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What is the current status on black hole information paradox?

Physics Asked on July 12, 2021

I assume information must be somehow preserved either by time dilation so object can take its time to reach the horizon and hawking radiation slowly kicks the information out as real particle as well as the infamous firewall to conveniently block information from entering beyond the boundary of no return, then there is an even bizarre one which analogous to a concept of water wave suggesting general relativity is not fundamental. When the wave seemingly disappeared, the water molecules are still present but moves in a much more random fashion so I like to know where are we now?

2 Answers

I do not think there is a satisfactory resolution in "mainstream physics", which is to say physics published in reputable journals. There are, instead, differing published opinions and approaches. This is my take on it, from my book, The Large and the Small

In the absence of measurement, there is no change in information, and consequently there is no change in the probabilities predicted in quantum theory. This requirement, applied to the evolution of quantum states, is described mathematically by unitarity. Hawking radiation then generates a paradox because the particles are entangled. A measurement of the outgoing particle, determining that it is, for example, an electron, must change the state of the ingoing particle, in this case ensuring that it is a positron. But the state of the ingoing particle has been destroyed by the structure of the black hole, which, according to the no-hair conjecture, preserves information on mass, charge and angular momentum, but not information on particle type.

Thus, according to quantum theory, if, due to random variations, an excess of a particular particle type were emitted during some phase of the life of the black hole, then an excess of the corresponding antiparticle should be emitted at other phases, to restore an exact balance. But according to the treatment of Hawking radiation, the emission of different particle types is always completely random, and unrelated to emission at any other time. The information paradox is exacerbated by the fact that, an observer falling through the event horizon sees nothing unusual at the horizon; he observes no change to the state of either particle.

The black hole information paradox divided physicists. Some, like Hawking, argued for the no-hair conjecture, that the information is truly destroyed by the black hole and that quantum theory needs revision. Others, like John Preskill, a quantum physicist at CalTec, stuck by quantum mechanics, finding no sensible way of changing it. In 1997 Preskill made a public bet with Hawking, the stake being an encyclopaedia of the winner’s choice. That year, Juan Maldacena, a physicist at Harvard, showed using string theory that information can be preserved on a boundary. A few years later Donald Marolf showed that this should be a general property of theories of quantum gravity, irrespective of string theory. Hawking accepted these arguments and in 2004 he published a paper theorising that quantum perturbations at the event horizon could allow the escape of information. He paid his bet, giving Preskill a baseball encyclopaedia “from which information can be retrieved at will”.

It was thought that Maldacena’s model had resolved the black hole information paradox, but in 2012 it was reanalysed by Ahmed Almheiri and James Sully, students of Joseph Polchinski, and Marolf at the University of California, Santa Barbara. They found that the entanglement issues were not resolved. Any emitted particle had to be entangled, not just with its pair but with all other Hawking radiation from the hole, but quantum mechanics forbids a quantum system from being entangled with more than one independent system, a result known as “the monogamy of entanglement”.

Reluctant to abandon quantum mechanics, the group sought to break the entanglement between a particle and its infalling pair. To do this they introduced a firewall at the event horizon, violating the equivalence principle at that point. “For us, firewalls seem like the least crazy option”, said Marolf. Others did not agree. Ted Jacobson, at the University of Maryland in College Park said “It was outrageous to claim that giving up Einstein’s equivalence principle is the best option”. Raphael Bousso, a string theorist at the University of California, Berkeley, agreed, saying “A firewall simply can’t appear in empty space, any more than a brick wall can suddenly appear in an empty field and smack you in the face” (assuming, of course, that empty space can suddenly appear in a collapsing star!!). Perhaps the only conclusion is that there is no firm conclusion. Bousso says of the information paradox, “It essentially pits quantum mechanics against general relativity, without giving us any clues as to which direction to go next”, while Don Page, of the University of Alberta says, “It’s a really beautiful argument proving that there’s something inconsistent in our thinking about black holes”.

It is far from clear that a firewall is a solution to the information paradox because entanglement of quantum states is not related to energy. It is certain that a black hole contains a singularity, where the equivalence principle breaks down. It follows that it is not possible to use the equivalence principle to prove that the event horizon itself is not the singularity, where matter congregates at indefinitely great density. In this case, both the Pauli exclusion principle and the uncertainty principle ensure that indefinitely high energies would be reached at the singularity. Then a black hole has an ultra-hot centre, indistinguishable from a firewall at the event horizon. In this case, the solution of the information paradox may be that unitarity is not violated because particles can only fall to the event horizon, not through it.

Answered by Charles Francis on July 12, 2021

If we are ungenerous, the OP's question is a duplicate.

More generous, it should be reformatted along the lines of, since this question was asked, has anything changed re BH information paradox?

Answer: Nothing has significantly changed since 2018.

Opinion: In the 2018 SE answer, there is a vague allusion to the solution being information that comes out in some version of the Hawkings radiation. IMO, this is the most compelling recent theory (firewalls are laughable), and its not that hard to understand

Hawking's famous black hole radiation is an example of so-called spontaneous emission of radiation, but it is only half of the story. There must also be the possibility of stimulated emission -– the process that puts the S in LASER. This is good, because otherwise we violate the no-quantum cloning theorem.

Answered by Mr Anderson on July 12, 2021

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