The Senior Common Room at St Anselm’s was unusually quiet.
Professor Quillibrace was reading a paper.
Mr Blottisham was reading the newspaper.
Miss Elowen Stray was looking out of the window.
There was, therefore, no obvious reason for the conversation to begin.
It began anyway.
“I have always thought,” said Blottisham, lowering the newspaper, “that the black hole information paradox is rather badly named.”
Quillibrace did not look up.
“Why?”
“Because it isn't really a paradox.”
“Excellent.”
Blottisham paused.
“Excellent?”
“Yes. You have reached a conclusion. We can now investigate why.”
“I mean,” said Blottisham, “that the information is obviously either there or it isn't.”
Quillibrace turned a page.
“A devastating contribution to theoretical physics.”
“I am being perfectly serious.”
“I feared as much.”
Elowen smiled.
“What do you think the paradox is, then, Mr Blottisham?”
“Quite simple. Something falls into a black hole. The black hole evaporates. The information comes out—or it doesn't.”
“Ah,” said Quillibrace.
Blottisham looked at him suspiciously.
“What?”
“You have already used the word out.”
“Of course.”
“Where did you obtain it?”
“From the English language, Professor.”
“Then I fear the English language may be partly responsible for the problem.”
Elowen turned from the window.
“That may be the interesting point.”
Blottisham sighed.
“I knew this was going to become philosophical.”
“It already has,” said Quillibrace. “The question is whether we have noticed.”
I. A problem created by success
Elowen sat down.
“Perhaps we should begin with the physics.”
“Thank you,” said Blottisham.
Quillibrace closed the paper.
“A black hole, in general relativity, contains a region from which nothing that crosses the event horizon can return to the outside.”
“Precisely,” said Blottisham. “Things go in. Nothing comes out.”
Quillibrace raised one finger.
“Classically.”
“Yes.”
“From inside the event horizon.”
“Yes.”
“Into the outside.”
“Yes.”
“Which means that you have already constructed an entire spatial architecture.”
Blottisham stared at him.
“I have described a black hole.”
“You have described a black hole using inside, outside, in and out.”
“That is how black holes work.”
“That is how we describe black holes.”
Elowen leaned forward.
“Those aren't necessarily the same thing.”
Blottisham looked between them.
“Are you suggesting there isn't an inside?”
“No,” said Elowen. “I'm suggesting that we should be careful about what the word inside contributes to the explanation.”
Quillibrace nodded.
“Quite.”
He took a pencil.
“General relativity gives us an extraordinarily precise account of the geometry of spacetime. The event horizon is not merely an imaginary line drawn around a cosmic object. It has a precise mathematical role.”
“And yet,” said Elowen, “our ordinary description immediately turns it into a kind of surface.”
“A boundary,” said Blottisham.
“Yes.”
“A boundary between inside and outside.”
“Yes.”
“So what's wrong with that?”
“Possibly nothing,” said Elowen. “But we should notice that the picture comes before the interpretation.”
Quillibrace looked mildly pleased.
“Miss Stray has put her finger on the problem.”
Blottisham frowned.
“What problem?”
“The problem that we have not yet reached.”
II. Enter quantum theory
Quillibrace continued.
“Quantum mechanics tells us something else. The evolution of a closed quantum system is unitary.”
Blottisham nodded.
“Meaning?”
“Meaning that the quantum state evolves in such a way that the distinctions encoded in the initial state are not simply erased by the fundamental dynamics.”
“So information is preserved.”
“In the relevant technical sense.”
“What other sense is there?”
Elowen smiled.
“That is precisely the question.”
Blottisham looked annoyed.
“I know what information is.”
Quillibrace raised an eyebrow.
“Do you?”
“Yes.”
“Excellent. Define it.”
Blottisham opened his mouth.
Then closed it.
“It is… information.”
Quillibrace waited.
Elowen intervened.
“Perhaps we should distinguish several things.”
She began counting on her fingers.
“A physical state.”
“A pattern in that state.”
“Something that can be recovered from the pattern.”
“Someone's knowledge of it.”
“And perhaps the meaning attributed to it.”
Blottisham looked at the list.
“They're all information.”
“Related,” said Elowen. “Not identical.”
Quillibrace nodded.
“In physics, information concerns the distinctions between possible physical states and the correlations that can be preserved through physical evolution. It is not necessarily a message. It is not necessarily knowledge. It is not necessarily meaning.”
“So when physicists say information is preserved—”
“They are not saying that the universe keeps a copy of the newspaper.”
Blottisham glanced at his newspaper.
“I hadn't thought it did.”
“You were about to.”
“I was not.”
“You were.”
Elowen smiled.
“Perhaps the important point is that information is relational.”
Quillibrace looked at her.
“Go on.”
“If we say that two quantum states contain different information, what matters is that they are physically distinguishable as different states. Information concerns the structure of the distinction.”
Blottisham looked dissatisfied.
“That's awfully abstract.”
“Yes,” said Elowen.
“Can't we just say the information is in the state?”
Quillibrace put down his pencil.
“We can.”
“And?”
“And then we have to explain what in means.”
Blottisham stared at him.
“I see where this is going.”
“No,” said Quillibrace. “But you are beginning to suspect.”
III. Hawking enters the room
“The difficulty,” said Elowen, “appears when black holes become quantum objects.”
“Hawking radiation,” said Blottisham.
“Indeed.”
Quillibrace resumed.
“Hawking's calculation showed that a black hole should emit radiation. The radiation has a thermal character. The black hole therefore has thermodynamic properties. It can have a temperature. It can lose energy. It can lose mass. In principle, it can evaporate.”
“So far, so good.”
“Rather remarkable, actually,” said Elowen.
“Certainly.”
Blottisham nodded.
“And then the black hole disappears.”
“Eventually, in the idealised scenario.”
“And everything that fell into it?”
Quillibrace looked at him.
“Yes.”
“That is the problem.”
“That is one way of putting it.”
Blottisham leaned back.
“If the radiation is thermal, then it doesn't tell us what specifically formed the black hole.”
“Precisely.”
“So two different initial states could produce the same final thermal radiation.”
“In the naive version of the argument, yes.”
“And therefore the information is lost.”
Quillibrace nodded.
“Now we have our paradox.”
Blottisham looked triumphant.
“There. I told you it was simple.”
“No.”
“No?”
“You have identified the contradiction.”
“Isn't that what a paradox is?”
“Not quite.”
Elowen looked thoughtful.
“The more interesting question is what kind of loss we're talking about.”
IV. Lost, inaccessible, destroyed
Quillibrace rose and went to the blackboard.
He wrote:
INACCESSIBLE ≠ DESTROYED
Blottisham read it.
“That's obvious.”
“Good.”
Quillibrace wrote beneath it:
SCRAMBLED ≠ DESTROYED
“Also obvious.”
Then:
UNREADABLE ≠ DESTROYED
“Yes.”
“And now,” said Quillibrace, “the important one.”
He wrote:
DISTINCT STATES → IDENTICAL FINAL STATE
Blottisham stopped smiling.
Elowen nodded.
“That is stronger.”
“Much stronger,” said Quillibrace.
“Suppose,” said Elowen, “I encrypt a message and lose the key. I cannot read it. That doesn't mean the information has ceased to exist physically.”
“Correct.”
“Suppose the information becomes distributed among an enormous number of particles in an impossibly complicated pattern.”
“Again,” said Quillibrace, “practical recovery may be impossible without fundamental information having been destroyed.”
“But if two genuinely different initial quantum states evolve into exactly the same final state…”
“Then the distinction itself has disappeared from the fundamental description.”
Blottisham frowned at the board.
“So the paradox isn't about whether anybody can get the information back.”
“Correct.”
“It's about whether the final physical state still contains the distinction between different possible pasts.”
“Now you understand the problem.”
Blottisham looked pleased.
“Excellent.”
Quillibrace erased the word.
“I wouldn't go that far.”
V. The box
Elowen reached for a piece of paper.
“Let's make it concrete.”
She wrote:
THE OWL HAS ARRIVED
Then underneath:
THE OWL HAS LEFT
“Suppose these are two possible messages in a box.”
Blottisham nodded.
“We throw the box into a black hole.”
“Yes.”
“The black hole evaporates.”
“Yes.”
“And then?”
“Where did the message go?”
Blottisham smiled.
“Exactly.”
Elowen shook her head.
“No. Notice the question.”
“What about it?”
“You have assumed that the message is something that can go somewhere.”
Blottisham looked at the two sentences.
“Well, it was in the box.”
“Was it?”
“The message was encoded in the physical state of the box.”
“Yes.”
“So it was in the box.”
“That's a useful description.”
“Thank you.”
“But it encourages a picture.”
“What picture?”
“That the information is a kind of object contained by the box.”
Quillibrace nodded.
“And once we have the object, we can imagine it being transferred.”
“From the box to the black hole.”
“Yes.”
“Then from the black hole to the radiation.”
“Yes.”
“And if we can't find it, it has been lost.”
“Yes.”
Blottisham looked from one to the other.
“That's not right?”
“It may be useful,” said Elowen. “But it is not innocent.”
Quillibrace returned to the board.
“Storage.”
He wrote it.
“Transfer.”
He wrote it.
“Destruction.”
Another word.
“Encoding.”
Another.
“Recovery.”
Another.
“There is nothing wrong with these words,” he said. “The danger begins when the metaphor ceases to be visible.”
Blottisham considered this.
“So information isn't a thing.”
“Not in the ordinary sense.”
“Then what is it?”
Elowen answered quietly.
“A way of talking about distinctions and relations among possible physical states.”
Blottisham looked disappointed.
“That's much less convenient.”
“Reality is under no obligation to be convenient.”
Quillibrace sat down.
“Nor to be intuitively picturable.”
VI. The black hole as a conceptual machine
Elowen glanced at the blackboard.
“Look at what we've done.”
Quillibrace waited.
“We began with a black hole.”
“A hole,” said Blottisham.
“Yes. Then an event horizon.”
“A boundary.”
“Things fall into it.”
“An interior.”
“Radiation comes out.”
“An exterior.”
“Information is stored.”
“A container.”
“Information is lost.”
“An object.”
“Information is encoded.”
“A message.”
“And then retrieved.”
“A destination.”
Quillibrace smiled.
“An impressive piece of conceptual architecture.”
Blottisham looked around the room.
“Where?”
“In your language.”
Elowen nodded.
“And language is doing more than reporting the physics. It is helping us construct the conceptual space in which the physics becomes intelligible.”
“Is that bad?”
“No,” she said. “It is unavoidable.”
Quillibrace added:
“And useful.”
Blottisham looked relieved.
“But?”
“Useful metaphors become dangerous when they become invisible.”
He pointed to stored.
“Information isn't necessarily sitting somewhere.”
He pointed to lost.
“Loss doesn't necessarily mean destruction.”
He pointed to inside.
“And inside and outside may not carry the metaphysical significance our ordinary spatial language suggests.”
Blottisham folded his arms.
“So what are we supposed to do?”
“Continue using the metaphors.”
“What?”
“More carefully.”
VII. The two stories
Quillibrace returned to his chair.
“Let us put the problem in its simplest form.”
He counted them off.
“Quantum mechanics tells us that physical evolution is unitary.”
“One.”
“General relativity, combined with Hawking's semiclassical calculation, gives us black holes that radiate thermally and can evaporate.”
“Two.”
“If the final radiation contains no sufficient structure to distinguish the different quantum states that formed the black hole, then distinct initial states appear to evolve into the same final state.”
“Three.”
“Which conflicts with the ordinary expectation of unitary quantum evolution.”
“Four.”
Blottisham nodded.
“So one of the theories is wrong.”
“Possibly.”
“Hawking's calculation is wrong.”
“Possibly.”
“Or the information gets out somehow.”
“Possibly.”
“Or…”
He hesitated.
“Or?”
Blottisham glanced at Elowen.
“Perhaps we're asking the wrong question.”
Elowen smiled.
“Now you're getting ahead of yourself.”
Quillibrace looked mildly impressed.
“Remarkably, Mr Blottisham has accidentally arrived at the beginning of the interesting part.”
“I do that occasionally.”
“Against considerable odds.”
VIII. When successful theories collide
Elowen looked at the rain beginning against the window.
“What makes the paradox so interesting is that it isn't simply a failure of one theory.”
“No,” said Quillibrace.
“Quantum mechanics works.”
“Yes.”
“General relativity works.”
“Yes.”
“Hawking's calculation is not the product of somebody forgetting a minus sign.”
“Correct.”
“Each framework has extraordinary empirical and conceptual success.”
“And yet,” said Quillibrace, “when they are brought together in this regime, something becomes unstable.”
Blottisham nodded.
“That's rather like putting two perfectly good chairs on top of one another.”
Quillibrace considered this.
“An unexpectedly good analogy.”
“Thank you.”
“It fails in several respects.”
“I knew there had to be a catch.”
Elowen laughed.
“But perhaps that is the point. The paradox arises not because our best descriptions have simply failed independently, but because their conceptual commitments become difficult to reconcile when both are required.”
Quillibrace nodded.
“And that is precisely the kind of situation in which scientific concepts begin to reveal their hidden assumptions.”
Blottisham looked at the board.
“So physics isn't necessarily telling us that one picture is false.”
“It may eventually do so.”
“But not necessarily.”
“No.”
“It may be telling us that the pictures don't fit together.”
“Exactly.”
Elowen smiled.
“And perhaps that is why the conceptual vocabulary becomes interesting.”
IX. The frontier
“Do we know the answer?” asked Blottisham.
“Not in the sense you mean.”
“But there are proposals.”
“Many.”
“Holography?”
“Yes.”
“Black-hole complementarity?”
“Yes.”
“AdS/CFT?”
“Yes.”
“The Page curve?”
“Yes.”
“Replica wormholes?”
“Yes.”
“Firewalls?”
“Yes.”
Blottisham looked at Elowen.
“That's quite a lot of yes.”
“It is,” she said.
“So which one is right?”
Quillibrace picked up the paper again.
“That remains a matter of active research.”
Blottisham frowned.
“That's unsatisfactory.”
“Science frequently is.”
“But surely one of these must be the answer.”
“Perhaps.”
“Or perhaps several are describing different aspects of a deeper structure.”
Elowen nodded.
“That possibility is worth keeping open.”
Blottisham looked at the list again.
“So we don't know what happens to the information.”
“We have increasingly sophisticated ideas about how it might be preserved.”
“But no universally accepted final conceptual resolution.”
“Correct.”
Blottisham sighed.
“Scientists really ought to publish fewer things until they know the answer.”
Quillibrace looked at him.
“An excellent proposal. I shall mention it to the Royal Society.”
X. What are we imagining?
There was a short silence.
Then Elowen said:
“I think there is a question underneath the physical question.”
Blottisham groaned.
“I knew it.”
Quillibrace ignored him.
“What question?”
“What are we imagining when we say that information is lost?”
Quillibrace nodded.
“Good.”
Elowen continued.
“We imagine information as something that can be stored.”
Blottisham pointed at her.
“Which it can.”
“Yes.”
“We imagine it as something that can be transferred.”
“Yes.”
“Which it can.”
“Yes.”
“Destroyed?”
“That depends upon what we mean by information.”
“Recovered?”
“Again, yes, in some senses.”
“So what's the problem?”
“The problem is that these everyday relations can make us imagine information as though it were a substance.”
Quillibrace added:
“And the physical question may concern something more fundamental: whether the distinctions among possible states remain encoded in the structure of physical evolution.”
Blottisham thought about this.
“So information is less like a thing and more like a relation.”
“Precisely.”
“And if the relation survives, the information survives.”
“Something like that.”
“And if the relation disappears…”
“Then we have the serious version of the problem.”
Blottisham nodded slowly.
“I think I see.”
Quillibrace raised an eyebrow.
“Do you?”
“I think the problem isn't that nobody can find the message.”
“No.”
“It is that the universe may cease to contain the distinction between the message and its alternative.”
Elowen smiled.
“Yes.”
Quillibrace leaned back.
“That is considerably better.”
Blottisham looked pleased.
“Thank you.”
“I was speaking to Miss Stray.”
XI. The frontier of language
Elowen stood and looked at the blackboard.
“Perhaps this is what makes the information paradox so philosophically interesting.”
Quillibrace waited.
“The physics is not being replaced by metaphorical analysis.”
“No.”
“The paradox is real.”
“Yes.”
“The calculations matter.”
“Very much.”
“But the concepts through which we understand the calculations may themselves be under pressure.”
Quillibrace nodded.
“The distinction between inside and outside.”
“The distinction between physical state and information.”
“The distinction between inaccessible and destroyed.”
“The distinction between observer and observed.”
“The distinction between boundary and object.”
“The distinction between description and reality.”
Blottisham looked at the list.
“That sounds rather alarming.”
“It is potentially productive,” said Elowen.
Quillibrace nodded.
“A paradox does not necessarily mean that nature is contradictory.”
“It might mean that our conceptual distinctions have reached their limits.”
“Exactly.”
Blottisham thought for a moment.
“So the black hole may not be the thing that has gone wrong.”
“No.”
“Perhaps our picture of the black hole has gone wrong.”
“Perhaps.”
“And our picture of information.”
“Yes.”
“And our picture of inside and outside.”
“Yes.”
“And our picture of loss.”
“Yes.”
Blottisham frowned.
“That leaves rather a lot of things that might be wrong.”
Quillibrace smiled.
“Or rather a lot of things that might need refinement.”
Elowen looked at him.
“That is perhaps a more charitable way of putting it.”
“I was attempting to be diplomatic.”
“You concealed it very well.”
XII. A question to take home
The Common Room clock struck six.
Blottisham folded his newspaper.
“So what are we actually supposed to take away from all this?”
Quillibrace answered immediately.
“The paradox remains.”
“That is not very encouraging.”
“It is accurate.”
Elowen gathered the papers.
“A quantum state falls into a black hole.”
“The black hole radiates.”
“The radiation appears thermal.”
“The black hole can evaporate.”
“And if the radiation contains no sufficient record of the original distinctions among quantum states…”
“…then information appears to be lost.”
“But quantum theory does not easily permit that.”
“So something has to change.”
Blottisham looked at the blackboard.
“Either our calculation.”
“Our interpretation.”
“Our theory.”
“Or our concepts.”
Quillibrace nodded.
“Possibly several.”
Elowen smiled.
“And perhaps that is where we should stop.”
“Stop?”
“For today.”
Blottisham looked surprised.
“Without solving it?”
“Yes.”
“Why?”
“Because the first question may not be What is the answer?”
Quillibrace finished the thought.
“It may be What are we imagining when we ask the question?”
Blottisham looked once more at the words on the board.
INSIDE
OUTSIDE
STORED
TRANSFERRED
LOST
RECOVERED
He frowned.
“I confess,” he said, “I had previously thought these were perfectly straightforward words.”
Quillibrace put on his coat.
“That,” he said, “is generally when they become dangerous.”
Elowen laughed.
They began to leave.
Blottisham paused at the door.
“One final question.”
Quillibrace sighed.
“Yes?”
“If information isn't a thing, why do physicists keep talking about it as though it were?”
Elowen looked back at the blackboard.
“Because sometimes the only way to see a new relation is to speak as though it were an old thing.”
Quillibrace considered this.
“A dangerous practice.”
“An indispensable one.”
Blottisham nodded.
“I suppose that is rather like metaphor.”
Quillibrace opened the door.
“Exactly.”
They stepped into the corridor.
Behind them, the blackboard remained covered in words.
None of them had changed.
And yet, somehow, none of them meant quite what they had meant when the conversation began.
No comments:
Post a Comment