The **black hole information paradox**[1] 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.[2][3] 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.

There are two main principles in play:[4]

The combination of the two means that information must always be preserved.

Starting in the mid-1970s, Stephen Hawking and Jacob Bekenstein put forward theoretical arguments based on general relativity and quantum field theory that not only appeared to be inconsistent with information conservation but which did not account for the information loss and which stated no reason for it. Specifically, Hawking's calculations[5] indicated that black hole evaporation via Hawking radiation does not preserve information. Today, many physicists believe that the holographic principle (specifically the AdS/CFT duality) demonstrates that Hawking's conclusion was incorrect, and that information is in fact preserved.[6] In 2004 Hawking himself conceded a bet he had made, agreeing that black hole evaporation does in fact preserve information.

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, information being defined as the difference between coarse grained (thermal) entropy and fine grained (quantum, von Neumann) entropy. This violates the law of conservation of information which corresponds to Liouville's theorem in classical physics and thus presents a physical paradox (see e.g. [7]).

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.[8]) 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".[9]