We normally think of black holes as these extremely esoteric objects that warp spacetime so much, that in Einstein's classical general relativity, nothing can escape from them, not even light. In the astrophysical context, black holes either form through the collapse of very massive stars, or at the very dense centers of galaxies (Figure 1 shows the jet emanating from the center of the accretion disk surrounding the black hole in the galaxy M87).

Figure 1. Compact Core of Galaxy M87. Credit: Tod R. Lauer, Sandra M. Faber/NASA.

Until the early 1970s, no one could see any relevance of these curious objects to what one might call everyday physics. All of that changed, however, when the famous physicist John Archibald Wheeler asked his then graduate student, Jacob Bekenstein: "What happens when you pour a cup of tea into a black hole?" The question may sound strange, but it actually addressed a fundamental problem in thermodynamics. According to the second law of thermodynamics, the entropy -- a measure of disorder -- of the universe as a whole, cannot decrease. The entropy of a cup of tea, for instance, where tea particles from a tea bag have already diffused, is higher than that of the original tea bag. However, if the tea is poured into a black hole, then according to classical general relativity, that entropy disappears from the universe. This suggests a way of violating the second law of thermodynamics, since we could drop all of our high-entropy mess into black holes, thereby reducing the entropy of the universe.

After thinking about this for a while, Bekenstein came up with a brilliant idea -- to identify the surface area of a black hole (in the appropriate units) with the black hole's own entropy! The reason was simple, when one throws something (e.g., pours a cup of tea) into a black hole, its surface area *increases*. This suggested that one could preserve the second law of thermodynamics if that increase (now identified as an increase in the black hole's entropy) more than offsets the reduction of entropy by the disappearing tea. Eventually, Bekenstein's idea led to Stephen Hawking's prediction of what is now known as "Hawking radiation" -- the suggestion that in the quantum realm, black holes are not entirely black, they can emit radiation.

In 1981, Bekenstein used that emerging field of black hole thermodynamics to propose an interesting new principle. He found that for *any* system that can be enclosed within a sphere of radius *R*, the ratio of the entropy of the system (expressed in the appropriate units) to its energy cannot exceed a certain value that is proportional to *R*. Remarkably, he then used this new limit to show that one can obtain an upper limit on the number of species of elementary particles -- quarks, leptons, and neutrinos -- which may exist. Specifically, he showed that a few analogous generations are permitted, but more than ten strain credulity.

Most amazingly, however, he demonstrated (by combining his thermodynamic limit with restrictions imposed by causality) that this same principle shows that an *ideal* (but non-parallel) digital computer cannot perform more than 10^{15} elementary arithmetical operations per second! Astonishing, isn't it? The physics of black holes placing limits on the rate at which information can be transferred. Bekenstein's work demonstrated yet again that even the most abstract concepts in physics can find unexpected applications in more familiar subjects.