The question sounds strange.
Can relations be quantised?
We know what it means to quantise a physical system.
We can quantise a field.
We can quantise a harmonic oscillator.
We can quantise angular momentum.
But a relation?
What would that even mean?
If Alice is standing two metres from Bob, what would it mean to quantise the relation between them?
Would the distance become a quantum object?
Would it exist in a superposition of different values?
Would Alice and Bob somehow be two metres apart and three metres apart simultaneously?
The language quickly becomes obscure.
Perhaps this is because we are trying to force a relational ontology into an ontology of things.
If relations are fundamental, however, we need to take the question seriously.
Perhaps the problem is not that relations cannot be quantised.
Perhaps we have not yet understood what it would mean for a relation to be quantum.
The thingness problem
Quantum theory has traditionally been interpreted in terms of things possessing quantum states.
An electron has a state.
A photon has a state.
A field has a state.
The quantum state tells us what can happen when the system interacts with something else.
This encourages an ontology in which the world is populated by entities, each carrying a state.
Relations then appear to be secondary.
There are things first.
The things subsequently enter into relations.
But our relational ontology reverses the order.
A particle is not fundamentally a tiny object possessing intrinsic properties which subsequently happens to interact.
It is an actualised instance of potential structure.
Its identity is partly constituted by the relations in which that actualisation participates.
The relation is therefore not merely something that happens to the thing.
It is part of what the thing is.
That changes the problem.
If relations help constitute physical identity, then quantising the relation may not mean adding quantum properties to an otherwise classical relationship.
It may mean describing the potential and actual structure of physical relations themselves.
A simple example
Suppose two events, A and B, occur.
There may be a spatial relation between them.
There may be a temporal relation.
There may be a causal relation.
In ordinary language, we are tempted to imagine:
first there are A and B;
then there is a relation between them.
But perhaps that is backwards.
The identity of A as a physical event is partly determined by its position within the network of relations.
Change all its relevant relations and we may no longer be talking about the same physical event.
This is familiar in less fundamental contexts.
A note in a melody is not fully identifiable independently of its relations to the surrounding notes.
A word in a sentence acquires much of its meaning from its relations to the other words.
A chess piece has a role defined partly by the structure of the game.
The piece is physically real.
But its being a bishop, in the relevant sense, is relational.
Likewise, perhaps physical entities are not fundamentally self-sufficient things which merely possess relations.
Perhaps they are stable patterns within relations.
If so, then asking whether relations can be quantum is no longer quite as strange.
It becomes:
Can the fundamental structures from which physical entities themselves emerge be quantum?
Quantum theory already contains relations
There is an important clue here.
Quantum mechanics is not actually as object-centred as its everyday language sometimes suggests.
The most revealing quantities in quantum theory are often relational.
An observable is not simply a property that a particle carries around with it.
It is something that acquires physical significance through a measurement interaction.
A measurement produces an outcome.
An outcome establishes a relation between physical systems.
The familiar language of “the particle has spin” can therefore conceal something important.
Spin is not simply a little classical arrow hidden inside the particle.
Its physical significance appears through particular interactions and possible measurement outcomes.
Quantum theory is saturated with relations.
The difficulty is that we often describe those relations using the language of properties belonging to things.
Entanglement makes the problem unavoidable
Quantum entanglement pushes this issue into the open.
Consider two quantum systems prepared in an entangled state.
It may be impossible to assign each system a complete independent state that fully captures the state of the pair.
The correlations between the systems are not merely additional information about two independently specified objects.
The joint state contains structure that belongs to the relationship.
This is one reason entanglement is so conceptually unsettling.
Our ordinary ontology expects:
two things + properties of each thing + perhaps a relation between them.
Quantum theory permits something more radical:
a relational structure that cannot be reduced to independently specified states of the relata.
This is already very close to a relational ontology.
The quantum world does not merely contain objects which happen to become correlated.
Sometimes the correlation is more fundamental than the independent description of the objects.
Information is relational
This also connects directly with our earlier investigation of the black-hole information problem.
We found that information is not naturally understood as a mysterious substance stored inside physical objects.
Information concerns distinctions.
And distinctions are relational.
To say that a system contains information is to say that its physical state stands in a structured relation to possible alternatives, measurements, or other systems.
A bit is not a tiny object labelled 0 or 1.
It is a distinction between alternatives.
A quantum state contains a richer structure of possible distinctions and correlations.
This suggests that information is relational through and through.
If physical information is relational, and quantum theory is fundamentally concerned with physical information, then perhaps it should not surprise us that quantum theory repeatedly resists an ontology of independent things.
The resistance may be telling us something.
What would a quantum relation be?
We can now return to the question.
Suppose A and B are physically distinct events.
We write:
A ≠ B
and suppose that a relation R connects them.
We might write:
R(A,B)
In a classical description, the relation has a definite value.
Perhaps the spatial interval is (d).
Perhaps the temporal interval is (τ).
Perhaps A can causally influence B.
The relation is determinate.
But suppose the underlying physical situation admits several possible relational structures.
Then the quantum description might not assign a single actual relation.
Instead, it might represent a structured set of potential relations.
This would be analogous to the wavefunction.
The wavefunction does not represent an actual particle distributed through all its possible positions.
It represents structured potential for actualisation.
Likewise, a quantum relational structure need not mean that an actual distance literally has several incompatible values simultaneously.
It could mean that several relational actualisations remain possible.
The distinction is essential.
Potential relation is not actual relation
This gives us a useful conceptual vocabulary.
A relation can be:
potential, as part of a quantum description of possible actualisations;
actual, when a physical event instantiates a particular relational structure;
persistent, when the relation remains stable across a sequence of events;
emergent, when large numbers of relations organise into a higher-level structure such as geometry.
This produces a hierarchy:
potential relation
↓
actual relation
↓
stable relational pattern
↓
emergent geometry
The hierarchy is not necessarily temporal.
It is ontological.
The potential does not happen “before” the actual in the ordinary sense.
Rather, the actual is an instantiation of what was previously available as potential.
This is precisely the distinction we drew between the wavefunction and particles.
The wavefunction is potential structure.
Particles are actual instances.
Now we can extend that distinction.
Perhaps geometry is a stable organisation of actualised relations.
Quantum geometry without quantum spacetime
This allows us to make an important distinction.
There is a great deal of difference between:
quantum spacetime
and
quantum relational structure from which spacetime emerges.
The first suggests that spacetime itself is a quantum object.
The second says that the underlying relations are quantum, while spacetime is the emergent classical organisation of those relations.
The two ideas are not equivalent.
Indeed, they predict different conceptual pictures of the fundamental level.
If spacetime is fundamental, we should expect some form of quantum geometry.
If spacetime is emergent, we should expect the fundamental description to become increasingly non-geometric as we go deeper.
This is a crucial point.
The absence of ordinary geometry at the fundamental level would not mean that geometry has disappeared.
It would mean that geometry is an emergent achievement.
The surprising possibility
We can now see why the question “Can relations be quantised?” may be more fruitful than “Can spacetime be quantised?”
The latter begins with an object.
The former begins with structure.
And structure may be closer to what quantum theory is actually telling us.
Suppose the fundamental physical description consists of:
possibilities for events;
rules governing their actualisation;
correlations among actualisations;
and transformations of the relational structures thereby produced.
Then there may be no need for fundamental particles moving through a fundamental spacetime.
There are processes of actualisation.
There are relations among their outcomes.
Stable patterns of those relations give us objects.
Large-scale patterns give us geometry.
And sufficiently stable geometry gives us the spacetime description.
The ontology has become dynamic.
Nothing needs to be permanently present as a fundamental object.
What persists are patterns.
A particle may be a relation that persists
This is perhaps the most radical consequence.
We usually imagine a particle as something that exists and then enters into relations.
But perhaps a particle is better understood as a persistent pattern of relations.
Its identity consists partly in the regularity with which certain interactions occur.
Its properties are expressed through the relations it can enter into.
Its trajectory is a sequence of actualised events connected by lawful relations.
In that sense, the particle is not something underneath the relations.
It is what the relations make stable.
This does not make particles unreal.
It explains their reality differently.
A whirlpool is not less real because it is a persistent pattern in water.
A particle may likewise be a persistent pattern in a deeper physical relational structure.
The relata may emerge with the relation
This brings us to a philosophical point that initially sounds alarming.
If relations are fundamental, what are the relations between?
Perhaps the answer is:
The relata are themselves emergent.
At the fundamental level, there may not be fully formed things waiting to be connected.
There may instead be a process of differentiation.
One actualisation becomes distinguishable from another.
A relation becomes established.
Repeated patterns of relations become stable.
Stable patterns acquire identities.
The world of things then emerges from a more primitive world of distinctions and relations.
This would explain why the wavefunction can be understood as potential structure rather than as a physical substance.
The potential is not a collection of little things waiting somewhere in advance.
It is a structured field of possible distinctions and relations.
Actuality creates the determinate relata.
Relation and instantiation
This brings the SFL notion of instantiation back into the centre of the argument.
A system of potential meanings can be instantiated in particular linguistic expressions.
The expression is actual.
The system of potential meanings is not another sentence sitting somewhere behind it.
It is the structured space of possibilities from which actual expressions can be drawn.
The analogy with quantum theory is striking.
The wavefunction describes a structured field of possible physical actualisations.
A particle event is an instantiation.
Now extend the analogy one step further.
A relational geometry may similarly be a structured field of possible relations among actual events.
The geometry is not necessarily a thing.
It is a potential structure of relational organisation, capable of being instantiated in particular physical histories.
This gives us a useful three-level distinction:
potential
instantiation
pattern
The first describes what can happen.
The second is what happens.
The third is what becomes stable across many happenings.
Perhaps physics has repeatedly confused these levels because our language tends to turn descriptions into nouns.
The metric revisited
We can now return to the metric.
If the metric represents relational structure, then a metric is not necessarily a physical substance.
It is a specification of possible and actual intervals among events.
A classical metric gives determinate geometric relations.
A deeper quantum description might give a structured potential for relational configurations.
The classical metric would then emerge when the relevant relations become sufficiently stable and definite.
This suggests a possible conceptual transition:
quantum relational potential
→
actualised relational events
→
classical relational geometry
That is not yet a theory.
But it is a radically different starting point for one.
What happens to curvature?
Our earlier reinterpretation of general relativity becomes important here.
We treated gravity not as the bending of a physical spacetime substance but as the systematic variation of spatial and temporal intervals through a gravitational field.
On that interpretation, curvature is not primarily a property possessed by a cosmic object called spacetime.
It describes a pattern in the relations among events.
If those relations are themselves emergent from quantum actualisations, then gravitational curvature becomes an emergent relational pattern.
We would no longer need to imagine a fundamental thing called curved spacetime.
We would need to explain how particular patterns of quantum actualisation produce the relational regularities represented by curved geometry.
Again, the direction of explanation changes.
Quantising relations is not quantising numbers
There is another source of confusion.
A relation such as distance can be represented by a number.
That number may be measured in metres.
We might then imagine that quantising the relation means turning the number into a quantum observable.
But the number is only the mathematical representation.
The physical relation is what matters.
This is similar to the distinction between temperature and the number displayed by a thermometer.
The number is a representation of a physical relation within a measurement procedure.
Quantising the number does not by itself tell us what is physically quantum.
Likewise, assigning a quantum operator to a metric component does not by itself settle the ontology.
We need to know what physical relation the operator represents.
The mathematics cannot answer that question on its own.
The deeper meaning of superposition
This becomes particularly important when discussing superposition.
If a relation is represented quantum mechanically, we may encounter a superposition of possible relational structures.
But a superposition should not automatically be interpreted as a collection of simultaneously actual classical alternatives.
Our relational interpretation of the wavefunction already gives us a better way to think about this.
The superposition represents structured potential.
Actualisation selects an instance.
Thus a quantum relational state might represent:
possible ways in which events could stand in relation.
It does not require us to imagine a classical world in which contradictory geometries literally coexist as physical substances.
The superposition belongs to the level of potential.
The actual relation belongs to the level of instantiation.
That distinction may dissolve some of the conceptual strangeness surrounding quantum geometry.
The emergence of classicality
If this picture is correct, one of the great questions becomes:
Why does the world appear geometrically definite?
Why do we experience a stable three-dimensional space?
Why do clocks and rulers give reproducible results?
Why does general relativity work so accurately?
The relational ontology suggests an answer in principle.
Large-scale stability.
When enormous numbers of physical actualisations become organised into persistent relational patterns, fluctuations at the underlying level can become irrelevant to the macroscopic description.
The result is a stable effective geometry.
This would be analogous to the emergence of temperature.
Individual molecules undergo complicated microscopic motions.
Yet temperature becomes a remarkably stable macroscopic variable.
Perhaps spacetime is similar.
The underlying relational structure may be quantum and highly dynamic.
But the large-scale geometry can nevertheless be extraordinarily smooth and stable.
The universe as a relational process
We can now begin to see a different picture of physical reality.
Not:
objects in spacetime interacting with one another.
But:
potential actualisations generating persistent relational structures from which objects and geometry emerge.
This is not merely a change of vocabulary.
It changes what counts as fundamental.
A particle is not necessarily fundamental.
A field need not be fundamental in its classical form.
Spacetime need not be fundamental.
Even geometry may not be fundamental.
What may be fundamental is the structured possibility of physical differentiation and relation.
That is a much more austere ontology.
And perhaps a more quantum one.
But can relations really be primary?
We should not pretend that this is an easy proposal.
The ordinary mathematical language of physics is built around states, variables and structures.
Even relational theories typically specify relations between identifiable systems.
So a genuinely relational ontology faces a difficult task:
How do we formulate a theory in which relations are primary without quietly smuggling objects back in as the things that possess the relations?
That is not a problem to be solved by philosophical declaration.
It is a problem for physics and mathematics.
But it is a legitimate problem.
And it may be more fruitful than beginning by assuming the existence of quantum spacetime.
A different conception of quantum gravity
We can now return to our original project.
Perhaps “quantum gravity” should not mean:
a quantum theory of the gravitational field on fundamental spacetime.
Perhaps it should mean something more like:
an account of how quantum relational potential gives rise to the stable causal and geometric structures described by general relativity.
That is almost a different subject.
Its central concepts would not necessarily be:
quantum spacetime
gravitons
metric fluctuations
but rather:
potential
actualisation
relation
correlation
constraint
causal structure
emergence
stability
And this is precisely where our broader conceptual investigation begins to converge with physics.
The question becomes evolutionary
If relations can be understood as potential structures that become instantiated and stabilised, then physical reality begins to look less like a collection of things and more like an evolving grammar.
Potential structures constrain what can be instantiated.
Actualisations modify the relational situation.
The modified situation affords new possibilities.
Some patterns disappear.
Others persist.
Some become stable enough to appear as objects.
Some become stable enough to appear as geometry.
The universe does not merely occupy a structure.
It continually produces structure.
And that may be what we have been missing when we ask how to quantise spacetime.
From quantum gravity to relational dynamics
The question with which we began was:
Can relations be quantised?
Perhaps the most promising answer is:
We should not begin by trying to quantise relations as though they were things.
Instead, we should ask how quantum theory represents potential relations, how actual events instantiate them, and how persistent relational structures emerge.
That is a subtler question.
But it may also be the more fundamental one.
The goal would no longer be to place quantum theory inside spacetime or to make spacetime itself quantum.
The goal would be to understand how geometry, causality and physical identity emerge from a deeper relational process.
If that process is quantum, then quantum gravity may turn out to be not the quantisation of gravity at all.
It may be the discovery of the relational dynamics from which gravity emerges.
The next question
We have now moved through three questions:
What are we trying to quantise?
Is spacetime fundamental?
Can relations be quantised?
Each question has pushed us further away from an ontology of independent things.
But this has brought us to a more fundamental question still.
If the wavefunction represents potential rather than actuality, and if relations themselves may belong to the structure of that potential, then we need to understand something that we have so far taken for granted.
How does a potential become an actual?
This is not simply the question of what happens when a measurement is made.
It is more basic than that.
A physical possibility is not yet a physical event.
A possible particle detection is not an actual detection.
A possible relation is not yet an actual relation.
Somehow, within the physical process, one of the possibilities becomes instantiated.
And once it does, the world has changed.
There is now an actual event where previously there was only potential.
Our use of the word instantiation is therefore doing much more work than it might initially appear.
If the wavefunction is a theory of potential instances, and particles are actual instances of that potential, then the central ontological question is not merely what the wavefunction represents.
It is:
What is an instantiation?
What makes an actual event an instance of one possibility rather than another?
How does actuality acquire determinate form?
And how does one actualisation alter the relational possibilities available for what comes next?
These questions matter for our investigation of quantum gravity because geometry cannot simply be assumed to exist before this process has been understood.
If spacetime is emergent, then geometry must ultimately arise from something.
And if what is fundamental is a structured field of potential relations, then the first step toward understanding the emergence of geometry must be to understand how those potential relations become actual.
Perhaps the sequence is something like:
potential
↓
instantiation
↓
actual event
↓
relation
↓
persistent relational pattern
↓
geometry
We should not yet assume that this is the correct sequence.
But it gives us a direction in which to investigate.
The crucial point is that actuality cannot simply be inserted into the theory as though it were another fundamental thing.
If potential and actual are two ontological categories, we need to understand their relationship.
And if actuality is instantiation, we need to understand what makes instantiation possible.
This takes us deeper than the question of quantum spacetime.
Indeed, it may take us deeper than the question of quantum gravity itself.
For perhaps the fundamental problem is not:
How do we quantise geometry?
Nor even:
How do quantum relations produce geometry?
Perhaps the prior question is:
How does possibility become actuality?
That is where we should go next.
Because before we can understand how actual relations might organise themselves into geometry, we first need to understand how there can be actual relations at all.
IV. From Potential to Actual will begin there.
🍷🙂