The Black Hole Information Paradox

The cosmos, empty space, is known to be full of virtual particles. They appear in pairs to conserve momentum and then recombine after a short while. In 1976 Hawking showed that black hole event horizons can separate these pairs by trapping the one on the wrong side of the horizon. The star-crossed lovers are unable to recombine, so one of them becomes real and is emitted as Hawking radiation. This means that whereas black holes can hoover up information-full objects such as flowers and manuscripts (see below left), they can only emit thermal, random, Hawking radiation (see below right). This means the information in the flower and the manuscripts has been lost.

Hawking, Kip Thorne and Roger Penrose were perfectly happy to have information destroyed, but Leonard Susskind and Gerard t’Hooft published a manuscript called The Black Hole War saying that Hawking was violating one of the laws of the universe: the conservation of information. Since when has that been a law? They argued that in quantum mechanics the wavefunction at any one time is supposed to be predictable from the wavefunction at any other time and if you lose information then you can't do that. You lose what they call the unitarity of the wavefunction. They suggested that the information that goes into the black hole survives and proposed the holographic principle which says that information is stored in horizons (a nice idea). Hawking conceded he had lost but Penrose and Thorne did not concede. In my opinion, there may be some merit to both approaches, if combined right.

The debate is at the heart of physics, which has still not come to grips with the new concept of information, but let us see what empiricism and a little logic can offer. Landauer’s principle (reference 1) argues that when computer memory is erased say from the complex 11010 to the uniform 00000, then this is a loss of information, and a reduction of disorder or entropy, which cannot be allowed, so heat must be released. This heat has now been observed (ref 2) whereas the 'unitarity of the wavefunction' has not. One point for information loss. Another point is that quantised inertia (QI) and therefore the observed galaxy rotation without dark matter can be derived beautifully by assuming information loss (ref 3).

The picture is not complete though. In QI, if you accelerate, a horizon obscures your backwards view of the world, erasing information and providing, via Landauer, exactly the right amount of energy to fuel the inertial back-push (ref 3). However, if you stop accelerating, then that information comes back again. Where was it hiding in the meantime? The QI approach may offer a compromise here since accelerating objects see Unruh radiation that inertial (unaccelerating) observers do not. In QI information is in the eye of the beholder. Each object has its own informational universe, and what has been deleted in one may be retrieved by negotiation from another.

References

Landauer, R., 1961. Irreversibility and heat generation in the computing process. IBM J. Research and Development. 5, 3, 183-191.

Hong et al., 2016. Experimental test of Landauer's principle in single-bit operations on nanomagnetic memory bits. Science Advances, 2, 3, e1501492 Link

McCulloch, M.E., 2020. Quantised inertia, and galaxy rotation, from information theory. Adv. in Astrophysics, 5, 4, 92-94. Link