Hawking’s information preservation and weather forecasting mess

Last month, a lot of newspapers and websites have been promoting this article on Nature referring to a recent preprint ¹ uploaded by Stephen W. Hawking to the internet repository ArXiv. In this work, summarizing what he talked about in a conference given last August, the English physicist argue that, since event horizons, the definitory property of black holes, cause so many problems when we try to look at the quantum physics near them, maybe there are no real physical black holes in nature.

First, we should make clear that this idea is not recent and nor even has been developed by Hawking. The argument that maybe black holes and event horizons are not exactly physical objects and that they may be substitute by other objects is as old as the problem that produced the controversy. A problem that, this time yes, was found by Professor Hawking in the 70’s and that we have talked here about no so much time ago: black holes (concretely, the combination of an event horizon and a singularity) seem to destroy information, a property that we do not like when dealing with a quantum theory. In his new work, the english physicist argue that these event horizons do not preserve a basic property of nature, called CPT (what we talked here about too). However, without any doubt, he is wrong. But before going to Hawking’s argument, let me talk a bit about media reaction to the preprint.

A lot of newspapers all around the globe, mimicking the article on Nature, have been remarking the phrase “there are no black holes” as the most important point in the preprint, relating it to astrophysical black holes as the ones in the center of galaxies. However, what Hawking really said is that there are no eternal black holes, a distinction which is not relevant for astrophysics but it does matter for a particle physicist. And the reason is that astrophysical black holes are not black holes, or better said, they are black holes in the infinity future. This is because when we think of the process of formation of a black hole, we note that there is some matter falling into a common point that, when packed thick enough, will form the dark star. However, due to relativistic effects, it takes infinite time, as seen by an external observer, for the matter to fall, which means that us, being in the exterior of the black hole, we will never see its formation. Of course, as I said, this is not relevant for astrophysics because for sufficient long times, all the experiments we can perform in the outside on the “almost” black hole will be indistinguishable of the ones performed around a real one. However, for the ones interested in understanding the behavior of quantum effects in gravitation, this difference is very important, because an astrophysical black hole does not imply any loss of information. What Stephen Hawking said is, thus, that maybe only astrophysical black holes do exist.

What the english does in his article to support its proposition is to take a particular black hole, the so called eternal AdS black hole (the eternal surname is just to distinguish it from astrophysical ones) which is conjectured to be described by some laws of physics very similar to the ones of electromagnetism (once again, AdS/CFT conjecture). This laws have the property that are CPT invariant and, more concrete, they are invariant under time reversal. Inverting time should not give a different result as relating effects to causes. However, what Hawking shows is, and this is a well-known fact, that the formation of a black hole with radiation and its evaporation are not equivalent processes under this symmetry. The first is not exactly the reverse of the second one, thus violating this fundamental law of nature. So, where is the mistake in Hawking’s argument?

The point that the english physicist is not taking into account is that a black hole is macroscopical system and thus the laws describing its behavior are statistical. Even if the microscopical laws that describe it are CPT invariant, the statistical ones governing the complet object have not to be also invariant. This can be seen with a simple example. Imagine that we have a puzzle. It is clear that the pieces of the puzzle are made of physical matter and thus the laws describing them at the microscopical level are CPT invariant (because the Standard Model is). However, going from a state in which the puzzle is ordered to a random one (by putting the puzzle inside a box and shaking it, for example) is not equivalent to the process of mounting the puzzle from a complete shuffled ensemble of pieces, this direction requires energy and thus the macroscopical laws describing the process of ordering the pieces are not CPT invariant. The same thing is happening with black holes when considered as single big objects.

The microscopical laws describing a black hole (the future theory of quantum gravity) are very sure to be CPT invariant. However, when considering the object as a whole, there is a coarse graining process and we lose important information of the microscopical description, arriving to effective theories that does not must to have the same properties of the microscopical one. This is the reason of why is so difficult to infer the structure of a fundamental theory by only looking at little pieces of it, as in the “Blind men and an elephant” parable.

So, concluding, the argument of Hawking is not correct due to the fact that he is using the microscopical description to look at macroscopical properties, thus mixing different regimes of application of the laws of nature. It is quite surprising that the physicist that in the seventies understood this difference so well that he derived the first known effect of Quantum Gravity is now losing the global picture and writing wrong conclusions. I guess that aging is inevitable.