page_title: Black hole information paradox
section_title: Hawking radiation
hierarchical_section_title: Black hole information paradox / Hawking radiation
caption_attribution_description: English: A Penrose diagram of a black hole which forms, and then completely evaporates away due to Hawking radiation. This illustrates the black hole information paradox.
context_page_description: The black hole information paradox is a puzzle resulting from the combination of quantum mechanics and general relativity. Calculations suggest that physical information could permanently disappear in a black hole, allowing many physical states to devolve into the same state. This is controversial because it violates a core precept of modern physics—that in principle the value of a wave function of a physical system at one point in time should determine its value at any other time. A fundamental postulate of the Copenhagen interpretation of quantum mechanics is that complete information about a system is encoded in its wave function up to when the wave function collapses. The evolution of the wave function is determined by a unitary operator, and unitarity implies that information is conserved in the quantum sense.
  As of November 2019, the paradox may have been resolved, at least for simplified models of gravity.
context_section_description: In 1973–75, Stephen Hawking and Jacob Bekenstein showed that black holes should slowly radiate away energy, which poses a problem. From the no-hair theorem, one would expect the Hawking radiation to be completely independent of the material entering the black hole. Nevertheless, if the material entering the black hole were a pure quantum state, the transformation of that state into the mixed state of Hawking radiation would destroy information about the original quantum state. This violates Liouville's theorem and presents a physical paradox.
  Hawking remained convinced that the equations of black-hole thermodynamics, together with the no-hair theorem, led to the conclusion that quantum information may be destroyed. This annoyed many physicists, notably John Preskill, who in 1997 bet Hawking and Kip Thorne that information was not lost in black holes. The implications that Hawking had opened led to a "battle" where Leonard Susskind and Gerard 't Hooft publicly 'declared war' on Hawking's solution, with Susskind publishing a popular book, The Black Hole War, about the debate in 2008. (The book carefully notes that the 'war' was purely a scientific one, and that at a personal level, the participants remained friends.) The solution to the problem that concluded the battle is the holographic principle, which was first proposed by 't Hooft but was given a precise string theory interpretation by Susskind. With this, "Susskind quashes Hawking in quarrel over quantum quandary".
  There are various ideas about how the paradox is solved. Since the 1997 proposal of the AdS/CFT correspondence, the predominant belief among physicists is that information is preserved and that Hawking radiation is not precisely thermal but receives quantum corrections that encode information about the black hole's interior. This viewpoint received further support in 2019 when researchers amended the computation of the entropy of the Hawking radiation in certain models, and showed that the radiation is in fact dual to the black hole interior at late times. Other possibilities include the information being contained in a Planckian remnant left over at the end of Hawking radiation or a modification of the laws of quantum mechanics to allow for non-unitary time evolution.
  In July 2004, Stephen Hawking published a paper presenting a theory that quantum perturbations of the event horizon could allow information to escape from a black hole, which would resolve the information paradox. His argument assumes the unitarity of the AdS/CFT correspondence which implies that an AdS black hole that is dual to a thermal conformal field theory. When announcing his result, Hawking also conceded the 1997 bet, paying Preskill with a baseball encyclopedia "from which information can be retrieved at will."
  According to Roger Penrose, loss of unitarity in quantum systems is not a problem: quantum measurements are by themselves already non-unitary. Penrose claims that quantum systems will in fact no longer evolve unitarily as soon as gravitation comes into play, precisely as in black holes. The Conformal Cyclic Cosmology advocated by Penrose critically depends on the condition that information is in fact lost in black holes. This new cosmological model might in the future be tested experimentally by detailed analysis of the cosmic microwave background radiation (CMB): if true, the CMB should exhibit circular patterns with slightly lower or slightly higher temperatures.   In November 2010, Penrose and V. G. Gurzadyan announced they had found evidence of such circular patterns, in data from the Wilkinson Microwave Anisotropy Probe (WMAP) corroborated by data from the BOOMERanG experiment.  The significance of the findings was subsequently debated by others.
caption: The Penrose diagram of a black hole which forms, and then completely evaporates away. Time shown on vertical axis from bottom to top; space shown on horizontal axis from left (radius zero) to right (growing radius).
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