Darkness visible

Natural History, Feb, 1997 by Neil de Grasse Tyson

Using curved space as a lens, astrophysicists take the measure of unseen matter.

One of the most mind-bending discoveries of twentieth-century astrophysics--predicted in 1911 by Albert Einstein and incorporated into his general theory of relativity in 1915--is that matter curves the fabric of space. More recently, the phenomenon has proved to have applications that are indispensable for probing dark matter in the universe.

But why should anybody believe that matter curves space? Support for the idea does not come from wishful thinking but from experiment. In what is now considered a classic test of general relativity, one can take advantage of a total solar eclipse to prove that starlight is bent in the curved space of the Sun's gravity. This measurement can be made only during an eclipse because, of course, stars are not otherwise visible from Earth during the daytime.

Contrary to popular belief, total solar eclipses are not rare. On average, one takes place somewhere on Earth's surface every one and a half years, although a particular location can go several hundred years without one. The perceived paucity derives from the narrowness of the eclipse path across Earth's surface. Opportunities to test Einstein's idea came immediately with the solar eclipses of 1916 and 1918, but both of these were unfavorable for several reasons, including a dearth of bright stars near the Sun's edge during totality. In addition, the First World War was raging, hindering the dissemination and digestion of general relativity, and making a safe and reliable eclipse expedition unfeasible.

By 1919, however, all was quiet, and the English astrophysicist Arthur Stanley Eddington mounted well-publicized dual expeditions (as a hedge against bad weather) to view the May 29 total solar eclipse from South America and from Africa. Eddington's goal was simple: to map the precise positions of stars in the vicinity of the Sun. The complete experiment, however, required that he map the same star field six months later, when Earth was on the other side of its orbit and the Sun's gravity safely out of the way. Only when the two images were compared could he reliably deduce whether the stellar positions had indeed changed.

To the world's astonishment, Eddington found a shift in stellar positions that agreed with Einstein's prediction of 1.75 arc seconds to within experimental accuracy. (The shift is an angle smaller than the thickness of a dime when viewed over the full length of a football field.) Einstein became an immediate celebrity. Actually, with hindsight we could have predicted that a light path would bend in response to gravity, using simple Newtonian laws and the equivalence of mass and energy. Isaac Newton himself had suspected such a thing. At the end of the second edition (1717) of his seminal treatise on optics, Newton presents the reader with some unsolved mysteries:

I shall conclude with proposing only some

Queries, [for] a further search to be made

by others.

Query 1. Do not bodies act upon light at

a distance, and by their action bend its

rays; and is not this action strongest at the

least distance?

But Newton's equations alone will give you the wrong answer--only half of what was predicted by Einstein's equations. Why? In relativity theory, where space and time are conjoined, time itself can also be thought of as bending in the presence of gravity--a concept for which there is no analogue in pre-twentieth-century physics. Light therefore takes slightly longer to pass the Sun than it otherwise would, which serves to increase the angle of deflection. We should thus speak not of the curvature of space but of the curvature of space-time.

The geometric ingredients are simple: all you need is an observer, a distant source of light, and a massive object that falls somewhere along, or close to, the observer's line of sight. In 1936, Einstein imagined a case in which two stars were perfectly aligned, with the background star serving as the light source and the foreground star serving as the source of curvature. In this layout, light paths can bend not only around to one side but also around to the other side. They can also bend above and below. Indeed, since space-time is curved everywhere in the foreground star's vicinity, perfect alignment will force the light to fan out into a complete "Einstein ring."

Perfect alignments on the sky are rare, but the varieties of light sources and gravity sources that produce visible bending are practically limitless. Because the action of curved space-time upon light greatly resembles the action of ordinary optical lenses, the phenomenon is known as gravitational lensing. A colleague of mine has even forged a career in mathematics by exploring the abstract theory of gravitational lenses--an elegant field in which one seeks to describe all possible lenses, alone and in combination, regardless of whether an example in the real universe is known or will ever be found. But there's no need to be jealous. Even if we tally only the more common lens configurations, we retain a veritable fun house of images.