Quantum Gravity
Relativity and quantum theory, the foundations upon which all of modern physics rests, were developed in the first quarter of the twentieth century. Their accuracy in predicting the results of experiment or observation is astounding; the symmetry principles at their core are among the most beautiful and profound concepts in science. The union of these two models of nature in relativistic quantum field theory led to the development of the standard model of elementary particles and their interactions. The standard model is incomplete, however, it lacks a quantum explanation of the gravitational force.
Gravity is the weakest of the four fundamental forces of nature. Although the effects of gravitational force are easily calculated by the classical laws developed by English physicist and mathematician Sir Isaac Newton in his Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) or by the modern relativity physics developed by German-American physicist Albert Einstein (1879-1955), the actual mechanisms of the gravitational force remain elusive.
Almost immediately upon completion of his special theory of relativity in 1905, Einstein realized his work was not yet done. Special relativity allowed only inertial observers, and thus was too restrictive. Any observer, Einstein felt, even an accelerated one, must be free to deduce physical law based on his own observations, and all observers must arrive at the same mathematical structure. By 1915, Einstein published the general theory of relativity. The general theory provides a structure for the geometry of space-time, and, because the effects of acceleration are indistinguishable from those of gravity, a theory of the gravitational force. In general relativity, gravity is a curvature of space-time.
The predictions of general relativity differ, of course, from those of Newtonian gravitational theory, but those differences become significant only for very strong gravitational fields--those produced by astronomical scale masses. General relativity has long been the purview of those physicists, astrophysicists, and cosmologists who regularly deal with such large scales.
From a purely pragmatic point of view it is not necessary to include gravity in the discussion of elementary particles and their interactions. The gravitational interaction between elementary particles is incredibly weak, twenty-nine orders of magnitude smaller than the weak force. At the elementary particle scale space-time is flat, and special relativity suffices. The (specially) relativistic quantum field theories describing all non-gravitational particle interactions, including the electroweak theory of Weinberg and Salam and quantum chromodynamics (the field theory of the strong nuclear force) work extremely well. Regardless, there are two important reasons why a quantum theory of gravity is necessary. The first reason is aesthetic: physicists argue that ours is a quantum universe, and all interactions, at the most fundamental level, must therefore have a quantum description. Quantum physics itself provides a second reason: Heisenberg's uncertainty relations demand that all fields undergo quantum fluctuations.
Consider a region of space in which the gravitational field vanishes. Quantum theory tells us that it is really the average value of the field that is zero; for very brief periods of time, and over very small regions of space, the field strength undulates, and may become relatively quite large. At the so-called Planck scale (10-33 cm), quantum fluctuations in the strength of the gravitational field become comparable to the strength of all other forces, and cannot be ignored. The Planck length is almost unimaginably tiny. Imagine a proton the size of the Milky Way galaxy. On that scale the Planck length would be about four inches. Accordingly, if we wish to understand the Universe at these scales, a quantum theory of gravity is a necessity.
Undulations in gravitational field strength are undulations in the space-time geometry. At the Planck scale, space-time is no longer the smooth, continuous manifold described by general relativity, but rather a frothy, roiling structure, dubbed "space-time foam" by American physicist John A. Wheeler (1911-). The heart of relativity theory, a smooth space-time described by Einstein's equations, is incompatible with the heart of quantum theory which allows uncertainty between physical observables. It is for this reason that all attempts to quantize general relativity have failed. All such theories are non-renormalizable: calculations of physically measurable quantities diverge; they yield infinite answers.
If somehow the behavior of space-time at the Planck scale and below never entered the theory, the divergences could be avoided. This is not possible, though, if the theory contains point particles. They are infinitesimally small, and thus require treatment at an extreme space-time scale. But if the fundamental entities had a finite size, space-time behavior at smaller scales would be irrelevant. String theory, which replaces the fundamental particles with Planck-sized strings, is renormalizable, and for that reason string theory may offer the best hope of yielding a viable quantum theory of gravity.
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