news & views

JACOB BEKENSTEIN Quantum pioneer Jacob Bekenstein (pictured), the father of gedanken experiment, Bekenstein felt he thermodynamics, passed away had to go further. What if the cup of tea in August. His insight, that black holes had so much that when it was should have an entropy proportional to thrown into a black hole, the increase in their area and a temperature proportional black hole entropy was not enough to to their surface gravity, is one of the most compensate for the decrease in entropy important discoveries in modern physics. due to its disappearance? Bekenstein

It continues to mystify researchers and BEKENSTEIN © YEHONADAV thus proposed an entropy bound given shapes our current quest for a quantum by a system’s energy and radius, arguing theory of gravity. that ordinary matter such as teacups This celebrated insight came out of a cannot have too much entropy. If an object famous conversation between Bekenstein violated his entropy bound, it could be and his PhD advisor, John Wheeler. A hot thrown into a black hole and the second cup of tea has entropy, as its macroscopic law of thermodynamics would be violated. description admits many possible This prompted a debate between microstates. A black hole, on the other Bekenstein and two other students of hand, has no entropy according to general Wheeler, Bill Unruh and Bob Wald. The relativity, being uniquely described by debate elegantly elucidated the intricacies of macroscopic quantities such as , powers by considering processes changing black hole thermodynamics, with Unruh and angular momentum and electric charge. the black hole area by a minimal amount. Wald arguing that the second law was saved This, Bekenstein dubbed ‘the no-hair He was even able to come remarkably close by the buoyancy force produced by black theorem’. But Wheeler was puzzled: what to getting the constant of proportionality hole radiation, and Bekenstein pushing for happens, he asked, if I throw the cup of tea right, conjecturing that it must be close his entropy bound. Whereas the outcome into the black hole? Initially, the entropy of to (1/2) ln 2 in natural units. of the debate suggested the entropy bound the system is given by the entropy of the The exact value of 1/4 was determined was not necessary, it is widely believed to cup of tea, but after the tea has fallen into two years later by Hawking, who wanted to hold, and the subject continues to inspire. the black hole, the total entropy is zero prove Bekenstein’s ideas about black hole Bekenstein generally carved out his own because only the black hole is left. The entropy wrong. Instead, Hawking showed path in his research, and was not swayed by second law of thermodynamics says that that black holes radiated at a temperature scientific trends. When it came to explaining the entropy of a closed system can only that behaved just as Bekenstein predicted. why the trajectories of stars in galaxies increase. Has the second law been violated? Using Bekenstein’s first law of black hole deviate from what predicts, Bekenstein’s answer was that the black thermodynamics, this fixed the black hole most scientists took the view that this was hole must have an entropy proportional to entropy as its area divided by four. due to dark matter. Bekenstein instead its area, and that the black hole’s increase Almost forty years on, this extraordinary believed that our theory of gravity required in entropy after absorbing the cup of tea result continues to reverberate. Any modification, a view he advocated in the would more than compensate for the potential theory of quantum gravity should early 1980s along with , decrease in entropy of the Universe due correctly predict the value of the black well before this idea become more popular. to the disappearance of that cup of tea. hole entropy. Indeed, as quantum gravity In 2004, he developed the first relativistic Bekenstein based his insight not only on is not driven by experiment, black hole modification of Newtonian dynamics to the teacup thought experiment, but also thermodynamics remains the only really account for the discrepancy. He explored on a then recently proven theorem by solid piece of information we have in our the idea that the fine-structure constant : the area of a black hole attempts to construct it. and gravitational coupling constant varied can only increase. Bekenstein realized that Likewise, popular insights into quantum over time, developed a quantum model for the non-decreasing of the black hole’s gravity, such as those provided by the black holes, and most recently, developed area was reminiscent of the second law anti-de Sitter/conformal field theory and promoted experiments to probe the of thermodynamics. (AdS/CFT) correspondence and the quantum nature of space–time. What is striking about Bekenstein’s , are directly inspired Despite his radical physical intuition, intuition is that he understood not only by Bekenstein’s insight that the entropy of and the immense influence of his ideas, he that the black hole must have an entropy a gravitating system can scale with its area, was a modest, quiet man, generous with which is a function of its area, but that it whereas for ordinary matter, it tends to scale his time, and more critical of his own work should be proportional to the area itself. with the volume. Since entropy is a measure than that of others. Bekenstein reached these conclusions of information, this could allow information through a number of considerations, about a volume of space–time to be encoded JONATHAN OPPENHEIM including the application of the second law in the boundary of that space–time. Jonathan Oppenheim is in the Department of to two merging black holes (ruling out an Although ascribing entropy to black Physics and Astronomy, University College London, entropy that scales as a power of the area holes appeared to rescue the second London WC1E 6BT, UK. that is less than 1). He dismissed higher law from Wheeler’s famous teacup e-mail: [email protected]

NATURE PHYSICS | VOL 11 | OCTOBER 2015 | www.nature.com/naturephysics 805

© 2015 Macmillan Publishers Limited. All rights reserved