Thursday, November 25, 2021

What is the Black Hole Information Paradox?

Black hole information paradox is a puzzle resulting from the combination of quantum mechanics and general relativity. The combination of the two means that information must always be preserved.

Calculations suggest that physical information could permanently disappear in a black hole, allowing many physical states to devolve into the same state. This is controversial because it violates a core precept of modern physics—that, in principle, the value of a wave function of a physical system at one point in time should determine its value at any other time.

A fundamental postulate of the Copenhagen interpretation of quantum mechanics is that complete information about a system is encoded in its wave function up to when the wave function collapses.

The evolution of the wave function is determined by a unitary operator, and unitarity implies that information is conserved in the quantum sense.

Starting in the mid-1970s, Stephen Hawking and Jacob Bekenstein put forward theoretical arguments based on general relativity and quantum field theory that not only appeared to be inconsistent with information conservation but which did not account for the information loss and which stated no reason for it.

Specifically, Hawking’s calculations indicated that black hole evaporation via Hawking radiation does not preserve information. Today, many physicists believe that the holographic principle demonstrates that Hawking’s conclusion was incorrect, and that information is in fact preserved.

Some of postulated solutions are that information gradually leaks out during the black-hole evaporation, information is irretrievably lost, Information is stored in a Planck-sized remnan or information suddenly escapes out during the final stage of black-hole evaporation.©APS/Alan Stonebraker

In 2016, Hawking et al. proposed new theories of information moving in and out of a black hole. The 2016 work posits that the information is saved in “soft particles”, low-energy versions of photons and other particles that exist in zero-energy empty space.

Significant progress was made in 2019, when Penington et al. discovered a class of semiclassical spacetime geometries that had been overlooked by Hawking and subsequent researchers. Hawking’s calculation appears to show that the Hawking radiation’s entropy increases throughout the lifetime of the black hole.

However, if the black hole formed from a known state (zero entropy), the entropy of the Hawking radiation must decrease back to zero once the black hole evaporates completely.

Penington et al. compute the entropy using the replica trick, and show that for sufficiently old black holes, one must consider solutions in which the replicas are connected by wormholes. The inclusion of these wormhole geometries prevents the entropy from increasing indefinitely.

This result appears to resolve the information paradox, at least in the simple gravity theories that they consider. Although the replicas do not have direct physical meaning, the appearance of wormholes carries over to a physical description of the system.

In particular, for sufficiently old black holes, one can perform operations on the Hawking radiation that affect the black hole interior. This result has implications for the related firewall paradox, and resembles the proposed ER=EPR resolution.

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