The Senior Common Room was unusually quiet.
Professor Quillibrace was reading the latest essay with a pencil in hand. Mr Blottisham had already reached the end and was looking dissatisfied.
Miss Elowen Stray was gazing into the middle distance in the way that usually meant she had noticed something nobody else had.
Mr Blottisham: I think we've made this unnecessarily complicated.
Professor Quillibrace: That is always an encouraging opening.
Mr Blottisham: The black hole evaporates. It loses energy. Its mass goes down. Its horizon gets smaller. Eventually the horizon disappears.
Professor Quillibrace: Yes.
Mr Blottisham: So what's the difficulty?
Professor Quillibrace: What happens next?
Mr Blottisham: Everything that was inside comes out.
Professor Quillibrace put down his pencil.
Professor Quillibrace: Why?
Mr Blottisham: Because there's no longer anything keeping it in.
Professor Quillibrace: What was keeping it in?
Mr Blottisham: The black hole.
Professor Quillibrace: That is not an answer.
Mr Blottisham: The gravity.
Professor Quillibrace: Also not quite an answer.
Mr Blottisham: The horizon, then.
Professor Quillibrace: Better. What is the horizon?
Mr Blottisham paused.
Mr Blottisham: The boundary of the black hole.
Professor Quillibrace: And what sort of boundary?
Mr Blottisham: The sort that stops things getting out.
Professor Quillibrace: You have just described a wall.
Mr Blottisham: I know what a horizon is.
Professor Quillibrace: I am beginning to wonder.
Miss Stray smiled.
Miss Stray: We seem to have arrived at the same problem again.
Mr Blottisham: Which problem?
Miss Stray: We keep turning a relationship into a thing.
Mr Blottisham: I don't see how that applies to evaporation.
Professor Quillibrace: It applies rather perfectly.
He picked up his pencil again.
Professor Quillibrace: We have inherited a very convenient picture. There is a black hole. It has an inside. Things fall inside. The horizon keeps them there. The black hole emits radiation. It gets smaller. Eventually the horizon disappears. Therefore the things inside are released.
He looked at Mr Blottisham.
Professor Quillibrace: It is almost a complete story.
Mr Blottisham: Yes.
Professor Quillibrace: And almost none of it should be taken literally.
There was a brief silence.
Miss Stray: Perhaps we should begin with the word itself.
Mr Blottisham: Evaporation?
Miss Stray: Yes.
Professor Quillibrace: An excellent place to start.
The puddle
Miss Stray: When water evaporates, we have a thing that remains recognisably the same kind of thing while losing some of its contents.
Mr Blottisham: Exactly.
Miss Stray: Molecules leave the puddle. The puddle gets smaller.
Professor Quillibrace: And eventually there is no puddle.
Miss Stray: So when we hear that a black hole evaporates, we naturally imagine the same sort of process.
Mr Blottisham: Which seems reasonable.
Professor Quillibrace: Up to a point.
Mr Blottisham: What point?
Professor Quillibrace: The black hole does lose mass.
Mr Blottisham: Good.
Professor Quillibrace: And for a simple non-rotating black hole, its characteristic horizon scale decreases as its mass decreases.
Mr Blottisham: Also good.
Professor Quillibrace: But that does not mean that there is a material black-hole substance which is gradually being removed from a container.
Mr Blottisham: I didn't say there was.
Professor Quillibrace: No. You merely keep talking as though there were.
Miss Stray laughed.
Mr Blottisham: All right. So what is actually changing?
Professor Quillibrace: The physical state of the system evolves. The spacetime geometry associated with that state evolves with it. And therefore the causal structure changes.
Mr Blottisham: That's an awfully elaborate way of saying the black hole gets smaller.
Professor Quillibrace: It is precisely the elaborate part that matters.
Miss Stray: Because "gets smaller" makes it sound as though there were a little black object whose boundary was contracting.
Professor Quillibrace: Whereas the horizon is not a material skin.
Mr Blottisham: Fine. The horizon isn't a skin.
Professor Quillibrace: Progress.
What is doing the trapping?
Mr Blottisham: But surely something still has to explain why things can't get out.
Professor Quillibrace: Certainly.
Mr Blottisham: So what is it?
Professor Quillibrace: The causal structure of spacetime.
Mr Blottisham: Which means?
Professor Quillibrace: Inside the event horizon, future-directed causal trajectories do not lead back out to distant infinity.
Mr Blottisham: So they're trapped.
Professor Quillibrace: In the relevant causal sense, yes.
Mr Blottisham: Then if the geometry changes enough, presumably they stop being trapped.
Professor Quillibrace: Now we have reached something interesting.
Miss Stray looked up.
Miss Stray: Because that sounds almost like what you were saying before.
Mr. Blottisham: Exactly.
Professor Quillibrace: Your intuition is pointing in a useful direction. But we have to formulate it carefully.
Mr Blottisham: I thought you were going to say I was wrong.
Professor Quillibrace: I generally prefer to say that you are approximately right in a dangerously misleading vocabulary.
Mr Blottisham: Thank you.
Professor Quillibrace: You're welcome.
The photon
Miss Stray: What happens to a photon that has fallen in?
Mr Blottisham: It can't get out.
Professor Quillibrace: For a sufficiently stationary black hole, once it is genuinely inside the event horizon, yes.
Miss Stray: And if the black hole is evaporating?
Professor Quillibrace paused.
Professor Quillibrace: Then we have to be more careful.
Mr Blottisham: Why?
Professor Quillibrace: Because an event horizon is not defined merely by asking whether light can escape at this particular moment.
Miss Stray: It is defined globally.
Professor Quillibrace: Precisely.
Mr Blottisham: Meaning?
Professor Quillibrace: Roughly, the event horizon separates events whose future can reach distant infinity from events whose future cannot.
Mr Blottisham: So it depends on the future.
Professor Quillibrace: Yes.
Mr Blottisham: That's rather inconvenient.
Professor Quillibrace: General relativity has never been particularly concerned with our convenience.
Miss Stray smiled.
Miss Stray: So if the complete future geometry says that the photon eventually reaches infinity, then strictly speaking it was not in the event-horizon region after all?
Professor Quillibrace: That is the subtle point.
Mr Blottisham: But how could the photon know that?
Professor Quillibrace looked at him.
Professor Quillibrace: It doesn't.
Mr Blottisham: Then why are we talking about the future?
Professor Quillibrace: Because the event horizon is a feature of the entire spacetime, not a local object announcing its presence to the photon.
Miss Stray: So the photon simply follows its worldline.
Professor Quillibrace: Exactly.
Mr Blottisham: Through a changing geometry.
Professor Quillibrace: Yes.
Mr Blottisham: Which means it isn't sitting there waiting for the horizon to move out of the way.
Professor Quillibrace: Now you are beginning to see the problem.
The door that isn't there
Mr Blottisham: But surely if the horizon eventually disappears, something changes.
Professor Quillibrace: Certainly.
Mr Blottisham: So why can't we say that the door opens?
Professor Quillibrace: Because there was no door.
Mr Blottisham: It's a metaphor.
Professor Quillibrace: A very persistent one.
Miss Stray: And perhaps an especially dangerous one here.
Mr Blottisham: Why?
Miss Stray: Because it makes us imagine that the objects inside remain in the same region while the boundary retreats around them.
Professor Quillibrace: Precisely.
Mr Blottisham: But isn't that roughly what happens?
Professor Quillibrace: No. The geometry itself is changing.
Mr Blottisham: So there isn't a fixed interior with a shrinking boundary?
Professor Quillibrace: Not in the simple sense your picture assumes.
Miss Stray: The distinction is important. We are not watching a room get smaller until its walls disappear.
Professor Quillibrace: Nor are we watching a room become larger until its occupants discover that the door is open.
Mr Blottisham: Then what are we watching?
Professor Quillibrace: A dynamical spacetime.
The room that isn't a room
Miss Stray looked thoughtful.
Miss Stray: Perhaps this is the same mistake we made with information.
Mr Blottisham: How?
Miss Stray: We asked where the information was.
Professor Quillibrace: And discovered that "where" may not be the right question.
Miss Stray: Now we ask where the objects inside the black hole go when the black hole disappears.
Professor Quillibrace: And again, perhaps the question contains too much of the answer.
Mr Blottisham: You mean "inside" is doing the same kind of work?
Professor Quillibrace: Exactly.
Mr Blottisham: But things really do fall into black holes.
Professor Quillibrace: Certainly.
Mr Blottisham: So surely they really are inside.
Professor Quillibrace: In the semiclassical spacetime description, yes.
Mr Blottisham: You keep saying "in the description".
Professor Quillibrace: Because we are discussing a problem at the boundary between general relativity and quantum theory. It would be unwise to assume that every feature of the semiclassical description survives unchanged into the ultimate quantum-gravitational account.
Miss Stray: So "inside" may be real without being fundamental.
Professor Quillibrace: That is an excellent way to put it.
But what actually happens?
Mr Blottisham: I still want to know what happens to the things that fell in.
Professor Quillibrace: So do I.
Mr Blottisham: Good.
Professor Quillibrace: Unfortunately, that is where our confidence ends.
Mr Blottisham: Surely physics knows what happens when the black hole evaporates.
Professor Quillibrace: Physics knows a great deal about the early and intermediate stages. It does not possess a universally accepted complete description of the final quantum-gravitational stage.
Miss Stray: So the disappearance of the horizon is not something we can simply extrapolate all the way down to zero size with confidence.
Professor Quillibrace: Correct.
Mr Blottisham: Because the semiclassical approximation eventually breaks down.
Professor Quillibrace: Yes.
Mr Blottisham: That's annoying.
Professor Quillibrace: It is also scientifically respectable.
Mr Blottisham: You academics do enjoy saying "we don't know".
Professor Quillibrace: Only when we don't know.
Evaporation is not emptying
Miss Stray: There is another thing bothering me.
Professor Quillibrace: What is it?
Miss Stray: If Hawking radiation isn't simply matter leaking out from inside, then what exactly are we imagining when we say the black hole emits radiation?
Professor Quillibrace: A quantum-field-theoretic process associated with quantum fields in curved spacetime.
Mr Blottisham: That sounds less picturesque.
Professor Quillibrace: Physics is not obliged to be picturesque.
Miss Stray: So the radiation should not be thought of as the black hole's contents escaping?
Professor Quillibrace: Not in that simple sense.
Mr Blottisham: Then "evaporation" really is a rather misleading word.
Professor Quillibrace: It is useful, provided we remember that it is a metaphor.
Mr Blottisham: Which we have just spent an entire series learning not to forget.
Professor Quillibrace: Exactly.
Miss Stray: The black hole loses mass, but it doesn't necessarily lose mass in the manner of a puddle losing molecules.
Professor Quillibrace: Correct.
Mr Blottisham: And it doesn't become empty.
Professor Quillibrace: Not in the ordinary sense.
Mr Blottisham: It changes.
Professor Quillibrace: Now you have it.
The disappearing horizon
Miss Stray: There is something rather beautiful about that.
Mr Blottisham: What?
Miss Stray: At first the horizon seems to be the thing that keeps everything in.
Professor Quillibrace: And then we discover that the horizon isn't a thing.
Miss Stray: It is a causal boundary.
Professor Quillibrace: Yes.
Miss Stray: And when the black hole evaporates completely, that causal boundary disappears.
Mr Blottisham: So what disappears isn't a wall.
Professor Quillibrace: Precisely.
Miss Stray: A regime of causal possibility disappears.
Professor Quillibrace smiled.
Professor Quillibrace: That is very well put.
Mr Blottisham: But then what happens to the information that was inaccessible because of that regime?
Professor Quillibrace: Ah.
Mr Blottisham: I recognise that "ah".
Professor Quillibrace: It is the sound one makes when a geometrical question becomes a quantum-gravitational one.
The information comes back
Mr Blottisham: Suppose we say that the information eventually becomes accessible again.
Professor Quillibrace: That is one possibility.
Mr Blottisham: Then haven't we solved the problem?
Professor Quillibrace: No.
Mr Blottisham: Why not?
Professor Quillibrace: Because accessibility is not the same as preservation.
Miss Stray: We have been here before.
Professor Quillibrace: Indeed.
Mr Blottisham: Explain.
Professor Quillibrace: Suppose two different quantum states, A and B, collapse into black holes.
Mr Blottisham: All right.
Professor Quillibrace: Suppose the black holes eventually evaporate.
Mr Blottisham: Fine.
Professor Quillibrace: If the final radiation is exactly the same quantum state in both cases, then A and B have become physically indistinguishable.
Mr Blottisham: So the distinction has been destroyed.
Professor Quillibrace: Exactly.
Miss Stray: It isn't enough for something to come out.
Professor Quillibrace: Correct.
Miss Stray: What matters is whether the final state still carries the distinctions that made the initial states different.
Professor Quillibrace: Yes.
Mr Blottisham: So even if everything "gets out", we could still have information loss.
Professor Quillibrace: Now you are using the word "gets" rather more cautiously.
The black hole does not let anything out
Mr Blottisham: Let me try again.
If the black hole evaporates, it doesn't necessarily let anything out.
Professor Quillibrace: Good.
Mr Blottisham: The universe simply evolves.
Professor Quillibrace: Yes.
Mr Blottisham: The geometry changes.
Professor Quillibrace: Yes.
Mr Blottisham: The causal structure changes.
Professor Quillibrace: Yes.
Mr Blottisham: The correlations change.
Professor Quillibrace: Yes.
Mr Blottisham: And eventually what we called the black hole no longer exists as that particular causal structure.
Professor Quillibrace: Very good.
Mr Blottisham looked pleased.
Mr Blottisham: I believe I have finally understood it.
Professor Quillibrace: You have understood the sentence.
Mr Blottisham: Isn't that the same thing?
Professor Quillibrace: No.
Miss Stray laughed.
The strange fate of the inside
Miss Stray: There is still something I find difficult.
Professor Quillibrace: What?
Miss Stray: If we say that something fell inside, and later the black hole is gone, it is difficult not to imagine that the thing must have either remained there or escaped.
Professor Quillibrace: That is because ordinary language gives us two choices.
Miss Stray: Remain or escape.
Professor Quillibrace: Yes.
Miss Stray: But perhaps the deeper description has neither.
Professor Quillibrace: Precisely.
Mr. Blottisham: What would it have instead?
Professor Quillibrace: Transformation.
Miss Stray: The quantum state remains a quantum state, while the geometrical and causal description changes.
Professor Quillibrace: Exactly.
Miss Stray: So what we call "the interior" might not survive as an interior.
Professor Quillibrace: Nor need the information survive in the same form.
Mr. Blottisham: But it could survive as correlations.
Professor Quillibrace: If evolution is unitary, that is the essential possibility we are trying to understand.
A final return to the puddle
Mr Blottisham picked up the essay.
Mr. Blottisham: I think I see what bothered me about the puddle analogy.
Professor Quillibrace: Do tell.
Mr. Blottisham: With the puddle, the object remains the same sort of object while becoming smaller.
Professor Quillibrace: Yes.
Mr. Blottisham: With the black hole, the thing that is changing is partly the very structure that made it a black hole.
Professor Quillibrace: Precisely.
Mr. Blottisham: So saying "the black hole gets smaller" is useful, but it doesn't tell us what is fundamentally happening.
Professor Quillibrace: Correct.
Miss Stray: It tells us that the mass and characteristic horizon scale decrease.
Professor Quillibrace: But the deeper story concerns the evolving geometry and causal structure.
Mr. Blottisham: And eventually the causal structure no longer contains the black-hole region.
Professor Quillibrace: Yes.
Mr. Blottisham: Which means that asking what happens to what was "inside" is really asking how the earlier description relates to the later one.
Professor Quillibrace looked genuinely pleased.
Professor Quillibrace: I think you have finally caught up with the essay.
Mr. Blottisham: I thought the essay was supposed to catch up with me.
Miss Stray: Perhaps neither of you is where you started.
The last question
The room fell quiet for a moment.
Miss Stray looked towards the window.
Miss Stray: There is something rather strange about where this leaves us.
Professor Quillibrace: Go on.
Miss Stray: We began by asking what happens when things fall into a black hole.
Professor Quillibrace: Yes.
Miss Stray: Then we asked what happens to the information.
Professor Quillibrace: Yes.
Miss Stray: And now we are asking what happens when the very causal structure that made the question meaningful changes.
Professor Quillibrace: Precisely.
Mr. Blottisham: Which means we have spent an entire discussion trying to find out where things go, only to discover that "where" may itself be changing.
Professor Quillibrace: That is the difficulty.
Miss Stray: And perhaps the clue.
Mr. Blottisham: To what?
Miss Stray: That the black hole does not merely disappear.
She paused.
Miss Stray: The geometry by which we recognised it as a black hole disappears.
Professor Quillibrace nodded.
Professor Quillibrace: And that may be the most useful way to think about evaporation.
Mr. Blottisham: So nothing necessarily escapes.
Professor Quillibrace: Not necessarily.
Mr. Blottisham: Nothing necessarily remains inside.
Professor Quillibrace: Correct.
Mr. Blottisham: The universe simply changes.
Professor Quillibrace: The universe is always changing.
Miss Stray: But in this case, it changes the very structure of what counts as accessible, trapped, inside and outside.
Professor Quillibrace closed the essay.
Professor Quillibrace: And that is why "evaporation" is such a dangerous word.
Mr. Blottisham: Because it makes us think a puddle has disappeared.
Professor Quillibrace: Yes.
Miss Stray: When perhaps what has disappeared is not a thing at all.
She looked towards the empty fireplace.
Miss Stray: Perhaps what has disappeared is a way of organising the possible relations among events.
There was a silence.
Then Mr Blottisham reached for the wine.
Mr. Blottisham: I think I preferred the puddle.
Professor Quillibrace: Naturally.
Miss Stray: It was easier to understand.
Professor Quillibrace: That is why metaphors are so useful.
Mr. Blottisham: And so dangerous.
Professor Quillibrace raised his glass.
Professor Quillibrace: Precisely.
And for once, nobody had anything more to add.
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