The Senior Common Room at St Anselm’s had acquired a new object.
It was not a particularly interesting object.
It was a small blackboard.
Professor Quillibrace had placed it beside the fireplace.
Mr Blottisham regarded it with suspicion.
Miss Elowen Stray was reading a book.
“What is that for?” asked Blottisham.
“Black holes.”
Blottisham looked at the board.
“There isn't one.”
“Precisely.”
“I mean there isn't a black hole on it.”
“That,” said Quillibrace, “is because I have not yet drawn one.”
Blottisham looked relieved.
“Good.”
Quillibrace picked up a piece of chalk.
Then he wrote:
BLACK HOLE
Blottisham nodded.
“There.”
“There what?”
“A black hole.”
Quillibrace looked at the words.
“That is two words.”
“Yes.”
“Neither of which is a black hole.”
Blottisham stared at him.
“This is going to be one of those afternoons.”
Elowen looked up from her book.
“I suspect it already is.”
I. The irresistible name
“What is wrong with the name?” asked Blottisham.
“Nothing,” said Quillibrace.
“Good.”
“It is extremely successful.”
“Exactly.”
Quillibrace underlined the words.
“Which is precisely why it deserves suspicion.”
Blottisham frowned.
“Suspicion?”
“Consider what happens when you hear the phrase black hole.”
“A dark hole.”
“Yes.”
“A hole from which nothing comes back.”
“Yes.”
“Something falls into it.”
“Yes.”
“Excellent. I think the name works.”
“It works magnificently.”
“Then why are you objecting?”
“I am not objecting to the metaphor.”
“You just said it deserves suspicion.”
“Successful metaphors deserve suspicion precisely because they cease to feel like metaphors.”
Elowen closed her book.
“That may be the difficulty.”
Blottisham looked at her.
“What difficulty?”
“We no longer notice what the name asks us to imagine.”
Quillibrace nodded.
“A black thing.”
He wrote:
BLACK
“A hole.”
He wrote:
HOLE
“Put them together.”
He drew a large circle.
“Something dark.”
Blottisham nodded.
“Something with an opening.”
Another nod.
“Something into which things can fall.”
“Yes.”
“Something from which nothing returns.”
“Yes.”
Quillibrace put down the chalk.
“Now tell me which of those things general relativity actually requires us to imagine.”
Blottisham paused.
“The hole.”
“No.”
“The darkness.”
“No.”
“The opening?”
“No.”
“The falling?”
“Not in the sense you mean.”
Blottisham looked annoyed.
“Well, what is left?”
“The geometry.”
II. The hole that isn't a hole
Quillibrace wrote:
GEOMETRY
“A black hole,” he said, “is not a hole punched through spacetime like a tunnel through a sheet.”
“So there isn't an opening.”
“Not in the ordinary sense.”
“Then where does everything go?”
“Into the black-hole interior.”
Blottisham pointed triumphantly.
“There! You just said interior.”
“I did.”
“So there is an inside.”
“Yes.”
“And an outside.”
“Yes.”
“Therefore—”
“No.”
Blottisham stopped.
“You cannot say yes and no at the same time.”
“I can when the words are being used in different senses.”
Elowen smiled.
“This is perhaps the central difficulty.”
Blottisham looked at her.
“What is?”
“The vocabulary survives while the relationship changes.”
Quillibrace nodded.
“Exactly.”
He wrote:
INSIDE / OUTSIDE
“A black hole has an interior and an exterior in a precise geometrical and causal sense.”
“Which sounds like an ordinary inside and outside.”
“It does.”
“But isn't.”
“Not necessarily.”
Blottisham looked at the drawing.
“So it isn't a container.”
“Correct.”
“But it has an inside.”
“Yes.”
“That seems unfair.”
“Reality is frequently unfair to language.”
III. The event horizon
Quillibrace drew a line around the circle.
“The event horizon.”
Blottisham pointed.
“The wall.”
“No.”
“The boundary.”
“Yes.”
“The surface.”
“In a certain mathematical sense.”
“The membrane.”
“No.”
“The barrier.”
“No.”
“Then what is it?”
“A boundary in the causal structure of spacetime.”
Blottisham looked at him.
“That is not remotely the same thing.”
“Correct.”
Elowen leaned forward.
“That difference is crucial.”
Quillibrace continued.
“If you put a fence around a field, the fence is an object. It occupies space. It physically separates two regions.”
“Yes.”
“If you build a wall between two rooms, the wall is there whether or not anyone is looking at it.”
“Yes.”
“If you reach the wall, you hit it.”
“Generally.”
“The event horizon does not work like that.”
“Why not?”
“Because it is not defined by a material surface. It is defined by what signals can and cannot do.”
Blottisham looked puzzled.
“So the horizon isn't something you hit.”
“Not necessarily.”
“What happens if you cross it?”
“You cross it.”
“That sounds obvious.”
“It is.”
“And?”
“And for a sufficiently large black hole, a freely falling observer need not notice anything locally dramatic at the moment of crossing.”
Blottisham stared at him.
“You mean there is no sign?”
“No.”
“No alarm?”
“No.”
“No flashing light?”
“No.”
“No cosmic announcement?”
Quillibrace looked at him.
“I believe you have now exhausted the possible safety features.”
Blottisham frowned.
“But if the horizon is so important—”
“It is.”
“Why can't you feel it?”
“Because its significance is global rather than necessarily local.”
Elowen nodded.
“That is the strange part.”
IV. A very unusual boundary
Quillibrace erased the line and redrew it.
“Think about ordinary boundaries.”
“A wall.”
“A fence.”
“A coastline.”
“A border.”
“Precisely. They separate regions because something physically occupies the boundary.”
He pointed to the horizon.
“The event horizon is different.”
“How?”
“It tells us about possible futures.”
Blottisham looked at him.
“Futures?”
“If you are outside the horizon, there are future-directed paths along which light can reach distant observers.”
“Yes.”
“If you are inside, there are no such future-directed paths leading back to that exterior region.”
“So the boundary tells us what can happen.”
“More precisely, what causal connections are available.”
Elowen smiled.
“So it isn't primarily saying, ‘This kind of stuff ends here.’”
“No.”
“It is saying, ‘From here, these possible causal futures are no longer available.’”
“Exactly.”
Blottisham considered this.
“That is a very peculiar sort of boundary.”
Quillibrace nodded.
“An unusually consequential one.”
“And you still call it a surface.”
“Because the mathematics permits a useful geometrical description of it as a surface.”
“But it isn't a surface.”
“It is a surface.”
Blottisham threw up his hands.
“You are doing it again.”
“Doing what?”
“Saying something is something and then immediately saying it isn't.”
Elowen laughed.
“Perhaps the problem is that surface has more than one conceptual use.”
Quillibrace nodded.
“A useful surface need not be a material surface.”
Blottisham sighed.
“I preferred fences.”
V. Inside and outside
Elowen walked to the board.
“Perhaps we should examine the word inside.”
“Again?” asked Blottisham.
“Again.”
She wrote:
INSIDE
“A box has an inside.”
“Yes.”
“A bottle has an inside.”
“Yes.”
“A room has an inside.”
“Yes.”
“And what do these have in common?”
“They contain things.”
“Exactly.”
“So when we say that something is inside a black hole, we naturally imagine containment.”
Blottisham nodded.
“Which is what I have been saying.”
“But the event horizon is not the wall of a container.”
“So?”
“So the word inside is doing something different.”
“What?”
“It is marking a region defined by causal structure.”
Blottisham looked at Quillibrace.
“Can I say something is inside without there being a container?”
“Certainly.”
“Where?”
“In mathematics.”
“That doesn't count.”
“On a map.”
“That counts.”
“Inside a triangle.”
“Yes.”
“There is no container.”
Blottisham paused.
“That is annoying.”
“It is also useful.”
Elowen continued.
“We often use spatial language to express relationships that are not literally about containment.”
“Such as?”
“Inside a political boundary.”
“That's still a boundary.”
“Yes, but not necessarily a wall.”
“Inside a set.”
“Exactly.”
“Inside a category.”
“Yes.”
Blottisham looked thoughtful.
“So perhaps inside doesn't always mean ‘contained by a thing’.”
“Now you're getting somewhere.”
Quillibrace smiled.
“Against considerable resistance.”
VI. Falling
Blottisham picked up the chalk.
“Fine. Let me try.”
He drew a small dot.
“This is an astronaut.”
“Very good.”
He drew the black hole.
“This is the black hole.”
“Yes.”
“And the astronaut falls into it.”
Quillibrace nodded.
“Now tell me what you mean by falls.”
Blottisham hesitated.
“Moves toward it.”
“Toward what?”
“The black hole.”
“Which is?”
“A region.”
“Good.”
“So the astronaut moves toward the region.”
“Better.”
“And then crosses the horizon.”
“Yes.”
“And then falls deeper inside.”
“Yes.”
“Where?”
Quillibrace waited.
Blottisham looked at the drawing.
“Toward the singularity.”
“Eventually, according to the classical picture.”
“So it is still like falling down a well.”
“Only if you are prepared to make the well into a rather peculiar piece of spacetime geometry.”
Elowen smiled.
“The important thing is that the astronaut is not falling through an opening into a pre-existing cavity.”
“What is happening, then?”
Quillibrace took the chalk.
“The astronaut is following a worldline through curved spacetime.”
Blottisham looked at the line.
“That doesn't sound like falling.”
“It is the more precise account of what falling means in general relativity.”
“So gravity isn't pulling the astronaut toward the hole?”
“Not in the Newtonian sense.”
“But the astronaut moves.”
“Yes.”
“Toward the black hole.”
“Yes.”
“Because of the geometry.”
“Yes.”
Blottisham stared at the board.
“I am beginning to see why physicists use metaphors.”
Quillibrace nodded.
“So am I.”
VII. The stage moves
Elowen looked at the diagram.
“We usually imagine space as the stage.”
“Yes,” said Quillibrace.
“Things move through space.”
“Yes.”
“And time passes.”
“Yes.”
“But general relativity refuses to keep space and time neatly separated.”
“Correct.”
“Spacetime has geometry.”
“Yes.”
“And that geometry determines the possible trajectories of matter and light.”
“Yes.”
“So the black hole is not simply an object sitting on the stage.”
“No.”
“It is a configuration of the stage itself.”
Quillibrace considered the phrase.
“Not bad.”
“Not bad?”
“Acceptable as a first approximation.”
Blottisham pointed at the diagram.
“So the stage is part of the actor.”
Quillibrace frowned.
“That metaphor is significantly worse.”
“But you understand what I mean.”
“I do.”
“Then it can't be that bad.”
“It can.”
Elowen laughed.
“But perhaps the point is that the distinction between object and background becomes unstable.”
Quillibrace nodded.
“In general relativity, geometry is not a passive container in the ordinary sense. It participates in determining physical possibilities.”
Blottisham looked impressed.
“So the black hole isn't merely in spacetime.”
“Correct.”
“It is a particular configuration of spacetime.”
“Precisely.”
“That is rather different from a hole.”
“Very.”
VIII. Who sees what?
Elowen returned to her chair.
“Now suppose an astronaut falls toward the horizon while someone else watches from far away.”
Blottisham nodded.
“The distant observer sees the astronaut approach the horizon.”
“Yes.”
“And eventually?”
“The received signals become increasingly delayed and redshifted.”
“So the distant observer doesn't simply watch the astronaut cross.”
“Not in the naive way.”
“But the astronaut crosses.”
“Yes.”
Blottisham frowned.
“How can both be true?”
“Because they are different descriptions associated with different paths through spacetime.”
“Then who is right?”
“Both.”
Blottisham looked annoyed.
“I dislike answers like that.”
“Relativity has been known to survive your preferences.”
Elowen smiled.
“The important point is that the horizon isn't an ordinary object whose crossing has one universal appearance for every observer.”
“Yet it isn't imaginary.”
“Exactly.”
“So observation matters.”
“Yes.”
“But the horizon remains physically real.”
“Yes.”
Blottisham shook his head.
“It's a very badly behaved boundary.”
Quillibrace nodded.
“Now you are beginning to appreciate it.”
IX. Local and global
Quillibrace wrote two words:
LOCAL
GLOBAL
“The horizon is locally uneventful for a sufficiently large freely falling observer.”
“And globally decisive.”
“Exactly.”
Blottisham looked at the two words.
“So I can cross something without noticing that I crossed it.”
“Yes.”
“That seems impossible.”
“You cross the equator without necessarily noticing.”
“That is different.”
“Why?”
“There isn't an equator around a black hole.”
Quillibrace paused.
“I shall not ask you to reconsider that sentence.”
Elowen laughed.
“The deeper point is that importance does not require local drama.”
She continued.
“A feature of spacetime can have enormous significance for the global causal structure without presenting itself as a local physical barrier.”
Blottisham nodded slowly.
“So the horizon matters because of what happens to possible future paths, not because it is something you bump into.”
“Precisely.”
“That's rather elegant.”
Quillibrace looked at him.
“I am relieved to hear it.”
X. The singularity
Blottisham looked at the centre of the diagram.
“And the singularity?”
Quillibrace sighed.
“The other word that causes trouble.”
He wrote:
SINGULARITY
Blottisham nodded.
“The infinitely dense point.”
“No.”
“The tiny point at the centre.”
“No.”
“The place where everything gets crushed.”
“No.”
“What, then?”
“In classical general relativity, a singularity is associated with a breakdown of the spacetime description.”
“So it isn't an object?”
“Not necessarily.”
“Then what is it?”
“One important mathematical characterisation involves geodesic incompleteness.”
Blottisham stared.
“I wish you hadn't said that.”
“I thought you would.”
Elowen smiled.
“The essential point is that certain paths through spacetime cannot be extended indefinitely within the classical theory.”
“So the theory stops giving us a complete description.”
“Exactly.”
Blottisham looked at the word.
“Then when people say there is an infinitely dense point at the centre…”
“They are translating a mathematical limit into a physical picture.”
“Is that wrong?”
“Not necessarily as an intuition.”
“But it might suggest that the theory has confidently predicted an actual little object.”
“Yes.”
“And it hasn't.”
“Not in that simple sense.”
Elowen nodded.
“Sometimes the boundary of a theory gets represented as though it were a feature of the world.”
Quillibrace smiled.
“A remarkably persistent human habit.”
XI. The theory's boundary becomes an object
Blottisham looked puzzled.
“Give me another example.”
Quillibrace thought.
“A divergence can become ‘infinite density’.”
“Right.”
“A breakdown of a classical description can become ‘the singularity’.”
“Yes.”
“A causally inaccessible region can become ‘inside the hole’.”
“Yes.”
Elowen added:
“And a mathematical boundary can become a physical surface.”
Blottisham looked at the board.
“So we turn limits of description into things.”
“Sometimes.”
“Why?”
“Because things are easier to imagine than limits.”
Blottisham nodded.
“That seems reasonable.”
“It is.”
“Then why are you complaining?”
“I am not complaining.”
“You're warning us.”
“Quite.”
Elowen smiled.
“The metaphors are useful because they make the abstract structure imaginable. But the danger comes when we forget which parts belong to the mathematics and which parts belong to the picture.”
Blottisham nodded.
“So the picture is a bridge.”
“Good.”
“But you can mistake the bridge for the landscape.”
Quillibrace looked at him.
“That is rather good.”
Blottisham brightened.
“I have my moments.”
XII. What does “black” mean?
Elowen pointed to the first word.
“We have not yet dealt with black.”
Blottisham looked at the board.
“Black means black.”
“No.”
“Here we go.”
Quillibrace intervened.
“Blackness ordinarily refers to a perceptual property.”
“A black surface absorbs light.”
“Yes.”
“But a black hole is not black in that sense.”
“It appears black because light from within the relevant region cannot reach a distant observer.”
“So blackness is relational.”
“Exactly.”
Elowen nodded.
“Which makes the word unexpectedly interesting.”
“How?”
“To say that something is black in the ordinary sense is to describe how it appears to an observer.”
“Yes.”
“And to say that a black hole is black is, more fundamentally, to describe a limitation on what information can reach a distant observer.”
Blottisham looked at her.
“So black already contains a relation between region and observer.”
“Yes.”
“And information?”
“Also relational.”
Quillibrace nodded.
“Now we are approaching the real difficulty.”
XIII. The hole becomes a relation
Quillibrace erased the drawing.
Then he wrote:
WHAT CAN CONNECT TO WHAT?
“A black hole,” he said, “can be understood less as a thing containing darkness and more as a region whose causal structure determines which signals can reach which exterior regions.”
Blottisham looked at him.
“That sounds less like an object.”
“It is.”
“More like a relation.”
“Exactly.”
Elowen nodded.
“The black hole has mass. It has angular momentum. It can merge. It can interact gravitationally.”
“Yes.”
“So it is certainly physical.”
“Of course.”
“But its defining feature is relational.”
“Precisely.”
Blottisham thought about this.
“A black hole is partly what it does to possible relationships.”
Quillibrace looked at him.
“That is a surprisingly good formulation.”
“Thank you.”
“Do not become accustomed to it.”
Elowen smiled.
“The black hole is physical, but its most distinctive property concerns the organisation of possible causal relations.”
“So the black hole isn't just something.”
“It is also a structure.”
“A structure of relations.”
“Yes.”
Blottisham looked at the empty board.
“That sounds rather less like a hole.”
“Indeed.”
XIV. The information problem returns
There was a pause.
Then Blottisham said:
“Wait.”
Quillibrace looked at him.
“If a black hole isn't really a container…”
“Yes?”
“…then what does it mean to say that information is inside it?”
Quillibrace smiled.
“Excellent.”
Blottisham looked pleased.
“Thank you.”
“I was speaking to the question.”
“Oh.”
Elowen leaned forward.
“That is exactly where the previous discussion returns.”
“If the horizon isn't a wall…”
“…what does it mean for information to cross it?”
“If blackness means that something cannot reach a particular observer…”
“…does invisibility amount to destruction?”
“If the interior isn't simply the inside of a box…”
“…what does it mean to say that information is stored there?”
Blottisham looked at the list.
“So the black-hole metaphor has already shaped the information paradox.”
“Yes,” said Elowen.
“Before we've even started discussing information.”
“Exactly.”
Quillibrace nodded.
“That is why the metaphor matters.”
XV. A conceptual horizon
Elowen stood and took the chalk.
She wrote:
INSIDE / OUTSIDE
Then:
LOCAL / GLOBAL
Then:
ACCESSIBLE / INACCESSIBLE
Then:
OBJECT / REGION
Then:
SURFACE / STRUCTURE
Then:
SPACE / TIME
Then:
DESCRIPTION / REALITY
Blottisham looked at the list.
“That is quite a lot of trouble for one hole.”
Quillibrace smiled.
“Especially one that isn't a hole.”
Elowen pointed to the pairs.
“Each distinction seemed obvious.”
“Yes.”
“But the black hole complicates each one.”
“Inside and outside become causal.”
“Local and global become different descriptions of the same geometry.”
“Object and region become difficult to separate.”
“Surface and structure come apart.”
“Space and time become intertwined.”
“And description and reality…”
Quillibrace paused.
“That one is always troublesome.”
Blottisham looked at him.
“Why?”
“Because the world does not come with labels attached.”
Elowen smiled.
“We bring the labels.”
XVI. The metaphor as a room
Blottisham looked again at the words BLACK HOLE.
“I think I understand what you're saying.”
Quillibrace raised an eyebrow.
“Do tell.”
“The metaphor helps us get into the problem.”
“Yes.”
“But then it keeps us inside.”
There was a brief silence.
Elowen smiled.
“That is rather good.”
Quillibrace nodded.
“Very good.”
Blottisham looked pleased.
“So the metaphor is like a room.”
Quillibrace frowned.
Blottisham laughed.
“I know. I know.”
Elowen continued.
“It gives us a place from which to think.”
“And then,” said Quillibrace, “we may mistake the room for the territory.”
Blottisham nodded.
“So black hole is useful.”
“Very.”
“But dangerous.”
“Potentially.”
“Because it suggests a hole.”
“Yes.”
“Which isn't a hole.”
“Yes.”
“And an inside.”
“Yes.”
“Which isn't an inside in the ordinary container sense.”
“Yes.”
“And a surface.”
“Yes.”
“Which isn't a surface you can bump into.”
“Yes.”
“And blackness.”
“Yes.”
“Which isn't really a colour.”
Quillibrace looked at him.
“You have finally grasped the title.”
XVII. The question gets harder
The room was quiet.
Elowen looked at the blackboard.
“We began with a simple question.”
“What is a black hole?”
“And we have made it harder.”
“Considerably.”
“But perhaps more precise.”
“Yes.”
“A black hole is not a cosmic cavity.”
“No.”
“Not a material object sitting inside otherwise ordinary space.”
“No.”
“Not a container with a wall.”
“No.”
“The event horizon is a causal boundary.”
“Yes.”
“The interior is defined through the causal structure of spacetime.”
“Yes.”
“The singularity may represent a breakdown of the classical description rather than a conventional object.”
“Yes.”
“And blackness is fundamentally about what can reach an observer.”
“Yes.”
Blottisham looked at the board.
“So perhaps the black hole is best thought of as a structure of possible relations.”
Quillibrace nodded.
“That would be a productive way to proceed.”
Elowen smiled.
“And now we have a problem.”
“What problem?”
“The word information.”
Blottisham sighed.
“I knew there was another one.”
XVIII. The next question
Quillibrace picked up his coat.
“The next time we meet, we shall have to ask what information actually is.”
Blottisham looked suspicious.
“We already did that.”
“We began to.”
“And?”
“We discovered that information is not obviously a thing.”
Blottisham groaned.
“Please don't tell me it isn't something you can put inside something.”
“Not in the straightforward sense.”
“And it can't be carried around like a parcel.”
“Not necessarily.”
“And it can't simply be lost.”
“Again, not necessarily.”
“And now you're going to tell me it isn't stored.”
Quillibrace paused.
“It can be useful to speak of storage.”
Blottisham looked hopeful.
“But?”
“But perhaps storage is another metaphor.”
Blottisham closed his eyes.
“Elowen?”
“Yes?”
“Does everything have to become a metaphor?”
She thought for a moment.
“No.”
Blottisham opened his eyes.
“Good.”
“Only everything we use to talk about it.”
He closed them again.
Quillibrace smiled.
“Come along.”
They walked toward the door.
Behind them, the blackboard remained covered with conceptual distinctions.
INSIDE / OUTSIDE
LOCAL / GLOBAL
ACCESSIBLE / INACCESSIBLE
OBJECT / REGION
SURFACE / STRUCTURE
SPACE / TIME
DESCRIPTION / REALITY
And above them all:
BLACK HOLE
Blottisham stopped.
“One thing.”
Quillibrace sighed.
“Yes?”
“If it isn't a hole…”
“Yes?”
“…why don't we call it something else?”
Elowen smiled.
“Because the metaphor was too good.”
Quillibrace opened the door.
“And because by the time we discovered how much trouble it caused…”
He paused.
“…everyone had already learned to use it.”
Blottisham nodded.
“That's rather like language.”
Quillibrace looked at him.
“Precisely.”
The door closed.
The blackboard remained.
The hole was still not there.
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