Black hole information paradox

There are 2 main relevant principles at work in the black hole information paradox: quantum determinism and reversibility.

"The idea behind Hawking radiation, is that the vacuum of empty space, cannot be empty, according to the Heisenberg uncertainty principle. However, there are these quantum fluctuations present. These are virtual particles or particle and anti-particle pairs. The negative energy particle will fall into the black hole, while the positive energy virtual particle, will escape the black hole as Hawking radiation, causing the black hole to lose mass. Hawking radiation is the thermal radiation that black holes are predicted to emit. It is caused by quantum effects. The temperature of the radiation is inversely proportional to the black hole's mass."

It has been demonstrated that there are quantum effects that would cause a black hole to emit black-body radiation at its event horizon. Hawking’s proposal that black holes are evaporating away physical information, will lead to a contradiction in physics. This contradiction is between quantum mechanics and general relativity. Indeed, Stephen Hawking, proposes that black holes are emitting a dim kind of radiation at the event horizon, as a consequence of quantum mechanics. These calculations, appear to suggest that physical information can be permanently lost, at a black hole event horizon. These were calculations that proposed that physical information could permanently disappear in a black hole.

This proposal, that black holes can slowly radiate away energy, possesses as problem. This proposal, in is contradiction to one of the fundamental tenets of quantum mechanics, known as the unitarity postulate of time evolution. According to this postulate, physical information, in the Copenhagen interpretation of quantum mechanics (which has implications such as wave-particle duality and the Heisenberg uncertainty principle), cannot be permanently lost or destroyed, however, the wave-function, that describes the state of a quantum system at a particular stage of time, as a probability amplitude of several different eigenstates or potential outcomes, that are only made certain upon the wave-function collapse, can only evolve from one state to another, in accordance with the Schrodinger equation, which shows how the wave-function of a quantum system will change with time.

This is a Penrose diagram of a black hole. A Penrose diagram depicts the causal relations between different points of spacetime. Time is shown along the vertical direction with space on the horizontal. In this particular Penrose diagram:

the black hole forms
the black hole completely evaporates away
physical information that falls into the black hole will hit the singularity

Black hole (artist depiction)

This was quite the inconsistency between general relativity and quantum mechanics and this contradiction was known as the black hole information paradox. A potential solution to the paradox, will be met in the holographic principle, in particular, the AdS/CFT correspondence, which shows how an AdS black hole, dual to a a collection of particles on a thermal CFT, can evolve in time while preserving the principles of quantum mechanics.

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