Hawking an Old Idea

On the one hand it is good to get members of the general public excited about scientific research, and so having some new excitement about something Stephen Hawking said, driven by gushingly written articles in the press and online, can be good. On the other hand, it is annoying that the thrust of the articles are largely that he’s stunned the world again with a brilliant and unlooked-for idea. People just lap this stuff up, unquestioningly. It is actually an old idea (and in fact one that is being mis-reported – see below). One’s instinct is to just say “Welcome, Stephen, we’ve been waiting for you to join us”, or “Come on in, the water’s lovely”, and just move on, but it seems so unfair. The thing that’s most puzzling in all of this is Hawking’s own paper (which is all of two pages of words – a transcript of a talk he gave in August), which makes no reference at all to (for example) Samir Mathur’s work, which has been explicitly saying essentially the same thing for well over a decade, with a very definite proposal for how it might work. That work has hardly been buried in obscurity. Samir and many other people who have liked his idea have been working out the consequences of the proposal in numerous papers for over a decade and reporting on their results at all the main conferences, and even talking to him about it (I note that Samir was in the audience during the August talk and even politely asked the speaker to compare and contrast the similar-sounding proposals). So it is puzzling that you get no hint from the paper’s citations that this is a well-considered and ongoing idea, even if (perhaps) in detail it may pan out differently from other suggestions.

What’s the idea?, you ask. Well, it is not, as you might get from most of the articles (somewhat confusingly), that black holes do not exist. It is that the black hole’s event horizon, thought of as a sharp “point of no return” boundary, may not exist. Instead, it is approximation or shorthand for the complicated physics (of both matter and spacetime) that happens in the vicinity of the black hole. Simply put, the horizon arises in classical solutions to classical (i.e. non-quantum) equations (such as in General Relativity) of gravity. (See an earlier post I did about them here, from which came the illustration above.) It is well defined in that context. By time you get to trying to understand quantum mechanically what might be going on, such a one-way barrier begins to look a bit shaky, as already hinted at by the discovery of Hawking radiation (back in the mid-70’s). It tells you that stuff seems to come back out of the black hole, when you consider quantum effects. The horizon is not a one-way barrier after all. That effect comes from a “semi-classical” attempt to do quantum gravity, and so is not the full answer, but a strong hint.

The nature of this hint, and the paradoxes it leads to, has occupied us for 40+ years, largely because we’ve been lacking a complete quantum theory of gravity within which we can simply ask the question “is there an horizon?” and compute the answer unambiguously. But gradually we have been building up (at least one) quantum theory of gravity, and it has allowed us to chip away at some parts of the black hole story (quantum mechanically), but mostly indirectly (such as verifying that black holes do have an underlying micro state description that quantifiably accounts for the entropy that Bekenstein suggested they have), but it has not yet allowed for unambiguous answers to that direct question. This is partly because it is not fully formulated yet (probably far from it), but it might also be in part because the question itself is a poor one. We shall see.

The quantum theory I’m referring to is string theory, and many of the features of string theory are well suited to supplying some of the answers needed to resolve some of the thorny paradoxes that appear when you combine classical gravity intuition with quantum mechanical intuition. (Some mild degree of non-locality that extended objects can give you that a point-based intuition struggles with; extra degrees of freedom at each point in spacetime that you get with compact extra dimensions, and so forth…) One of the biggest, oldest, and most explicit hints from string theory is that spacetime is an approximate description that can break down in certain regimes. We’ve known this for decades, and we have good models for how to handle such breakdowns (breaksdown?) in certain situations (dualities of various sorts that you might have heard of are sometimes such models).

(I should note that we may ultimately end up with several different complete quantum theories of gravity, each with quite a different detailed language for how they deal with black holes. Many of them might be complete theories that nature chose not to have anything to do with! String theory might be just one of them. One might hope that those theories will ultimately yield the means by which we can tell them apart through observation and/or experiment, but that could be a long way off, both theoretically and experimentally.)

The trouble has been that I think that while people might be prepared to accept that the classical nature of very small black holes might be considerably modified by your favourite effect in your favourite quantum gravity theory, they have had a lot of difficulty with the idea that a spacetime description could break down even for a very large black hole’s horizon where the gravity is not particularly strong. The thought has been that the classical spacetime geometry description should be good in such a regime. So there’s not been much focus (in many sectors of the community) on the making the idea of “fuzzying-up” the horizon (and removing it altogether) work in a quantum theory, since it is thought of as perhaps a non-generic solution to the problem. Instead, the horizon has been taken as a given, and then arguments made back and forth about what ought to happen given that it is there.

Many of us, due to various dualities and frameworks derive from string theory (early ones, and more famous later ones like AdS/CFT), have suspected that the horizon is simply a red herring for a long time (and others outside the context of string theory have expressed that idea in one shape or form for a while too). I’ll freely admit to having this suspicion but not really spending time on trying to make it into anything since there were so many things to work on (including all the delicious consequences of AdS/CFT that I’ve told you about here from time to time), and my (still present) gut feeling that it is a difficult issue to tackle head on without a better more explicit formulation of quantum gravity (whether it be string theory or something else) in hand.

But people like Samir Mathur (and his followers) have tried (for over a decade now) to make very explicit headway using existing hints from string theory (see a summary page here), writing lots of substantial papers along the way, and (whether it works or not – time will tell) it is a shame to see him ignored and have many of his ideas and suggestions attributed to Hawking’s two-page note.

-cvj