In the first essay, we asked whether the black hole information paradox might contain an assumption that usually remains invisible.
We saw that our ordinary language encourages us to imagine information as something that physical things possess. A particle can carry information. A physical system can store information. A black hole can swallow information. Hawking radiation can, perhaps, return information.
This language is extraordinarily useful.
But usefulness is not ontology.
The question we now need to ask is deceptively simple:
What is information?
The question is more difficult than it first appears.
We can count bits. We can encode messages. We can calculate entropy. We can transmit information from one system to another. None of this, by itself, tells us what information is.
A thermometer can tell us the temperature.
A photograph can tell us what stood in front of a camera.
A DNA sequence can carry information about an organism.
A quantum state can encode information.
A black hole, apparently, can threaten to destroy it.
But in each case, what exactly is the thing being called information?
Perhaps the answer begins with something more elementary than messages, data or states.
Perhaps information begins with difference.
Information requires alternatives
Suppose there is only one possible state.
There is no distinction to be made.
If something can be either A or B, however, then the actual occurrence of A rather than B makes a difference.
We can represent that difference as information.
This observation is elementary, but it has an important consequence.
Information does not seem to exist independently of a space of possibilities.
A red light carries information because other states were possible: green, amber, perhaps no light at all.
A thermometer reading of twenty degrees is informative because other temperatures were possible.
A binary bit has information because it could have been 0 or 1.
The information is not a little substance contained inside the red light, the thermometer, or the bit.
The information lies in the distinction among possibilities made actual.
This gives us our first relational formulation:
Information is not primarily a thing; it is a relation between an actual state and a structured space of possible states.
That formulation is already rather different from the language in which the black hole paradox is usually expressed.
The actual and the possible
Consider a simple example.
Imagine a room in which a lamp can be either on or off.
If the lamp is on, something has been actualised.
But the information conveyed by the state “on” depends upon the possibility that the lamp could instead have been “off”.
The actual state does not carry its information in isolation.
It is informative relative to alternatives.
The same point applies to a more complicated system.
Suppose a particle can be detected in several possible locations. A particular detection is an actual event. Its informational significance depends upon the alternatives that were available to it.
The information is therefore not simply inside the particle.
It concerns the relation between:
what could have happened;
what did happen;
and the structure connecting those possibilities.
This is why information is inherently relational.
There is no information without some distinction that could have been otherwise.
A message is not information by itself
This becomes clearer if we consider language.
Take the sequence:
CAT
It is tempting to say that the three letters contain information.
But they do not do so simply by existing.
Their informational significance depends upon a system of distinctions.
The sequence is meaningful because the letters could have been arranged differently. The alphabet provides alternatives. The language provides further distinctions. The reader possesses a system within which those distinctions can matter.
Even the physical inscription is not itself the information.
The ink on the page is one actual configuration of matter.
What makes it informative is its relation to a structured field of alternatives and interpretations.
This does not mean that information is subjective.
The physical distinctions are real.
The informational relation is real.
What it means is that information is not adequately described as a self-contained substance sitting inside the ink.
The same physical principle appears at every level.
A state is informative because it excludes, distinguishes, or constrains alternatives.
Information is therefore inseparable from possibility.
Information and constraint
We can sharpen the idea.
Suppose we know that a physical system can occupy one of a thousand possible states.
If we discover that it occupies one particular state, the range of possibilities has been narrowed.
Information can therefore be understood as a constraint upon possibility.
This is particularly important for physics.
A physical state does not merely tell us what is.
It can tell us what is not.
If a particle is detected here, it was not detected there.
If a system has a particular energy, certain other energies are excluded.
If two quantum systems are entangled, their possible joint states are constrained in ways that cannot be reduced to independent descriptions of the two systems.
Information, on this view, is intimately related to the structure of what can and cannot occur.
This suggests another formulation:
Information is the structure of distinctions and constraints within a space of possibility.
That formulation will become increasingly important as we return to quantum theory.
Because the wavefunction, on our interpretation, is precisely concerned with such a space.
The climate analogy
Our earlier analogy with climate can now do some work.
A climate does not tell us what the weather will be on a particular day.
It tells us something about the space of possible weathers.
It constrains possibility.
Some weathers are more probable than others. Some are effectively excluded. Others are common. Still others are possible only under unusual conditions.
When a particular weather occurs, it is an actual instance within that structured field of potential.
The weather is not contained inside the climate.
Nor is the climate a ghostly collection of future weather events.
The relation is one between potential and actual.
This is close to what we mean by the wavefunction in our relational interpretation.
The wavefunction is not a physical container full of unrealised particles.
It is a structured account of potential instantiations.
A particle event is an actual instance.
And information concerns the relation between those actualisations and the structured field of possibilities in which they occur.
This is beginning to suggest something important.
Perhaps quantum information is not information stored in quantum objects in quite the way our ordinary language suggests.
Perhaps it is information about the structure of possible instantiations.
The temptation to make information a substance
Why, then, do we so naturally speak of information as though it were a thing?
Partly because information behaves, in certain respects, like something that can be moved.
A message can be sent.
A file can be copied.
A memory can be transferred.
A quantum state can be transmitted.
The metaphor of information as an object is therefore extraordinarily productive.
But metaphors become dangerous when their grammatical convenience is mistaken for ontology.
Consider money.
We can say that money is transferred from one account to another.
That does not mean that a little physical substance called “money” travels through the banking system.
The transaction is a change in a network of relations.
The same caution may apply to information.
When we say that information has been transferred, perhaps what has actually changed is the relational structure of distinctions and possibilities between physical systems.
This does not make the transfer unreal.
It changes what we think the transfer consists in.
And that distinction may be crucial for black holes.
What does it mean to lose information?
We can now return to the central problem.
Suppose information is not a substance.
Then what would it mean for information to be destroyed?
It cannot simply mean that a physical object containing information has ceased to exist.
Objects disappear all the time without information necessarily being destroyed.
A piece of paper can burn, while the information once encoded on it survives in another form: perhaps in someone's memory, perhaps in a photograph, perhaps in the chemical and physical correlations produced by the burning.
Conversely, an object can survive while the information associated with some distinction becomes inaccessible.
So “information loss” must mean something more precise.
Perhaps it means that distinctions that previously existed within a physical relational structure can no longer be reconstructed.
Or perhaps it means that the correlations required to distinguish one possible history from another have ceased to exist.
Or perhaps it means something else again.
The point is that we cannot settle the black hole problem until we know what we mean by loss.
And that requires knowing what information is.
Information and correlation
This brings us to one of the most important concepts in modern physics:
correlation.
If two systems are correlated, knowledge of one can constrain what we can say about the other.
The informational content of a system may therefore depend not merely upon its individual state, but upon its relations with other systems.
This is particularly striking in quantum mechanics.
An entangled state cannot always be understood as two independently specified objects, each carrying its own complete state.
The information may reside in the relation.
This is precisely the direction in which relational ontology points.
If information can be constituted by correlations, then it is not merely something possessed by objects.
It is something that exists between them—or, more strongly, something that helps constitute what the objects themselves are as physically distinguishable entities.
This gives us a possible hierarchy:
possibility → distinction → constraint → correlation → information
The terms are not identical.
But they may be different aspects of the same relational structure.
And if that is right, then the phrase “information inside a black hole” becomes much less straightforward.
Inside relative to what?
Information belonging to which system?
Correlations with which exterior?
And what happens to a relation when one of the regions participating in it becomes inaccessible?
These are no longer merely technical questions.
They are ontological questions.
The black hole problem looks different
We can now return to the familiar narrative.
Matter falls into a black hole.
The ordinary description encourages us to imagine that the matter carries information with it.
But suppose an actual particle is an instance of quantum potential.
Then its informational significance does not reside simply in the particle as an isolated object.
It resides in the structure of possibilities of which that event is an actualisation, together with its correlations and relations to other physical events.
The particle crossing the horizon therefore need not be imagined as carrying a little packet of information across an invisible boundary.
Something more interesting has happened.
The relational conditions under which that actual event can be related to other events have changed.
The horizon matters because it changes which future-directed relations remain available to distant observers.
That is already enough to make us suspicious of the ordinary formulation of information loss.
Perhaps what has become inaccessible is not a substance called information, but a set of relations through which distinctions could previously be reconstructed.
And that is a very different claim.
Preservation is relational too
The same point applies to information preservation.
We often say that quantum theory requires information to be preserved.
But preserved how?
If a system evolves from state A to state B, what makes us say that the information in A survives in B?
Not necessarily that some material entity carrying information has travelled from A to B.
Rather, there must be a sufficiently structured relation between the possible states at the two times for the distinctions present in one description to remain recoverable in the other.
Preservation is therefore itself relational.
This gives us a provocative reformulation:
Information is preserved when the relevant distinctions among possibilities remain represented in the relational structure of the evolving system.
Information is lost when that structure no longer supports those distinctions.
Now we have a formulation of the problem that does not require information to be a substance.
And perhaps that is exactly what we need.
The danger of asking where information is
There is therefore something potentially misleading about the question:
Where is the information?
The question assumes that information has a location in the same sense that a physical object does.
But if information is relational, location is not necessarily the right category.
A correlation is not located at one end of itself.
A constraint is not sitting inside one of the alternatives it constrains.
A distinction is not a substance occupying a volume.
Information may be instantiated in physical systems, represented by physical states, transmitted through physical processes and recovered from physical correlations.
But none of these facts requires information itself to be a physical object.
The black hole paradox may therefore be partly sustained by a grammatical mistake.
We have turned a relation into a thing.
And once we have done so, we can ask where the thing went.
But physics speaks in bits
At this point, someone might reasonably object.
Physics has precise mathematical definitions of information. Entropy is quantitative. Quantum information theory is a rigorous discipline. Bits and qubits are not merely metaphors.
Quite so.
Nothing in this investigation requires abandoning the mathematics.
The issue is not whether information can be quantified.
It plainly can.
The issue is what the mathematical quantity represents.
A temperature can be precisely measured without temperature being a substance.
Entropy can be precisely calculated without entropy being a material object.
Likewise, information can be precisely quantified without information being a thing that physically travels from one place to another.
Our concern is therefore interpretive rather than computational.
We are asking what kind of entity—or, perhaps, what kind of relation—the mathematics is describing.
That distinction will become increasingly important.
Information without an information substance
We can now state the position more positively.
Information is not an additional ingredient of the physical world, alongside matter, energy and spacetime.
It is a way in which the physical world is structured by distinctions, possibilities, constraints and correlations.
A physical system is informative because its actual state stands in a determinate relation to alternative possible states.
A correlation is informative because the state of one system constrains the possible states of another.
A memory is informative because its physical configuration preserves distinctions that can be recovered.
A quantum state is informative because it specifies a structured space of possible outcomes and their relations.
In each case, information emerges from organisation within possibility.
This makes information deeply compatible with relational ontology.
Indeed, it may be difficult to give a fully relational ontology without something very much like this conception of information.
For if reality is fundamentally relational, then the meaningful distinctions within those relations are not incidental.
They are part of what makes a physical world intelligible at all.
And now the black hole
We can finally see why the black hole information paradox may be more interesting than the familiar question suggests.
If information is a relation between actuality and possibility, then black-hole evaporation does not present us with a simple question about whether a thing called information survives.
It presents us with a question about the continuity of relational structure.
A collapsing star establishes one extraordinarily complex physical configuration.
A black hole forms.
An event horizon alters the possible relations between interior and exterior events.
Quantum fields around the horizon generate radiation.
The black hole evaporates.
At the end of the process, what remains of the distinctions and correlations that characterised the initial state?
That is a legitimate and profound question.
But it is no longer:
Where did the information go?
It is:
How is the relational structure of possibility transformed by gravitational collapse and evaporation?
And now the paradox begins to look different.
Perhaps the central issue is not whether information has fallen into a black hole like an object falling into a box.
Perhaps the issue is whether the relations that made the initial state informationally distinct remain encoded in the final physical structure.
That is a much more subtle problem.
And it brings us directly to the quantum side of our investigation.
Because to understand what happens to information in a black hole, we first need to understand what a quantum state is when we stop treating the wavefunction as a thing.
That will be our next step.
The wavefunction is not a thing. It is a space of potential.
And if that is right, then the black hole has not merely swallowed a physical system.
It has confronted us with a transformation in the relation between potential and actual.
That is where the next essay begins.