosophy), reveals a strong tendency toward the unification of theories explaining different aspects of the universe. The work of Newton, an English physicist and mathematician, advanced that of the Italian astronomer and physicist Galileo Galilei and unified the theories of celestial mechanics with empirically testable theories of gravity into a theory of universal gravitation. By asserting a mutual gravitational attraction between all particles in the universe, Newton's theory brought a mathematical and scientific unification to the cosmos for the first time.

In the early years of the twentieth century, the German-American physicist Albert Einstein unified Newton's universal gravitation with theories of space-time geometry (made possible by revolutionary advances in nineteenth-century mathematics) to assert his general theory of relativity in 1916.

At the dawn of the twenty-first century, general relativity remains the only theory describing the gravitational force. This is significant because the other great theory explaining the cosmos—quantum theory and the resulting standard model—does not yet include a theory of gravity. The standard model presently accounts for the strong and electroweak forces. Because quantum theory and relativity theory are inconsistent and mutually exclusive on some key postulates, their reconciliation and fusion to unify all four underlying forces has occupied the bulk of theoretical physics during the twentieth century.

Development of the Standard Model

The standard model of particle physics is the result of more than a century of theoretical unifications. The inclusive sweep toward the standard model began with James Clerk Maxwell's work of 1864, in which he combined the empirical laws of electricity and magnetism into a single set of equations. These included as solutions electromagnetic waves that traveled through space and interacted with matter exactly as light does. The theory of electromagnetism removed the need for the concept of an ether (a medium in the vacuum of space akin to the medium of water through which water waves travel), and provided an elegant elaboration of light in an electromagnetic spectrum. Indeed the electromagnetic spectrum, ranging from radio waves to x rays and gamma rays, continues to provide the most accessible and profound evidence of the unification of natural phenomena. Radio waves, microwaves, infrared, the visible light of our everyday existence (including the colors of the rainbow), ultraviolet light, x rays, and gamma rays are all forms of light that differ only in terms of wavelength and frequency.

Advances in quantum theory—made possible by the work of the German physicist Max Planck and Einstein, and subsequently in the 1920s by the Austrian physicist Erwin Schrödinger and the German physicist Werner Heisenberg—established the photon or light quantum as the carrier particle (boson) of the electromagnetic force.

In the 1940s and 1950s, the theory of electromagnetism was reconciled with quantum theory through the independent work of the U.S. physicist Richard Feynman, the U.S. physicist Julian Schwinger, and the Japanese physicist Shin'ichiro Tomonaga. The reconciled theory was termed quantum electrodynamics (QED), and asserts that the particle vacuum consists of electron-positron fields. Electron-positron pairs (positively charged electron antiparticles) manifest themselves when photons interact with these fields. The QED theory describes and accurately predicts the subsequent interactions of these electrons, positrons, and photons. According to QED, electromagnetic force-carrying photons, unlike solid particles, can exist as virtual particles constantly exchanged between charged particles such as electrons. The theory also shows that the forces of electricity stem from the common exchange of virtual photons, and that only under special circumstances do photons become observable as light.

The development of a weak force theory (or weak interaction theory) built upon theories describing the nature and interactions of beta particles (specifically beta decay) and neutrinos. The existence of this different set of force-carrying particles (termed W+, W-, and Z⁰ bosons) was verified in 1983 by the Italian physicist Carlo Rubbia and the Dutch physicist Simon van der Meer at CERN (the European Organization for Nuclear Research in Geneva, Switzerland). Weak force interactions such as those associated with radioactive decay also produce neutrinos, which was first postulated by the Italian-American atomic physicist Enrico Fermi in the 1930s. Fermi spurred the experimental quest and discovery of the neutrino by asserting that neutrinos must exist in order to explain what would otherwise be a violation of the law of conservation of energy in beta decay.

In 1967 the theories of electromagnetism and weak forces were unified by Weinberg, Salam, and the U.S. physicist Sheldon Lee Glashow. The Glashow-Weinberg-Salam theory states that both forces are derived from a single underlying electroweak force. Accordingly, photons, W+, W-, and Z⁰ particles are lower-energy manifestations with a common origin. Electroweak force interactions, predicted by electroweak theory, have been observed and verified by experiments in the largest particle accelerators.

The best conceptual example, often advanced by Weinberg, the British physicist Stephen Hawking, and others, likens the higher-energy electroweak state to a ball spinning rapidly around the top track of a whirling roulette wheel. At this high-energy state the ball takes on no particular number; it is only when the energy drops and the wheel slows that the ball drops into a characteristic state described as "12" or "16." At the higher-energy states achievable in large particle accelerators, photons, W+, W-, and Z⁰ particles lose their individual characteristics. Correspondingly, weak force and electromagnetic interactions begin to act the same and are unified into an electroweak force.

This concept of the electroweak force is joined by the strong force theory (or strong interaction theory)—a theory derived from theories and data describing the existence and behavior of protons, neutrons, and pions—to form the standard model.

Unifying the Electroweak, Strong, and Gravitational Forces

Following research lines similar to the development of the QED and electroweak theories, physicists at the beginning of the twenty-first century are seeking a unified theory of the electroweak and strong forces that can be reconciled with relativity theory. A very large roulette wheel in the form of a large particle accelerator will be needed to achieve the energy levels that mathematical calculations predict will be needed to fuse the electroweak and strong forces. Although physicists cannot currently construct accelerators that are capable of achieving such high energy levels, they may be able to advance and verify a unified theory based upon interactions and phenomena that are observable at realistically achievable energy levels.

Other unified theories, including quantum chromodynamics (a quantum field theory of strong force interactions), establish an undeniable trend toward a unification of forces that is consistent with the big bang theory. Our experience with the four fundamental forces breaks down with the increasing temperature and pressures of a condensed universe. Within the first few millionths of a second of the big bang, these forces evolved from underlying unified forces. Following the ascending energy tail simply retraces the path of evolution of these forces.

Precise and quantitative observations of particles at the achievable energy levels of our current large accelerators may yield evidence of a grand unified theory, by leading to explanations for particle behavior that is inconsistent with the standard model. For example, recent experiments at the Fermi National Accelerator Laboratory in Batavia, Illinois, have shown inconsistencies in the rare interactions of neutrinos.

By extending existing data, it is already possible to argue for string and supersymmetry theories. Assuming that grand unified forces and fields do exist, a number of exotic particles may provide evidence of these theories. Most importantly, if these exotic particles exist in the low ranges of their predicted energies, physicists may be able to detect those particles in large-diameter accelerators. Moreover, the standard model has been repeatedly confirmed by experiment. At energies up to 200 gigaelectronvolts (GeV) the model accounts for all the observed particles, and there is no reason to doubt that the asyet-undiscovered particles predicted by it will eventually turn up.

The Dutch physicist Gerardus 't Hooft and the Dutch-American physicist Martinus J. G. Veltman have been studying unification energies and problems dealing with the reconciliation of quantum and relativity theory. Their work has allowed very precise and accurate mathematical calculations of the energy levels at which particles may exist. Analyses by 't Hooft and Veltman indicate that the Higgs particle—which is needed to verify a critical part of gauge theory (assertions concerning the similarity of space) and is an important milestone on the path to a grand unified theory—may be observable at the Large Hadron Collider set to be working at CERN by 2005.

Along with advances in technology and the expected experimental harvest of new particles, there are also theoretical advances, such as the loop quantum gravity hypothesis, that may provide an alternative to current string-theory unifications of quantum theory with general relativity. Regardless, arguments against an achievable grand unified theory fail to look back upon the long path of theoretical unification in physics, and simply make the eventual conquest of a theory of everything more tantalizing and challenging.

—BRENDA WILMOTH LERNER

Viewpoint: No, a grand unified theory of the fundamental forces is not within the reach of physicists today.

There are both technological and theoretical obstacles to a reachable grand unified theory of physics. Fundamentally, one of the major theoretical hurdles to a reachable synthesis of current theories of particles and force interactions into a grand unification theory is the need to reconcile the evolving principles of quantum theory with the principles of general relativity that were advanced by the German-American physicist Albert Einstein in 1916. This synthesis is made difficult because the unification of quantum mechanics (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. Thus, physicists are at least a step away theoretically from truly attempting a grand unified theory of the electroweak and strong forces.

As traditionally used by physicists, a grand unified theory is a theory that would reconcile the electroweak force (the unified combination of electricity, magnetism, and the weak nuclear force) 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."

The Standard Model

Quantum field theory (how subatomic particles interact and exert forces on one another) is part of the so-called standard model of atomic particles, forces, and interactions developed by the U.S. theoretical physicist Murray Gell-Mann and others in the latter half of the twentieth century (i.e., the standard model is a field theory). Quantum field theory remains an area of intense theoretical and experimental research. Until field theory is itself fully reconciled with relativity theory, however, it is impossible to achieve the type of synthesis and reconciliation accomplished by other partial unification theories, such as the unification of electromagnetism and relativity found in quantum electrodynamics (QED theory), quantum chromodynamics (QCD theory), or the unification of electromagnetism with the weak force (which was achieved by the U.S. physicist Sheldon Lee Glashow, Pakistani physicist Abdus Salam, and U.S. physicist Steven Weinberg in the advancement of electroweak theory).

According to modern field theory and the standard model, particles are manifestations of field and particles interact (exert forces) through fields. For every particle (e.g., quarks and leptons—one form of a lepton is the electron), there must be an associated 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 Z⁰particles. Eight different forms of gluons are exchanged in a gluon field to produce the strong force.

Technological Constraints

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. Experiments at high energy levels have revealed the existence of a number of new particles, but there is a seeming chaos to the mass of particles unless explained by the presence of other, nondirectional fields termed "scalar fields." The fields must be scalar, meaning directionless, or else space itself would seem to be directional—a fact that would contradict many physics experiments that establish the uniformity or nondirectionality of space.

The particles sought after to verify the existence of the scalar fields are Higgs particles. A Higgs particle is theorized to be the manifestation or quantum particle of the scalar field, much as the photon is the manifestation or quantum particle of the electromagnetic field. Higgs particles must have masses comparable to the mass equivalent to 175 gigaelectronvolts (GeV)—the mass-energy contained in the heaviest known particle, the top quark. This is already about 175 times the mass energy of the proton. According to some mathematical models, the Higgs particles may be hundreds of times more massive than protons and much more massive than the top quark.

Fully exploring and verifying the existence of scalar fields, and the particles associated with them, will require accelerating particles to tremendous energies. This is the research goal of high-energy physicists, especially those working with larger accelerators such as those at the Fermi National Accelerator Laboratory in Batavia, Illinois, and CERN (European Organization for Nuclear Research) in Geneva, Switzerland. If Higgs particles exist at the lower end of the mass energy scale ("low end" only in comparison to the energies needed for strong force fusion, but still 350,000 times greater then the mass energy of the electron), they may be detectable at the accelerators presently conducting high-energy physics experiments. If greater energies are required, the near-term development of a grand unified theory will depend upon the completion and results of the Large Hadron Collider at CERN.

Regardless, the energy requirements required to identify the particles associated with a unified field required by a grand unified theory are greater still. Most mathematical calculations involving quantum field indicate that unification of the fields may require an energy of 10¹⁶ GeV. Some models allow the additional fusion of the gravitational force at 10¹⁸ GeV.

Supersymmetry and technicolor force theories (a variation of strong force theory) may offer a solution to the hierarchy problem of increasing masses and energies because they may permit the discovery of particles that are a manifestation of fused strong force at much lower masses and energies than 10¹⁶ GeV. However, these theoretical refinements, if valid, still predict particles too massive and energetic to create and thus are unverifiable at our present levels of technology.

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 (specifically its diameter). Alas, archiving the energy levels required to find the particles of a grand unified force would require an accelerator larger than our entire solar system.

Although there are those who argue that a grand unified theory is within our collective theoretical grasp because of the success of QED, QCD, and electroweak theory, the technological constraints of energy production mean that any grand unified theory will be based upon evidence derived from interactions or anomalies in the standard model that are observable at our much more modestly attainable energy levels.

In contrast, the partial unified theory contained by reconciling electromagnetism with the weak force (a force that acts at the subatomic level to transform quarks and other subatomic particles in processes such as beta decay) is largely testable by the energies achievable by the largest particle accelerators. When quantum electrodynamic (QED) theory was made more reliable by a process termed "renormalization" (allowing positive infinities to cancel out negative infinities) by the U.S. physicist Richard Feynman, U.S. physicist Julian Schwinger, and Japanese physicist Shin'ichiro Tomonaga, the theory reconciling quantum theory with relativity theory advanced by QED was highly testable. Accordingly, there is a valid question as to whether we have, or can even envision, the type of technology and engineering that would allow testing of a grand unified theory.

Theoretical Constraints

There are also theoretical constraints. Perhaps more important than technological limitations, there are fundamental differences in the theoretical underpinnings of how the fundamental forces of nature (i.e., the electromagnetic, weak, strong, and gravitational forces) are depicted by quantum theory and relativity theory.

The attempt at a fusion of quantum field theory with electromagnetism is not new. In fact, during the first half of the twentieth century, Einstein devoted considerable time to an attempted unified field theory that would describe the electromagnetic field and the gravitational field as different manifestations derived from a single unified field. Einstein failed, and at the beginning of the twenty-first century there remains no empirical basis for a quantum explanation of gravity. 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, and that gravity can be absolutely ruled out of the advancement of future unified theories. The problem is that it may not be possible to rule out gravity and to develop a unified theory of electroweak and strong forces that ignores gravity. Moreover, although electromagnetism and weak interactions coherently combine to form electroweak theory, strong force actions among quarks (the fundamental particles comprising neutrons and protons) are not fully mathematically reconcilable with electroweak theory.

Quantum theory was principally developed during the first half of the twentieth century through the independent work on various parts of the theory by the German physicist Max Planck, Danish physicist Niels Bohr, Austrian physicist Erwin Schrödinger, English physicist Paul Dirac, and German physicist Werner Heisenberg. Quantum mechanics fully describes wave particle duality and the phenomena of superposition in terms 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 the curvature or force of gravity.

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.

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, which acts as the boson or carrier of 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).

M theory is a fusion of various string theories that postulate the particles exist as different vibrations of an underlying fundamental string entity. An energy of 10¹⁶ GeV is still required to open the six or more extra dimensions required by M theory.

The development of relativity theory was guided by the development of gravitation theory, and the development of the quantum standard model was facilitated by the gauge theory of electrodynamics and the assertion of local gauge invariance. As Weinberg points out in his elegant essay of the achievability of a grand unified theory (1999), in essence, string and M theories are not so guided—in fact, they require us to guess at the physical realities of extra dimensions that, by definition, we cannot access. This only compounds the already profound difficulties of verifying principles of quantum and relativity theory grounded in accessible space-time dimensions.

Conclusion

Given our modest technologies, the only way to verify a grand unified theory will be to advance a theory that accounts for all measurable values and constants. This approach imparts a testability/disproveability defect into such theory. In keeping with the principle that a scientific theory must account for all data as well as be able to make accurate predictions about the nature and interactions of particles, such a unified theory may be as shaky as the "ether" of physics before relativity. The best we may be able to hope for in the near future is a unified theory that seems pretty good, but will fall short of the verification of relativity and quantum theory as they now exist.

All the hope for a reachable unified theory depends upon whether the ultimate unified field is consistent and in accord with relativity theory (e.g., renormalizable). Recent experiments indicating a possible small mass for the neutrino, if verified, may allow us insight into whether or not nonrenormalizable interactions extend beyond the gravitational force. Nature may dictate that the gravitational force remains nonrenormalizable. If that is the ultimate truth, then the quest for unification must come to a dead end. The question is whether that dead end is past the point where a grand unified theory might be obtainable.

Predicting the proximity of any major theoretical advance is usually folly, but the chances are very good that any formulation of a unified theory will prove elusive, at least through the first half of the twenty-first century. The irreconcilability of current quantum theory with general relativity theory seems clear. Those who argue that a grand unified theory is reachable in the near future, however, hang their theoretical hat on the fact that quantum theory, with its dependence on particles and quantum fields to manifest forces, does not require a quantum theory of gravity. Nevertheless, they are also dangerously and somewhat blindly counting out any role for gravity at the energy levels required by a grand unified theory.

—K. LEE LERNER

KEY TERMS

ELECTROWEAK FORCE:

A unification of the fundamental force of electromagnetism (that light is carried by quantum packets called photons, manifested by alternating fields of electricity and magnetism) and the weak nuclear force.

FIELD THEORY:

A concept first advanced by the Scottish physicist James Clerk Maxwell 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 Isaac Newton set out the classical theory of gravity in his Philosophiae Naturalis Principia Mathematica (1687). According to classical theory, gravitational force, always attractive between two objects, increases directly and proportionately with the 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 called a graviton.

LOCAL GAUGE INVARIANCE:

A concept that asserts that all field equations ultimately contain symmetries in space and time. Gauge theories depend on the difference between values as opposed to absolute values.

STRONG FORCE (OR STRONG INTERACTIONS):

A force that binds quarks together to form protons and neutrons and holds together the electrically repelling positively charged protons within the atomic nucleus.

UNIFIED FIELD THEORY:

A theory describing how a single set of particles and fields can become (or underlies) 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 other particles involved in a force interaction (e.g., the exchange of virtual photons between charged particles involved in electromagnetic force interactions). Virtual particles do not exist outside of the force interaction exchange. Indeed, if manifested outside the virtual exchange process, they would no longer be virtual and would violate the laws of conservation of energy. Virtual particles do not need to follow the laws of the conservation of energy if the exchange of virtual particles takes place in such a manner that the product of the energy discrepancies (energy imbalance) and the duration of the imbalance remains within Planck's constant as dictated by the Heisenberg uncertainty principle.

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, which is the basis of carbon-14 dating.

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