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The Quantum Quandary: Unifying Quantum Field Theory and General Relativity -
Two theories define modern physics. Quantum Field Theory describes the properties and interactions of elementary particles, and every experiment to date has confirmed its quantum view of nature on atomic scales. General relativity, on the other hand, amounts to a theory of gravity—the distortion of space by mass. Every observation to date has confirmed its view of nature on astronomic mass scales. These two theories are not just the obscure musings of theoretical physicists. Both models are entirely functional and have found application in technologies ranging from global positioning systems (GPS) to lasers to microwave ovens. The only cause for hesitation in evaluating the theories is that, in truth, they present opposing views formed upon different axioms. Hear the dilemma that gives physicists restless nights: “We don’t yet have a theory of quantum gravity.” The physicist’s challenge, thus, is to unify the theories of quantum field theory and general relativity.
The Twin Champions of the Twentieth Century
The triumph of nineteenth century thinking in physics was “the field”—a function defined precisely over all space. The concept of the gravitational field, for example, allows us to predict the gravitational force acting on a body at any point in space. Similarly, Maxwell’s field equations provide a working knowledge of electric and magnetic phenomena. As the nineteenth century concluded, however, the field theories could still not account for certain phenomena, such as radiation.
Classical mechanics with its field theories was not incorrect, but rather incomplete. As such, a new theory was needed to explain radiation and atomic structure—a theory that burgeoned into the field of quantum mechanics. Thus, the protagonist of physics was no longer a discrete particle in the classical sense but a wave function, which gives the probability distribution of a particle’s position over all space. In order to make successful field theories fit into the new quantum framework, physicists would have to “quantize” each force formerly modeled as a field—that is, reformulate them using probability. By the 1970s they were successful, and this new descrďption of elementary particle dynamics, free from the classical field theories, was entitled Quantum Field Theory.
In the meantime, Einstein was thinking big. In 1917, he introduced another field theory— general relativity—which describes interactions of bodies on astronomical scales. This field theory did not describe a property in space, such as the force exerted on a positive charge at a given point, but rather a property of space—in space-time. This difficult concept can be visualized through its two-dimensional analog. If prior field theories, such as that of the electromagnetic field, provided the value of the electric field at a given point on a page, then general relativity would describe the curve of the page itself. This same mathematics generalizes to higher dimensions in which the term curvature describes the distortion of space by mass. Einstein’s revolutionary idea has been verified consistently by observation.
The Missing Link/ Despite its success, the theory of general relativity fails to take into account probability and uncertainty, which are the foundation of Quantum Field Theory. The distortion of space that general relativity describes references a point mass with precise coordinates rather than a wave function defined over all space. Equivalently, the standard model fails to incorporate the revolutionary axiom of general relativity: mass distorts space.
When physicists try to quantize gravity with the hope of unifying the two theories, they run up against some heavy obstacles. Unlike electromagnetism, the nuclear strong force, and the nuclear weak force, gravity does not act in space—it is an act of space. “It’s like having the rug pulled out from under us,” explains Vincent Moncrief, professor of physics and mathematics and instructor of a graduate class on general relativity. “Other forces were quantized in the arena, but with gravity you are forced to quantize the arena itself.” General relativity makes reference to a definite position that is permissible on macroscopic scales but forbidden on small scales. If a mass distorts space but the mass is not “located” anywhere, then things get tricky. While negligible under most conditions, the inconsistency between general relativity and Quantum Field Theory becomes glaring at high energy-densities. Thus, the stage is set for a dramatic revolution in physics.
Some theorists preserve the hope that gravity will be integrated into the Standard Model, which characterizes forces by their exchange particles—photons, gluons, and bosons. Since gravity is a type of force, it may have an exchange particle as well. “Of course physicists are very resourceful. We call [the particle] the graviton. That’s the easy part—naming it,” explains Charles Baltay, professor of physics and instructor of a seminar on the problems of unification. But to say that little is known about the graviton would be an understatement—it may not even be a sensible construct.
An alternative approach to this problem is to build a theory on a new foundation, which would support both general relativity and Quantum Field Theory as limiting cases. These include string theory, loop gravity, and several other candidates. String theory was first proposed as a potential unifier in 1974, and theorists are still trying to flesh it out. Although plentiful in startling premises, such as the existence of twenty-six dimensions beyond the ordinary four, the theory has yet to make a prediction of natural phenomena. Among its promises, however, is the theoretical derivation of the mass of the electron, which is today purely based on empirical measurement.
Diagnosing the Elements
At present, theorists need some hints as experimentalists are scrambling to find flaws in either of the theories, any departure from which would lend direction to the pursuit of unification. “The problem with the standard model,” explains Richard Easther, professor of physics and member of the high energy particle physics group, “is that we know it works.” So far, at least. The Large Hadron Collider (LHC) at CERN, in Switzerland, is scheduled for operation in 2007 and will test the standard model at higher energies than ever before.
Quieter experiments by David DeMille, professor of experimental atomic physics, and colleagues here at Yale are also looking for hints about the variations in electron structure predicted by some Grand Unified Theories (GUTs). Under the Standard Model, the electron itself is predicted to carry a small electric dipole moment—on the order of 10-40 (e.cm), which is beyond the limit of experimental detection. Extensions of the Standard Model predict an electric dipole moment some nine orders of magnitude larger, which places it within the range of the most sensitive experiments. Measuring the dipole moment requires large electric fields, and the DeMille group is attempting to use the inter-atomic electric fields of molecules to detect the dipole moment. These inter-atomic fields are five orders of magnitude greater than any field produced by macroscopic techniques. If the group still cannot detect an electric dipole moment, they will have eliminated many contenders for the unifying theory and many extensions of the standard model. If they do find the dipole moment, however, then they will have encountered a phenomenon outside of the canon of contemporary thinking.
Baltay is engaged in an attempt to find deviations from general relativity by conducting a survey of vast numbers of gravitationally lensed quasars. Gravitational lensing is a consequence of general relativity in which the distortion of space causes light to bend around an object, for example a galaxy or quasar. This effect, however, has only been confirmed in small samples. Baltay’s collaborative group, Quasar Equatorial Survey Team (QUEST), is developing technology that will observe 600,000 quasars, of which a hundred or so will exhibit gravitational lensing. Such resolution could reveal deviations from general relativity previously obscured by less thorough observation.
While Baltay searches for defects, one discovery from the 1990s—the outward acceleration of the universe—exposes the unsettling rift between the two theories. Overtly, this acceleration is not forbidden by general relativity; in fact, it is explicitly permitted. Although masses attract, the universe en masse is accelerating outward. Today the outward acceleration is thought to be evidence of a substance called dark energy whose only known property is that it causes this acceleration.
While particle theorists are eager to accommodate for some phenomena outside the Standard Model, such as a higher electron dipole moment, the existence of dark energy came as a real surprise. “No one expected it to be there, and there is no theoretical model for it that seems at all satisfactory,” DeMille notes. “It has been a very long time since something so obviously fundamental was observed, without any theoretical anticipation of its existence.”
The Challenge of Unification
Even if experimentalists successfully find flaws in either theory, it is unlikely that either general relativity or the Standard Model will ever fall by the wayside. A GPS receiver, such as the ones installed in BMWs, testifies to the practical utility of both general relativity and quantum mechanics. Without corrections given by general relativity, the GPS receiver would be limited to a precision of about one hundred feet. Without the guidance of quantum mechanics, the electronics used to process the signal could not have been conceived or constructed. Neither theory was “cooked” to explain GPS orbits or microprocessors, but applications of both theories abound. If you ever find yourself in a BMW, and the GPS tells you to “go right onto Orange Street” just as you approach an intersection, you are listening to the confirmation of both theories. Both theories reign in their own domain.
As theorists toil to resolve the dissonance between the two theories, the question is whether they already have the tools to do so. “There have been times in the history of physics when we are confronted with a problem so big that it is not timely to solve it,” notes Thomas Appelquist, Eugene Higgens Professor of Physics. Einstein spent the last thirty years of his life trying to unify the forces. Without knowledge of the weak force, which had not yet been discovered, however, he could not have finished the puzzle. He was still missing pieces.
Unification is the most prominent mystery in physics, and there may be a long way to go before it becomes surmountable. In the meantime, no expansion of physical intuition goes unrewarded with practical applications. The maturation of classical mechanics accompanied the industrial revolution; the maturation of quantum mechanics seeded the information revolution. Without those advances, how could we be brought to such fantastic questions?
courtesy ~ ANTHONY GARVAN.
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--Last edited by saucer on 2007-01-03 00:16:07 --
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