Black Hole Information Paradox

The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could permanently disappear in a black hole, allowing many physical states to evolve into the same state. This is controversial because it violates a commonly assumed tenet of science—that in principle complete information about a physical system at one point in time should determine its state at any other time. A fundamental postulate of quantum mechanics is that complete information about a system is encoded in its wave function. 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: quantum determinism, and reversibility. Quantum determinism means that given a present wave function, its future changes are uniquely determined by the evolution operator. Reversibility refers to the fact that the evolution operator has an inverse, meaning that the past wave functions are similarly unique. The combination of the two means that information must always be preserved.

Starting in the mid 1970’s, Stephen Hawking and Jacob Bekenstein put forward theoretical arguments based on general relativity and quantum field theory that appeared to be inconsistent with information conservation. Specifically, Hawking’s calculations 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. In 2004 Hawking himself conceded a bet he had made, agreeing that black hole evaporation does in fact preserve information.