# Notes

## Section 15: The Phenomenon of Gravity

History [of gravity theory]

With the Earth believed to be the center of the universe, gravity did not seem to require much explanation: it was just a force bringing things to a natural place. But with the advent of Copernican astronomy in the 1500s something more was needed. In the early 1600s Galileo noted that the force of gravity seems to depend only on the mass of an object, and not on any of its other features. In 1687 Isaac Newton then suggested a universal inverse square law of gravity between objects. In the 1700s and 1800s all sorts of celestial mechanics was done on the basis of this—with occasional observational anomalies being resolved for example by the discovery of new planets. Starting in the mid-1800s there were attempts to formulate gravity in the same way as electromagnetism—and in 1900 it was for example suggested that gravitational effects might propagate at the speed of light. Following his introduction of relativity theory in 1905, Albert Einstein began to seek a theory of gravity that would fit in with it. Ordinary special relativity has the feature that it assumes that systems behave the same regardless of their overall velocity—but not regardless of their acceleration. In 1907 Einstein then suggested the equivalence principle that gravity always locally has the same effect as an acceleration. (This principle requires only slightly more than Galileo's idea of the equivalence of gravitational and inertial mass, which has now been verified to the 10^-12 level.) But by 1912 Einstein realized that if the effective laws of physics were somehow to remain the same in systems with different accelerations (or in different gravitational fields) then this would require a change in their perceived geometry. And building on ideas of differential geometry and tensor calculus from the late 1800s Einstein then began to formulate the concept that gravity is associated with curvature of space. In the late 1800s Ernst Mach had argued that phenomena like acceleration and rotation could ultimately be defined only relative to matter in the universe. And partly on this basis Einstein used the idea that curvature in space must be like a field produced by matter—leading eventually to his formulation in 1915 of the standard Einstein equations for general relativity. An immediate prediction of these was a deviation from the inverse square law, explaining an observed precession in the orbit of Mercury. After a dramatic verification in 1919 of predicted bending of light by the Sun, general relativity began to be widely accepted. In the 1920s expansion of the universe was discovered, and this was seen to be consistent with general relativity. In the 1940s study of the evolution of stars then led to discussion of what became known as black holes. But for the most part general relativity was still viewed as being highly elegant though of little practical relevance. In the 1960s, however, more work began to be done on it. The discovery of the cosmic microwave background in 1965 led to increasing interest in cosmology. Precision tests—particularly with spacecraft—were designed. In calculations it was sometimes difficult to tell what was a genuine effect, and what was just a feature of the particular coordinates used. But a variety of increasingly abstract mathematical methods were developed, leading notably to general theorems about inevitability of singularities. Detailed calculations tended to require complicated symbolic tensor manipulation (with some associated problems being NP-complete), but with the development of computer algebra this gradually became more feasible—and by the mid-1970s approximate numerical methods were also being used. Various alternative formulations of general relativity were proposed, based for example on tetrads, spinors and twistors (and more recently on connection, loop and non-commutative geometry methods)—but none led to any great simplification. Meanwhile, there continued to be ever more accurate experimental tests of general relativity in the solar system—and at least in the weak gravitational fields available there (with metrics differing from the identity by at most one part in 10^6), all have worked out to around the 10^-3 level. Starting in the 1960s, more and more ambitious gravitational wave detectors have been built—although none as yet have actually observed anything. Measurements done on a binary pulsar system are nevertheless consistent at a 10^-3 level with the emission of gravitational radiation in a fairly strong gravitational field at the rate implied by general relativity. And since the 1980s there has been increasing conviction that at least indirect effects of black holes associated with very strong gravitational fields are being observed.

Over the years, some variants of general relativity have been proposed. At least when formulated in terms of tensors, none have quite the simplicity of the original theory—but some lead to rather different predictions, such as an absence of singularities like black holes. Ever since quantum theory began in the early 1900s there has been discussion of quantum gravity—and almost every major method developed for handling other quantum phenomena has been tried on gravity. Starting in the 1980s a variety of methods more specific to quantum gravity were also pursued, but none have yet had convincing success. (See page 1054.)

From Stephen Wolfram: A New Kind of Science [citation]