In response to a question (about the recent status of Hawking's 2004 claims) from David Goss, let us start with some well-known history. Hawking was the first person who in 1974 successfully merged (even though just approximately, in what we call the "semiclassical approximation") the laws of general relativity with the laws of quantum field theory to derive a nontrivial quantitative result - namely the Hawking radiation, including its spectrum. Via thermodynamics, it can be also used to derive the black hole entropy.
Hawking's framework to calculate and his insights are beautiful. Many theoretical physicists believe that he deserves a Nobel prize, and we're just unlucky that there are not too many small, radiating black holes around. In one of the unlikely scenarios of "low energy gravity", the LHC could be producing small, radiating black holes - which would be a terrific news for Hawking. But there also exists a confirmation that is the second most convincing one after the experiments: his calculation of the Bekenstein-Hawking entropy has been confirmed by string theory, for very many different non-trivial examples of black holes.
Hawking's and similar calculations have one unpleasant aspect only: they also seem to imply that the initial matter, forming the black hole, is evolving into a mixed thermal state (the radiation that remains after the black hole evaporates) which is completely universal and only depends on some "major" observables describing the initial state such as the total charge and total mass. All the details of the initial state are lost.
This is worrisome: a pure state may evolve into a mixed state. If it were really so, then we would talk about the "information loss". Such a process would violate unitarity - an essential feature of quantum theory that guarantees that a pure state evolves into another pure state, as Schrödinger's equation or the unitary S-matrix imply, and the total probability of all outcomes always equals one. In Hawking's approximation, it is simply true that pure states evolve into mixed states.
Is it true even if you study the black holes with an exact theory? There have been different opinions about this question. Some of them disappeared: for example, the idea that the information is preserved in a "remnant" that is left after the black hole evaporates became very unpopular once it was seen that such a remnant violates the entropy bounds (it carries too much entropy per a very small volume) and nothing like these remnants was seen in string theory.
Well, only two possible answers were left:
- the information is preserved because of quantum effects that are not visible in the semiclassical approximation, or
- the information is lost, as Hawking originally thought, and quantum mechanics must be modified. No one knew exactly how such a modification could look like.
The mainstream approach, I would say, was always that quantum mechanics is preserved in the full theory and the apparent information loss is just an artifact of the semiclassical approximation. This point of view became even stronger when string theory explained the microscopic origin of the black hole entropy, starting with the papers of Strominger and Vafa. In this framework, one obtains the right entropy, and moreover she has a complete control over the quantum states if the "string coupling" is chosen weak. At the weak coupling, the information is manifestly preserved, and it is very natural to think that the same must be true at any coupling. Hawking's own arguments can be circumvented by some sort of stringy non-locality that becomes important in the presence of black holes. Also, the AdS/CFT correspondence and Matrix theory allow the black holes to be described within a completely unitary mathematical formalism. String theory seems to resolve the subtleties connected with the black holes without sacrificing any principles of quantum mechanics - which is one of the reasons why we find this theory so impressive.
Hawking himself realized that these stringy achievements were very strong arguments in favor of the preserved information after all. But he only "switched" to the mainstream opinion in the summer of 2004 when he announced that he had solved the problem and explained why the information is preserved. He also officially declared a defeat in his bet.
Of course, the physicists, much like the laypeople, were interested in Hawking's resolution. Hawking's new answer looks right, and it would be even better if he could really resolve the apparent paradox that appears in the semiclassical approximation. All of us know that Hawking has the capacity to solve such problems. Many people thought that Hawking was inspired by a paper by Maldacena
However, the interviews for media show that Hawking was not quite saying the same things as Maldacena. The immediate predictions of many people who were interested in the subject - and their understanding of Hawking's new insights and the problems with these insights - were the following:
- Hawking wants to express the information loss quantitatively in terms of the correlation functions that usually decay exponentially in the presence of the black hole - you may think about the damped "quasinormal ringing modes" that bring the black hole closer to its perfect, e.g. spherical shape
- Hawking wants to argue that the correlators also get a contribution from the path integral configurations that don't contain any black holes. You know, this is the standard and key rule of Feynman's approach to quantum mechanics - one must sum over all configurations, including the configurations that the loop quantum gravity people don't find convenient. ;-) These contributions from the "nearly empty spacetime" may be small at the beginning, but at late times they eventually dominate because they are not exponentially supressed. The late time behavior would therefore have the same information properties as an empty spacetime, and the information would therefore be manifestly preserved
- Hawking 2004 does not explain how do the "trivial spacetime" configurations conspire in such a way that they "seem" to behave just like dynamics near a black hole. Intuitively, a particular process of formation and evaporation of a black hole is dominated by the black hole intermediate states. By rejecting this assumption, Hawking becomes marginally inconsistent with his old calculations. For example, a possible loophole would be that the dominant "trivial spacetime" contributions to the path integral will "approach" the states that are very close to the black hole (something I've been calling an "almost black hole"), but then the full analysis requires us to understand quantum gravity in the Planckian regime (stretched horizons etc.) which seems as a non-trivial question not answered by Hawking's 2004 interviews
- Nearly everyone in the "mainstream" knew that there can be some special quantum gravity phenomena that will resemble the black hole, but avoid the information loss, but Hawking's 2004 argument does not seem to illuminate these new potential phenomena
- Because this line of reasoning has been kind of tried, it did not lead to an answer of the question, and an important "missing piece" also seems to be missing in Hawking's interviews, it's reasonable to expect that Hawking did not really solve the information loss paradox in a "final and satisfactory" way, and one would predict that there would not be any technical paper following the interviews that would explain physics behind his interviews in detail
So far, these predictions seem to hold, don't they? I'm happy that Hawking joined the information consevatives and all of us still face more or less the same remaining puzzles.