There is something peculiar about the black hole information paradox.
It is usually presented as one of the deepest conflicts in modern physics. General relativity says one thing about what happens when matter collapses into a black hole. Quantum theory says something apparently incompatible about what happens to the information associated with that matter. Hawking radiation seems to allow the black hole eventually to disappear, leaving us with an uncomfortable question:
What happened to the information?
The question sounds straightforward.
Perhaps that is the problem.
Not because the physics is straightforward—it certainly is not—but because the question may already contain assumptions about what information is, where it resides, and what it means for something to persist through a physical process.
We are accustomed to imagining the world as a collection of things. Things have properties. Things carry information. Things enter into relations with other things. When something moves, changes, collapses, or disappears, we naturally ask what happened to the thing and to the properties it possessed.
This way of thinking is so deeply embedded in ordinary language that it can become invisible.
The black hole information paradox may be an unusually dramatic case in which that invisibility becomes a problem.
Perhaps the paradox is not simply a conflict between two physical theories.
Perhaps it is partly a conflict between two theories and an ontology we have quietly imposed upon them.
That is the possibility we want to investigate.
The familiar paradox
The basic story is well known.
A sufficiently massive star can undergo gravitational collapse. According to general relativity, the collapse can produce a black hole: a region from which, once the event horizon has formed, no future-directed signal can escape to the distant exterior.
Quantum field theory, meanwhile, tells us that the vacuum surrounding a black hole is not quite empty. Quantum effects near the horizon result in what we describe as Hawking radiation. The black hole therefore loses energy and, in the conventional picture, can eventually evaporate.
The difficulty appears when we consider what has happened to the information associated with whatever formed the black hole.
Quantum theory, in its standard unitary formulation, does not permit arbitrary destruction of information. If we know the complete quantum state of a closed system at one time, its later state is determined by unitary evolution. The evolution may make information extraordinarily difficult to recover, but it does not simply erase it.
A black hole seems to create precisely such an erasure.
Matter falls through the horizon. The details of that matter appear to become inaccessible from outside. Hawking radiation appears, at least in the original semiclassical treatment, to be thermal and therefore not to carry the detailed information required to reconstruct the initial state. The black hole then evaporates.
We seem to have arrived at:
Hence the paradox.
But notice the grammar of the argument.
Information went in.
Information was in the black hole.
Information came out.
Information was therefore treated rather like a physical possession that can be transported from one location to another.
This may be perfectly legitimate shorthand.
But what if it isn't merely shorthand?
What if the shorthand has begun to determine what we think the physics must mean?
Information as a possession
Consider the ordinary expression:
The particle carries information.
It sounds harmless.
But what does it mean?
There is an implicit picture here. First there is a particle. Then there is information associated with it. The particle possesses, contains, or carries that information as one of its properties.
The same picture appears when we say that information is stored in a physical system.
We imagine a system as something that exists in its own right, and information as something encoded in its state.
This is a remarkably powerful way of speaking. It underlies much of information theory, computation and quantum information.
But there is another possibility.
Perhaps information is not fundamentally something that a thing possesses.
Perhaps information is a feature of relations among possibilities and actualisations.
This is a much more radical proposal.
It does not deny that we can store information in a computer, encode it in a quantum state, or transmit it through a physical system. It asks what these familiar statements mean at the ontological level.
Suppose, for example, that a particular physical state can occur in one of several possible configurations. What makes the state informative is not that it contains a mysterious substance called information. What makes it informative is that its actual configuration stands in a structured relation to a space of alternatives.
Information concerns distinctions among possibilities.
And that immediately changes the black hole question.
Instead of asking:
Where is the information?
we might ask:
What relations among possibilities constitute the information?
The two questions are not equivalent.
The quantum problem
This distinction becomes especially important in quantum theory.
We are accustomed to speaking of the wavefunction as though it were the state of a physical system. That is perfectly natural within ordinary quantum language.
But there is another way to construe it.
The wavefunction can be understood as describing a structured field of potential instantiations.
The distinction is subtle but important.
A possibility is not yet an actuality.
A particle detection, for example, is an actual event. It is an instance of what the quantum state made possible. The wavefunction, on this view, is not itself a collection of already-existing particles waiting to reveal themselves. It specifies a space of possible actualisations and the relations among those possibilities.
We can borrow an analogy from climate.
A climate does not contain all the possible weathers that might occur tomorrow. Rather, it describes a structured field of possibilities within which particular weathers can occur.
The weather is actual.
The climate is potential.
Likewise, we might say:
The wavefunction is a theory of potential instances; the particle is an actual instance of that potential.
This distinction will matter greatly later.
For if information is fundamentally concerned with the organisation of potential and actual, then asking what happens to information when a particle crosses a black-hole horizon is no longer simply asking what happens to a physical object carrying a physical possession.
We may instead be asking what happens to a network of relations between potential and actual.
But we are getting ahead of ourselves.
There is another side to the story.
The gravitational problem
General relativity presents us with a parallel conceptual difficulty.
We commonly say that mass curves spacetime.
This is such a familiar expression that it is easy to forget how metaphorical it is.
We picture spacetime as something like a four-dimensional fabric. Matter bends the fabric, and objects then move along the resulting curves.
The picture is useful.
But perhaps we should ask what it is actually representing.
There is another way of describing the gravitational effect: spatial intervals become systematically altered in relation to mass, while temporal intervals are altered as well. In the direction of a massive body's centre, spatial and temporal measures behave differently from those far away.
The geometry of spacetime gives us an extraordinarily powerful mathematical representation of these relations.
But the geometry need not therefore be interpreted as a physical substance called spacetime that has literally acquired a new shape.
On this reading, gravity is fundamentally relational.
What changes is not necessarily a thing called spacetime, but the relations among spatial and temporal intervals.
The geodesic then expresses the structure of possible paths through that relational geometry.
This is a small shift in language.
Its consequences may be large.
Things first, relations second
We can now see the deeper assumption beginning to emerge.
Much of our ordinary physical language encourages us to think:
things exist first, and relations occur between them.
There are particles.
There is spacetime.
There are quantum states.
There is information.
There is a horizon.
And then these things enter into various relations.
But what if this order is backwards?
What if relations are not secondary features added to independently existing things?
What if relations are ontologically prior, and what we call things are relatively stable patterns or actualisations within those relations?
This is the possibility we shall call, for the purposes of this investigation, relational ontology.
It is not merely the claim that everything is connected.
That would be much too weak.
The stronger claim is that what something is cannot be fully specified independently of the relations within which it exists.
An electron is not first a completely determinate little object which subsequently enters into relationships.
A physical event is not first an isolated occurrence to which relations are later attached.
And information is not first a substance sitting inside a thing.
The entities we identify emerge within structured relations.
If this is right, then the black hole information paradox begins to look rather different.
The paradox before the paradox
We can now return to our original question.
What happened to the information?
The ordinary question seems to presuppose at least three things.
First, that information is something that can be possessed by a physical system.
Second, that the system possessing it retains a sufficiently determinate identity through the physical process for us to say that the same information has gone somewhere else.
Third, that the relevant physical relations—between system, environment, observer, spacetime, horizon and possible states—are secondary to the things themselves.
But perhaps none of these assumptions is fundamental.
Perhaps information is relational.
Perhaps physical identity is relational.
Perhaps even the geometry through which physical processes occur is relational.
If so, the black hole does not confront us with a mysterious substance called information entering a mysterious object called a black hole and subsequently disappearing.
It confronts us with something more subtle:
a radical transformation in the relations through which physical possibilities become actualities and through which actual events remain related to one another.
That is not yet a solution.
Indeed, we should be careful.
It would be intellectually cheap to announce that the paradox has disappeared simply because we have changed our vocabulary.
The physics still has to be respected.
Hawking radiation still has to be understood.
Quantum evolution still has to be understood.
The horizon still has to be understood.
And if information really is preserved, we must still explain what that preservation means.
But perhaps we should not begin by trying to solve the paradox.
Perhaps we should begin by asking whether we have formulated the right problem.
A different investigation
This series will therefore proceed differently from the usual discussions of the black hole information paradox.
We will not begin with the competing proposals for quantum gravity.
We will not assume that information is a substance.
We will not assume that particles are self-subsistent bearers of properties.
We will not assume that spacetime is a physical container whose geometry subsequently becomes distorted.
Instead, we will ask what happens when we reconstruct the problem from a relational ontology.
The questions will gradually change.
What is information if it is not a thing?
What is a quantum state if it describes potential rather than an independently existing physical object?
What is a particle if it is an actualisation of potential?
What is gravitational geometry if it expresses relations among intervals rather than the curvature of a substantial spacetime?
What is an event horizon if it is understood relationally?
And finally:
What exactly is supposed to be lost when a black hole evaporates?
Perhaps the answer will turn out to be that information really is lost, and that relational ontology does not save us.
Perhaps the answer will require a deeper theory.
Or perhaps we will discover something stranger.
Perhaps the famous paradox depends upon an ontology that makes the paradox inevitable.
In that case, solving the problem would not mean finding the missing information.
It would mean discovering why we thought there had to be a missing thing in the first place.
And that would leave us with a rather different question.
Not:
Where did the information go?
But:
What relations would have to persist for us to say that the information had gone anywhere at all?
That is where our investigation begins.
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