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Relativity, Cosmology, and Time

Black Hole Information Paradox (2018 Edition)

Black Hole Information Paradox Before getting to the essential point of whether black hole destroys information or not, it is necessary to clarify the meaning of information (Figure 09xaa). According to Leonard Susskind, who played a principle role in the debate, entropy is hidden information. This view considers the basic units (or bits) of information to be the microscopic particles, which can be atoms, elementary particles, or down to the smallest unit the size of Planck length (~ 10-33cm). They are hidden because its existence is not known to us. Once we are aware of its presence (such as an electron in a collision experiment), it becomes information, and generates events that we can keep track of. The information is said to be conserved because we can always recover the original event by time reversal operations (at least in theory, which asserts that the laws of physics are the same in both forward and backward time directions, the "Second Law of Thermodynamics" notwithstanding because it is actually applicable to one or at most few particles).

Figure 09xaa Black Hole Information Paradox

Such explanation in layman's language is rather confusing, it is impossible to follow the arguments for the paradox if it is taken literally. Here's the clarification involving mathematical definitions of :
See "Short-cut to the Introduction of Quantum Theory" from unitary operator to non-relativistic quantum mechanics and quantum field theory.

The Paradox - Since a black hole is characterized only by its mass, angular momentum (for a rotating one), and electric charge (if it contains any), the "No Hair theorem" (Figure 09xd2) dictates that all other information (called "hair") "disappears" behind the event horizon and is permanently inaccessible to external observers. It is argued that the event horizon acts like a measuring device to collapse
No-hair Theorem the superposition in the decoherent process. If that's the case, there would be no problem with the loss of information, because the superposition is terminated normally. The paradox is about the existence of the "measuring device" - there is none at the event horizon according to general relativity. Or else the superposition is somehow trapped inside the black hole, for which plenty of opinions are proposed about its fate - whether it is lost forever or can be recovered eventually.

Figure 09xd2 No-hair Theorem [view large image]

See "Black Hole Information Paradox" for further detail; and the history plus various bizarre proposals in the image below from "New Scientist".

See 2021 perspective by Paul Davies in "The black hole paradox that thwarts our understanding of reality".

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