# Informing Physics: Jacob Bekenstein and the Informational Turn in Theoretical Physics

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## Abstract

In his PhD dissertation in the early 1970s, the Mexican-Israeli theoretical physicist Jacob Bekenstein developed the thermodynamics of black holes using a generalized version of the second law of thermodynamics. This work made it possible for physicists to describe and analyze black holes using information-theoretical concepts. It also helped to transform information theory into a fundamental and foundational concept in theoretical physics. The story of Bekenstein’s work—which was initially opposed by many scientists, including Stephen Hawking—highlights the transformation within physics towards an information-oriented scientific mode of theorizing. This “informational turn” amounted to a mild-mannered revolution within physics, revolutionary without being rebellious.

## Keywords

Black holes thermodynamics black hole thermodynamics information theory information entropy generalized second law information bound quantum information theory Maxwell’s demon John Wheeler Jacob Bekenstein Stephen Hawking## Notes

### Acknowledgements

I would like to thank Professor Jacob Bekenstein for allowing me to meet with him and learn first-hand about his work in black hole thermodynamics, its development and ramifications. I would also like to thank Professor Silvan S. Schweber for the constant support and for suffering through the various drafts. This work was made possible thanks to the support of the Edelstein Center, Hebrew University, Jerusalem.

## References

- 1.The name of the gravitational singularity was popularized by John A. Wheeler. According to Bekenstein,
*Of Gravity, Black Holes and Information*(Rome: Di Renzo Editore, 2006), 24, in a lecture before a large audience. Wheeler was looking for a shorthand version of “completely gravitationally collapsed object,” and picked up the name as a suggestion from “a voice in the audience.” Wheeler gave an account of the first printed use of “black hole” in the Proceedings of the American Association for the Advancement of Science (AAAS) in New York, speaking in front of the Society of Sigma Xi; John Archibald Wheeler,*Geons, Black Holes and Quantum Foam: A Life in Physics*(New York: Norton, 1999), 296. Tired of using the long aforementioned phrase, Wheeler took up the suggested “black hole” from the audience. The term was reported even earlier by Ann Ewing in “‘Black Holes’ in Space,”*Science News Letter*, January 18, 1964, 39. The combination “black hole” was famously used in reference to “The Black Hole of Calcutta,” a dungeon in Fort William, where numerous English and Anglo-Indian soldiers and civilians were held and many died. Leonard Susskind,*The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics*(New York: Little, Brown, 2008), 288–289, describes meeting a fellow “Black Hole Expert” in an English bar, who turned out to be speaking not of his specialty but of the one in India. Also cf. Tom Siegfried, “50 Years Later, It’s Hard to Say Who Named Black Holes,”*Science News Letter*, December 23, 2013, http://ln.is/www.sciencenews.org/R71Q, accessed January 2, 2014. - 2.The Bekensteins moved to Mexico with other families escaping Nazi oppression to a country with relatively lax immigration laws and possibilities of prolonged temporary visits;
*cf.*Adina Cimet,*Ashkenazi Jews in Mexico: Ideologies in the Structuring of a Community*(Albany, NY: SUNY Press, 1997), 13, 22, 112. The Bekensteins and many other families found a temporary haven there, though their final destination was New York. This was reached, however, with great effort. Jacob’s father made his way to the US first illegally—and was even arrested—eventually securing passage for the rest of the family.Google Scholar - 3.The Unified Honors Program (still in place) condensed the required courses in a way that forced Bekenstein to take the second part of the electromagnetic theory course, given by David Stoler, before the first. This made his first acquaintance with Green’s functions very challenging.Google Scholar
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*Of Gravity, Black Holes and Information*(ref. 1) 30–31. Wheeler tells the story a little differently, with Bekenstein coming up with the idea and himself coining the “No-Hair Theorem,” which Feynman, his older student, found in poor taste. John Archibald Wheeler, “Feynman and Jacob Bekenstein,” accessed June 21, 2012, http://www.webofstories.com/play/9549. - 20.“The Wheeler demon hides information in a black hole. More precisely, it throws there the entropy which signaled some process whereby information in a physical system was lost through mixing with environment. Effectively it hides information. Of course nowadays when we know that the black hole will eventually evaporate we can think of the whole process as an erasure.” J. Bekenstein to author, July 15, 2011.Google Scholar
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*Zeitschrift für Physik***53**(1929), 840–856. Szilard conjectured that the entropy cost of sorting lies in acquiring the information. Later, Bennett showed that the process of manipulating information is reversible and that the core of the entropy cost was—counterintuitively—in the erasure: Charles H. Bennett, “Logical Reversibility of Computation,”*IBM Journal of Research and Development***17**(1973), 525–32.Google Scholar - 36.Bekenstein, “The Limits of Information” (ref. 26), 110–1; Harvey Leff and Andrew F. Rex, eds.,
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*Physical Review D***9**(1974), 3292–300. If*P*is the probability of a given alphabetical occurrence that is not foreseeable (expressed mathematically as a binary configuration, a register of bits*x*_{i}), Shannon defined the information entropy as*H(x)*= –*∑*_{i}*P(x*_{i}*) ln (P(x*_{i}*))*; by comparison, Boltzmann defined entropy as*S*= –*k ∑*_{i}*P*_{i}*ln (P*_{i}*)*where*P*_{i}represents the possible physical configurations and*k*is Boltzmann’s constant. In later expositions of black hole entropy, this homology is more pronounced than in Bekenstein’s dissertation, when such a connection via the informational context was not yet intuitive for other physicists.Google Scholar - 40.Ibid.Google Scholar
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*Lonely Hearts of the Cosmos: The Scientific Quest for the Secret of the Universe*(New York: HarperCollins, 1991), 107, 112; Michael White and John R. Gribbin,*Stephen Hawking: A Life in Science*(Washington, DC: Joseph Henry Press, 2002), 124–5. For Hawking’s acceptance, see Stephen W. Hawking,*A Brief History of Time: From the Big Bang to Black Holes*(New York: Bantam Books, 1988), 99. For the trivialization of Bekenstein’s “basically correct” idea, see Stephen W. Hawking,*Black Holes And Baby Universes And Other Essays*(New York: Bantam Books, 1994), 105.Google Scholar - 59.Bardeen, Carter, and Hawking, “The Four Laws of Black Hole Mechanics” (ref. 57).Google Scholar
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*The Black Hole War*(ref. 1), 438.Google Scholar - 73.This happened in the mansion of physics enthusiast and motivational seminar guru Jack Rosenberg, where the EST (Erhard Seminars Training, named after his lucrative self-help programs) conference/workshop was held in San Francisco, 1983. The participants included such outstanding theorists as Frank Wilczek, Murray Gell-Mann, Sheldon Glashow, Dave Finkelstein, Savas Dimopoulos, Gerard ‘t Hooft, Stephen Hawking, and Leonard Susskind. Hawking, through his translator (due to his then unassisted but deteriorating speech) Martin Rocek, conveyed the prospect of total information annihilation (ibid., 17–20).Google Scholar
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*Physical Review Letters*. A second version was published in the*Physical Review*: Jacob D. Bekenstein, “Communication and Energy,”*Physical Review***A****37**(1988), 3437–49.Google Scholar - 86.Two complementary research agendas connect the many disciplines involved in quantum information: 1) the applicability of information and computation theories (transmission, compression, cryptography, quantum computation) in a quantum setting; 2) the formulation of quantum mechanics in information theoretical terms, with such no-go theorems (such as the no-cloning theorem, the no deleting theorem) and bounds such as the Holevo bound on the amount of information that can be known about a quantum system. See Michael A. Nielsen and Isaac L. Chuang,
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