**G**reat science sometimes produces a legacy that outstrips not only the imagination of its practitioners but also their intentions. A case in point is the early development of the theory of black holes and, above all, the role played in it by Albert Einstein. In 1939 Einstein published a paper in the journal *Annals of Mathematics* with the daunting title On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses. With it, Einstein sought to prove that black holes--celestial objects so dense that their gravity prevents even light from escaping--were impossible.

The irony is that, to make his case, he used his own general theory of relativity and gravitation, published in 1916--the very theory that is now used to argue that black holes are not only possible but, for many astronomical objects, inevitable. Indeed, a few months after Einstein's rejection of black holes appeared--and with no reference to it--J. Robert Oppenheimer and his student Hartland S. Snyder published a paper entitled On Continued Gravitational Contraction. That work used Einstein's general theory of relativity to show, for the first time in the context of modern physics, how black holes could form.

Perhaps even more ironically, the modern study of black holes, and more generally that of collapsing stars, builds on a completely different aspect of Einstein's legacy--namely, his invention of quantum-statistical mechanics. Without the effects predicted by quantum statistics, every astronomical object would eventually collapse into a black hole, yielding a universe that would bear no resemblance to the one we actually live in.

**Bose, Einstein and Statistics**

EINSTEIN'S CREATION of quantum statistics was inspired by a letter he received in June 1924 from a then unknown young Indian physicist named Satyendra Nath Bose. Along with Bose's letter came a manuscript that had already been rejected by one British scientific publication. After reading the manuscript, Einstein translated it himself into German and arranged to have it published in the prestigious journal *Zeitschrift fr Physik*.

Why did Einstein think that this manuscript was so important? For two decades he had been struggling with the nature of electromagnetic radiation--especially the radiation trapped inside a heated container that attains the same temperature as its walls. At the start of the 20th century German physicist Max Planck had discovered the mathematical function that describes how the various wavelengths, or colors, of this black body radiation vary in intensity. It turns out that the form of this spectrum does not depend on the material of the container walls. Only the temperature of the radiation matters. (A striking example of black-body radiation is the photons left over from the big bang, in which case the entire universe is the container. The temperature of these photons has been measured at 2.726 0.002 kelvins.)

Somewhat serendipitously, Bose had worked out the statistical mechanics of black-body radiation--that is, he derived the Planck law from a mathematical, quantum-mechanical perspective. That outcome caught Einstein's attention. But being Einstein, he took the matter a step further. He used the same methods to examine the statistical mechanics of a gas of massive molecules obeying the same kinds of rules that Bose had used for the photons. He derived the analogue of the Planck law for this case and noticed something absolutely remarkable. If one cools the gas of particles obeying so-called Bose-Einstein statistics, then at a certain critical temperature all the molecules suddenly collect themselves into a degenerate, or single, state. That state is now known as Bose-Einstein condensation (although Bose had nothing to do with it).

An interesting example is a gas made up of the common isotope helium 4, whose nucleus consists of two protons and two neutrons. At a temperature of 2.18 kelvins, this gas turns into a liquid that has the most uncanny properties one can imagine, including frictionless ow (that is, superuidity). More than a decade ago U.S. researchers accomplished the difficult task of cooling other kinds of atoms to several billionths of a kelvin to achieve a Bose-Einstein condensate.