The Senior Common Room at St Anselm’s was unusually quiet.
Professor Quillibrace was standing at the window, looking out across the quadrangle.
Mr Blottisham was reading the newspaper with the expression of a man who had discovered that the world was once again failing to behave sensibly.
Miss Elowen Stray was turning the pages of the latest essay.
She looked up.
Miss Stray: There is something rather odd about this business with the event horizon.
Mr Blottisham: Only something?
Miss Stray: We keep calling it a boundary.
Mr Blottisham: It is a boundary.
Miss Stray: Yes. But what is it a boundary of?
Mr Blottisham lowered the newspaper.
Mr Blottisham: Of the black hole.
Professor Quillibrace: That answer merely moves the question one noun to the right.
Mr Blottisham: I was afraid you were going to say that.
Professor Quillibrace turned from the window.
Professor Quillibrace: We have a remarkably persistent habit of assuming that every boundary must have something on either side of it which the boundary separates.
Miss Stray: Like a wall.
Mr Blottisham: Or a fence.
Professor Quillibrace: Or a border.
Miss Stray: But the event horizon isn't a wall.
Mr Blottisham: No. It is a one-way door.
Professor Quillibrace: Which is considerably better.
Mr Blottisham: Thank you.
Professor Quillibrace: Unfortunately, it is still wrong.
Mr Blottisham sighed.
Mr Blottisham: I knew there was a catch.
The boundary that isn't a thing
Miss Stray: The essay says that the event horizon is a boundary in causal structure rather than a material surface.
Mr Blottisham: Yes.
Miss Stray: I think that's the part I find most interesting.
Mr Blottisham: Why?
Miss Stray: Because it means the boundary isn't defined by what is there.
Professor Quillibrace: Excellent.
Miss Stray: It is defined by what can happen.
There was a brief silence.
Mr Blottisham: That's an unnecessarily philosophical way of saying that things can't get out.
Professor Quillibrace: On the contrary. It is a physically precise way of saying something that our ordinary language encourages us to misunderstand.
He picked up a pencil.
Professor Quillibrace: A wall is a thing which imposes a constraint. The event horizon is a feature of the structure that determines which future-directed causal paths are available.
Mr Blottisham: So the horizon doesn't stop you leaving.
Professor Quillibrace: Correct.
Mr Blottisham: It merely means that leaving is not among the possibilities.
Professor Quillibrace: Precisely.
Miss Stray: Which makes the phrase "trapped inside" slightly misleading.
Professor Quillibrace: Very.
Mr Blottisham: But surely if you're inside a black hole and can't get out, you're trapped.
Professor Quillibrace: In ordinary conversation, yes.
Miss Stray: But physically?
Professor Quillibrace: Physically, the more interesting statement is that the causal structure does not permit an outward-directed future trajectory that reaches the exterior.
Mr Blottisham stared at him.
Mr Blottisham: That sounds remarkably like being trapped.
Professor Quillibrace: It is.
Mr Blottisham: Thank you.
Professor Quillibrace: But without the unnecessary image of a cosmic jailer.
The cosmic jailer
Miss Stray: I hadn't thought of it that way.
Mr Blottisham: I hadn't either. But now that you've mentioned it, I rather like the cosmic jailer.
Professor Quillibrace: Naturally.
Mr Blottisham: Perhaps the black hole simply refuses parole.
Miss Stray: On what grounds?
Mr Blottisham: Irreversible causal misconduct.
Professor Quillibrace: I see that the morning is going to be difficult.
Miss Stray smiled.
Miss Stray: But there is something important about the metaphor, isn't there?
Professor Quillibrace: Yes. The jailer metaphor makes the horizon sound like an agent which prevents things from escaping.
Miss Stray: Whereas the geometry itself determines what is possible.
Professor Quillibrace: Exactly.
Mr Blottisham: So there isn't anything doing the trapping.
Professor Quillibrace: Not in the ordinary sense.
Miss Stray: The structure of spacetime is enough.
Professor Quillibrace: And that is one of the genuinely remarkable conceptual achievements of general relativity.
He put down the pencil.
Professor Quillibrace: Geometry does not merely describe where things are. It participates in determining what can happen.
Inside and outside
Miss Stray returned to the essay.
Miss Stray: There's another thing I noticed.
Mr Blottisham: The fact that you noticed it suggests that it will soon become my problem.
Miss Stray: We keep saying "inside" and "outside."
Professor Quillibrace: Yes.
Miss Stray: But those words sound much more straightforward than they really are.
Mr Blottisham: Inside means inside.
Professor Quillibrace: Does it?
Mr Blottisham: Surely.
Professor Quillibrace: Inside a box?
Mr Blottisham: Yes.
Professor Quillibrace: Inside a country?
Mr Blottisham: More or less.
Professor Quillibrace: Inside a black hole?
Mr Blottisham paused.
Mr Blottisham: Ah.
Miss Stray: That's the problem.
Professor Quillibrace: The word "inside" encourages us to imagine spatial enclosure. But the decisive distinction at an event horizon is causal.
Miss Stray: So "inside" really means something like "in a region from which signals cannot reach the relevant exterior."
Professor Quillibrace: Better.
Mr Blottisham: Which means that "outside" is not simply another place.
Professor Quillibrace: Precisely. It is a region from which those signals can still reach the exterior.
Miss Stray: So the boundary separates different possibilities rather than different substances.
Professor Quillibrace: Now you have it.
Mr Blottisham folded the newspaper.
Mr Blottisham: I dislike this.
Miss Stray: Why?
Mr Blottisham: Because I was perfectly happy with inside and outside.
Professor Quillibrace: Most metaphors are perfectly happy until you ask them to do physics.
A horizon made of future
Miss Stray: There's something even stranger.
Mr Blottisham: Of course there is.
Miss Stray: The event horizon is defined in relation to the future.
Professor Quillibrace: Yes.
Miss Stray: So we draw it as though it were a thing sitting there in space, but its definition depends upon what can ultimately happen.
Mr Blottisham: You mean the horizon somehow knows the future?
Professor Quillibrace: No.
Mr Blottisham: Good.
Professor Quillibrace: The mathematical definition depends upon the global causal structure of spacetime. That is not the same thing as an object possessing foreknowledge.
Mr Blottisham: I was about to object.
Miss Stray: But it does mean that the horizon isn't simply a local surface.
Professor Quillibrace: Correct.
Miss Stray: Which is extraordinary.
Professor Quillibrace: It is one of those features of relativity that become stranger the more precisely you state them.
Mr Blottisham: I preferred it when it was a dark sphere.
Professor Quillibrace: That was an image.
Mr Blottisham: It was a good image.
Professor Quillibrace: It was.
Mr Blottisham: Thank you.
Professor Quillibrace: And it was not the thing itself.
Mr Blottisham sighed.
The astronaut
Miss Stray: What about the astronaut crossing the horizon?
Mr Blottisham: Now there's a reassuring subject.
Miss Stray: From the astronaut's perspective, nothing locally dramatic has to happen at the horizon.
Professor Quillibrace: Correct.
Mr Blottisham: But from far away, the astronaut appears to freeze near it.
Professor Quillibrace: In an appropriate sense, yes.
Mr Blottisham: So which is actually happening?
Professor Quillibrace: Both descriptions are valid within their respective frames and coordinates.
Mr Blottisham: That sounds suspiciously diplomatic.
Professor Quillibrace: It is mathematical.
Miss Stray: Perhaps the point is that there isn't one ordinary object called "the horizon" whose behaviour everyone is watching.
Professor Quillibrace: Exactly.
Miss Stray: The horizon is a feature of the causal structure connecting events and observers.
Professor Quillibrace: Yes.
Mr Blottisham: So the observer matters.
Professor Quillibrace: The observer's position in the causal structure matters.
Miss Stray: But that doesn't make the horizon subjective.
Professor Quillibrace: An important distinction.
He returned to the window.
Professor Quillibrace: The horizon is not created by somebody looking at it. But what information is accessible to an observer depends upon the observer's causal relationship to events.
Miss Stray: So accessibility is relational without reality becoming subjective.
Professor Quillibrace: Precisely.
The horizon and information
Mr Blottisham: Which brings us back to information.
Professor Quillibrace: Inevitably.
Miss Stray: We said in the previous essay that information is relational.
Professor Quillibrace: Yes.
Miss Stray: And now the horizon turns out to be relational too.
Mr Blottisham: Are you suggesting that the horizon and information are secretly dating?
Professor Quillibrace: I am suggesting that they are both concepts whose significance lies partly in relationships rather than substances.
Mr Blottisham: Much less entertaining.
Miss Stray: But quite interesting.
Professor Quillibrace: Information concerns distinctions and correlations among physical states. The horizon constrains which causal relations can exist between events.
Miss Stray: So the horizon constrains the possible organisation of information.
Professor Quillibrace: Exactly.
Mr Blottisham frowned.
Mr Blottisham: So a causal boundary becomes an information boundary.
Professor Quillibrace: That is a very useful way of putting it.
Mr Blottisham: Without being an information wall.
Professor Quillibrace: Correct.
Mr Blottisham: This is becoming unnecessarily subtle.
Miss Stray: I think that's because the physics is subtle.
Mr Blottisham: I prefer theories with furniture.
The missing information
Miss Stray: But now I see why the disappearance of the horizon matters.
Professor Quillibrace: Go on.
Miss Stray: If information falls across the horizon, then from outside it becomes inaccessible. But if the black hole eventually evaporates, the horizon disappears.
Mr Blottisham: And there goes the cosmic filing cabinet.
Professor Quillibrace: There was never a cosmic filing cabinet.
Mr Blottisham: We have established that.
Miss Stray: But that's exactly the problem. If we imagined information as being stored inside, then evaporation leaves us asking where the stored information went.
Professor Quillibrace: And that question already assumes too much.
Miss Stray: Because information isn't a substance.
Professor Quillibrace: And the horizon isn't a container.
Mr Blottisham: So we have a non-substance in a non-container.
Professor Quillibrace: You are learning.
A boundary without a surface
Miss Stray looked thoughtful.
Miss Stray: Perhaps the most interesting phrase in the essay is "a boundary without a surface."
Mr Blottisham: It sounds like something the Dean would say about a committee.
Professor Quillibrace: An excellent example.
Miss Stray: A committee can have a boundary without there being a physical line around it.
Mr Blottisham: Although sometimes there is a physical door.
Professor Quillibrace: And sometimes the door is locked.
Miss Stray: But the point is that a boundary can be a difference in organisation.
Professor Quillibrace: Yes.
Miss Stray: It doesn't have to be a thing.
Professor Quillibrace: That is worth dwelling upon.
He took the pencil again.
Professor Quillibrace: We tend to think that reality consists of things, and that relations merely connect the things. But modern physics repeatedly complicates that picture.
Mr Blottisham: Objects first, relationships second?
Professor Quillibrace: That is the habitual picture.
Miss Stray: And perhaps sometimes the relationship is the more fundamental feature.
Professor Quillibrace: Perhaps.
The membrane
Mr Blottisham: But physicists themselves sometimes talk about the horizon as a membrane.
Miss Stray: The membrane paradigm.
Professor Quillibrace: Indeed.
Mr Blottisham: So surely we're allowed to think of it as a membrane.
Professor Quillibrace: We are allowed to use the model.
Mr Blottisham: Ah.
Professor Quillibrace: That does not mean we should mistake the model for ontology.
Miss Stray: The membrane is useful because it captures certain relationships.
Professor Quillibrace: Exactly.
Mr Blottisham: So when the physicist says "membrane", the physicist may mean "behaves mathematically in certain respects as though there were a membrane."
Professor Quillibrace: Yes.
Mr Blottisham: And when the popular article says "membrane", it means "there is a membrane."
Professor Quillibrace: Frequently.
Mr Blottisham: I see.
He looked pleased.
Mr Blottisham: So the problem isn't metaphor.
Professor Quillibrace: No.
Mr Blottisham: It's forgetting that it is metaphor.
Professor Quillibrace: Now you are learning very quickly.
The horizon acquires entropy
Miss Stray turned another page.
Miss Stray: Then there's the really strange part.
Mr Blottisham: The part involving entropy?
Miss Stray: Yes.
Professor Quillibrace: Black-hole thermodynamics.
Miss Stray: The entropy is proportional to the area of the horizon.
Mr Blottisham: Why not the volume?
Professor Quillibrace: Precisely.
Mr Blottisham: I knew you would say that.
Professor Quillibrace: Our ordinary intuition about storage is volumetric.
Miss Stray: A larger room contains more things.
Mr Blottisham: A larger hard drive stores more data.
Professor Quillibrace: Yet black-hole entropy scales with area.
Miss Stray: Which makes the boundary itself suddenly look informationally important.
Professor Quillibrace: Very much so.
Mr Blottisham: Perhaps the universe has discovered shelving.
Professor Quillibrace: Or perhaps we should resist that metaphor too.
Mr Blottisham: I was afraid of that.
Does the boundary contain the interior?
Miss Stray: The temptation is to say that the information is stored on the horizon.
Professor Quillibrace: Yes.
Miss Stray: But that sounds almost as though we've simply moved the storage metaphor from the inside to the surface.
Professor Quillibrace: Exactly.
Mr Blottisham: We have upgraded the filing cabinet to a filing membrane.
Professor Quillibrace: Which is not a conceptual improvement.
Miss Stray: The deeper question is why the number of possible states associated with the black hole scales with its boundary area.
Professor Quillibrace: Yes.
Miss Stray: Not "what is written on the surface?"
Professor Quillibrace: Precisely.
Mr Blottisham: So the area is a clue, not an answer.
Professor Quillibrace: An excellent formulation.
Holographic
Miss Stray: And this is where holography comes in.
Mr Blottisham: I knew we were heading there.
Professor Quillibrace: The holographic principle is one of those cases where the metaphor is extraordinarily suggestive and extraordinarily dangerous.
Miss Stray: Because a hologram is an image.
Professor Quillibrace: Yes.
Mr Blottisham: So saying the universe is holographic makes one imagine that reality is a projection.
Professor Quillibrace: Which is not what the slogan, by itself, establishes.
Miss Stray: The deeper idea is that a description formulated in terms of degrees of freedom associated with a boundary can encode the same physical content as a description involving a volume.
Professor Quillibrace: Very roughly, yes.
Mr Blottisham: So the boundary doesn't necessarily contain a little picture of what's inside.
Professor Quillibrace: Correct.
Miss Stray: It may be that what we call the interior can be described through another set of degrees of freedom.
Professor Quillibrace: And that possibility is far more radical than simply putting information on a surface.
The trouble with location
There was a longer silence.
Miss Stray looked back at the first page.
Miss Stray: I think this changes the question we've been asking.
Mr Blottisham: Which question?
Miss Stray: "Where is the information?"
Professor Quillibrace: Yes.
Miss Stray: We have been assuming that information must have a location.
Mr Blottisham: Inside or outside.
Miss Stray: Exactly.
Professor Quillibrace: And if information is fundamentally relational, that assumption may already be too strong.
Miss Stray: A correlation isn't necessarily located in one of the systems it relates.
Professor Quillibrace: Correct.
Miss Stray: And a boundary isn't necessarily a thing located between two things.
Professor Quillibrace: Correct.
Miss Stray: So perhaps the question "Where is the information?" is itself built from the wrong ontology.
Mr Blottisham looked at Professor Quillibrace.
Mr Blottisham: You know, she has a point.
Professor Quillibrace: She does.
Mr Blottisham: That's becoming quite a habit.
What if inside and outside are emergent?
Miss Stray: Suppose, just for a moment, that spacetime itself isn't fundamental.
Mr Blottisham: Must we?
Miss Stray: Suppose the geometry emerges from deeper relationships.
Professor Quillibrace: A perfectly respectable possibility.
Miss Stray: Then perhaps the horizon emerges too.
Professor Quillibrace: Yes.
Miss Stray: And if the horizon emerges, then perhaps "inside" and "outside" emerge with it.
Mr Blottisham: Meaning that the distinction between them isn't fundamental either?
Professor Quillibrace: That would be one possible implication.
Mr Blottisham: Then what is fundamental?
Professor Quillibrace smiled.
Professor Quillibrace: That, Mr Blottisham, is generally what one discovers at the end of an essay rather than the beginning.
Mr Blottisham: Very inconvenient.
The shape of the problem
Miss Stray: It seems to me that the argument has shifted.
Professor Quillibrace: How so?
Miss Stray: We began by asking what happens to information at a black hole.
Mr Blottisham: Then we asked what "lost" means.
Miss Stray: Then we asked what the horizon is.
Professor Quillibrace: And?
Miss Stray: Now I'm wondering whether the real question is what we mean by where.
Professor Quillibrace looked pleased.
Professor Quillibrace: Yes.
Mr Blottisham: That sounds ominous.
Professor Quillibrace: It is promising.
Miss Stray: Because if information can be encoded in correlations, and if correlations are not necessarily localised in ordinary spatial objects, then asking where information is may be like asking where a relationship is.
Mr Blottisham: In the room?
Miss Stray: Between the people.
Mr Blottisham: That seems annoyingly sensible.
The Common Room gets quiet
For a while nobody spoke.
Outside, the gardener was pushing a wheelbarrow across the quadrangle.
Mr Blottisham watched him.
Mr Blottisham: I have just realised something.
Professor Quillibrace: This should be interesting.
Mr Blottisham: We started with a line.
Miss Stray: The horizon.
Mr Blottisham: Yes.
Miss Stray: And now the line has disappeared.
Professor Quillibrace: Not disappeared.
Mr Blottisham: Become less substantial.
Professor Quillibrace: Better.
Miss Stray: It was never a wall.
Mr Blottisham: It was a difference in possible futures.
Professor Quillibrace: Yes.
Mr Blottisham: And the more we investigate it, the more the boundary seems to belong to the relations rather than the things.
Professor Quillibrace nodded.
Professor Quillibrace: That is the interesting lesson.
Miss Stray: A boundary can be real without being a thing.
Professor Quillibrace: And information can be real without being a substance.
Mr Blottisham: Which means the two things we thought we were locating—
He paused.
Mr Blottisham: —may not be the sort of things that have locations.
Miss Stray smiled.
Miss Stray: Then perhaps the black hole isn't hiding information somewhere.
Professor Quillibrace: Perhaps.
Miss Stray: Perhaps it is changing the relationships in which information can be found.
Professor Quillibrace looked once more through the window.
Professor Quillibrace: And if that is so, then the horizon has done something rather remarkable.
Mr Blottisham: What?
Professor Quillibrace: It has turned a question about location into a question about structure.
Mr Blottisham considered this.
Mr Blottisham: I suppose that's progress.
Professor Quillibrace: It may be.
Mr Blottisham: Although I still think a filing cabinet would have been easier.
Miss Stray: Perhaps.
She closed the essay.
Miss Stray: But I don't think the universe is obliged to be easy to file.
There was a pause.
Professor Quillibrace: An unfortunate omission in the original design.
Mr Blottisham: I shall raise it with the appropriate committee.
And the Common Room returned, with some relief, to its tea.