The combination of the two means that information must always be preserved. These are the principles of quantum determinism, which means that given a present wave function, its future changes are uniquely determined by the evolution operator and also the principle of reversibility, which refers to the fact that the evolution operator has an inverse, meaning that the past wave functions are similarly unique. The Schrödinger equation obeys two principles that are relevant for the paradox. In quantum mechanics, the evolution of the state is governed by the Schrödinger equation. Taken together these puzzles about black hole evaporation have implications for how gravity and quantum mechanics must be combined, leading to the information paradox remaining an active field of research within quantum gravity.
In recent years, several extensions of the original paradox have been explored. However, views differ as to how precisely Hawking's calculation should be corrected. This means that the predictions of quantum mechanics are correct whereas Hawking's original argument that relied on general relativity must be corrected. It is now generally believed that information is preserved in black-hole evaporation. The evolution of the wave function is determined by a unitary operator, and unitarity implies that the wave function at any instant of time can be used to determine the wave function either in the past or the future. Specifically, in quantum mechanics the state of the system is encoded by its wave function. However, this violates a core precept of both classical and quantum physics-that, in principle, the state of a system at one point in time should determine its value at any other time. Therefore, information about the details of the initial state would be permanently lost. Since many different states can have the same mass, charge and angular momentum this suggests that many initial physical states could evolve into the same final state. Hawking's calculation suggests that the final state of radiation would retain information only about the total mass, electric charge and angular momentum of the initial state. The information paradox appears when one considers a process in which a black hole is formed through a physical process and then evaporates away entirely through Hawking radiation. Hawking also argued that the detailed form of the radiation would be independent of the initial state of the black hole and would depend only on its mass, electric charge and angular momentum. In the 1970s, Stephen Hawking applied the rules of quantum mechanics to such systems and found that an isolated black hole would emit a form of radiation called Hawking radiation.
The theory of general relativity predicts the existence of black holes that are regions of spacetime from which nothing - not even light - can escape. The black hole information paradox is a puzzle that appears when the predictions of quantum mechanics and general relativity are combined. The first image (silhouette or shadow) of a black hole, taken of the supermassive black hole in M87 with the Event Horizon Telescope, released in April 2019.
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