We ended the previous essay with a question that may seem almost embarrassingly simple:
Is spacetime fundamental?
The question is easy to ask because we are accustomed to treating spacetime as the most obvious thing in the universe.
Everything happens somewhere.
Everything happens sometime.
Objects occupy space.
Events occur in time.
Motion takes place through spacetime.
And general relativity appears to give us a theory of spacetime itself.
So why should we hesitate?
Because there is a difference between saying that spacetime is real and saying that spacetime is fundamental.
That distinction may be crucial.
A thing can be real without being ontologically basic.
Temperature is real.
Pressure is real.
Climate is real.
None of these is fundamental in the sense of existing independently of the physical relations from which they emerge.
Perhaps spacetime belongs to the same category.
Perhaps it is real precisely because something more fundamental gives rise to it.
And if so, perhaps the problem of quantum gravity has been formulated backwards.
We have been trying to quantise spacetime before asking whether spacetime is the sort of thing that should be quantised at all.
Real does not mean fundamental
Consider a wave.
A wave is real.
It can move.
It can carry energy.
It can break against a shore.
We can measure its wavelength and frequency.
But a wave is not a fundamental object in the same sense as the individual physical processes from which it arises.
The wave is a pattern.
Its reality lies in the organisation of something else.
The same is true of a whirlpool.
A whirlpool is not unreal because it is constituted by water in motion.
Quite the opposite.
Its reality consists in the persistence of a relational pattern through changing material configurations.
The water molecules composing the whirlpool do not remain in the same places.
Yet the whirlpool remains recognisable.
The pattern is real.
The pattern is also emergent.
This gives us a useful distinction:
Emergent does not mean imaginary.
It means that the reality of a phenomenon lies in the organisation of more basic processes rather than in its existence as an independent substance.
If spacetime is emergent, therefore, we should not imagine that we have discovered that space and time are somehow unreal.
We would have discovered something much more interesting:
spacetime is a real relational structure produced by something deeper.
The temptation of the stage
Our ordinary picture of the universe begins with a stage.
Space is the arena.
Time is the succession in which events occur.
Objects then enter the arena, interact, move and disappear.
This picture is so deeply embedded in ordinary thought that it is difficult to imagine anything else.
But general relativity already undermined it.
Space and time are not passive containers.
Their geometry is dynamically related to the physical processes occurring within them.
The stage participates in the drama.
It is not simply a stage anymore.
This is one of the conceptual revolutions of Einstein's theory.
But perhaps we stopped halfway.
We abandoned the idea of spacetime as a fixed container, yet continued to think of spacetime as a fundamental thing whose geometry can change.
Perhaps the next conceptual step is to ask whether even that is too object-like.
If spacetime is relational, then it may be less like a substance and more like a pattern of possible relations among physical events.
What is space?
The question sounds trivial.
Space is where things are.
But what does “where” mean?
Suppose there are two physical events.
We can measure a spatial interval between them.
That interval is real.
But it is not an object occupying the space between them.
It is a relation between the events.
Now consider three events.
Their spatial relations can be compared.
Add more events.
A structured system of relations emerges.
With sufficiently many events and sufficiently regular relations, we can represent the structure mathematically as a geometry.
The geometry is not added to the events from outside.
It is the systematic organisation of their relations.
This suggests an inversion of the usual picture.
Instead of:
space first, things second
we might have:
physical relations first, spatial structure second.
Space would then be a way of representing a particular organisation of relations.
This is not yet a theory of emergent spacetime.
But it changes what such a theory would need to explain.
What is time?
Time presents an even more difficult problem.
We ordinarily imagine time as something that flows.
Events occur within it.
One moment becomes another.
But physics has never needed quite so simple a picture.
Relativity tells us that temporal intervals depend upon the physical circumstances of observers.
Clocks do not all measure the same elapsed time between events.
Gravitational fields affect the rate at which clocks run.
Motion affects the relation between temporal intervals.
There is therefore no single universal temporal substance flowing uniformly through the universe.
What exists physically are measurable relations among events and the readings of physical clocks.
This suggests another possibility:
time may be a relational structure rather than an independent dimension through which events move.
That does not make time unreal.
It makes time something we must explain.
The clock is not time
This distinction matters because clocks provide such a powerful temptation.
A clock ticks.
We observe a sequence of readings.
We call the difference between the readings “time”.
But the clock is a physical system undergoing change.
Its reading is a relation between successive physical states.
We infer temporal structure from such relations.
This is why different physical clocks can disagree about elapsed time without one of them being “wrong”.
They are tracing different paths through the physical relational structure.
General relativity makes this explicit.
Proper time is not something floating independently of physical systems.
It is associated with a particular worldline through spacetime.
Time is therefore already more relational than ordinary language suggests.
If that is true at the level of general relativity, perhaps we should not be surprised if time turns out to be emergent at a deeper level.
Spacetime as the organisation of events
We can now formulate a more relational conception.
Instead of imagining spacetime as a container within which events occur, imagine a network of physical events and the relations among them.
Some relations are spatial.
Some are temporal.
Some are causal.
The geometry expresses the systematic structure of those relations.
On this view:
Spacetime is not the container of physical relations. It is the structured representation of those relations.
That is a profound inversion.
The traditional picture says:
spacetime → relations among things
The relational picture suggests:
relations among events → spacetime structure
If the second direction is correct, then spacetime is not fundamental in the same way that the relations themselves are.
And that immediately changes the quantum-gravity problem.
What would it mean to quantise a relation?
Suppose Alice and Bob are separated by a distance.
If the distance is a relation, we can still ask whether that relation has quantum behaviour.
But notice what we are no longer doing.
We are not imagining a little quantum substance called “distance”.
We are asking whether the possible relations between physical events are themselves structured quantum mechanically.
That is a much more subtle question.
And perhaps it is the question we should have been asking all along.
The distinction becomes particularly important at very small scales.
If spacetime geometry is emergent, then at the Planck scale there may be no smooth geometry waiting to be quantised.
There may instead be some more primitive structure of physical possibilities and relations from which smooth geometry emerges only in an appropriate limit.
This would radically change our expectations.
We would not expect the fundamental world to look like tiny pieces of spacetime.
We would expect it to look unlike spacetime altogether.
The Planck scale may be telling us something
The Planck scale is often imagined as the scale at which spacetime itself becomes “quantum”.
That phrase is suggestive.
But it may conceal an assumption.
Perhaps the Planck scale is not where ordinary spacetime acquires strange quantum properties.
Perhaps it is where the spacetime description ceases to be fundamental.
The distinction is subtle but important.
Imagine a fluid.
At large scales, it has pressure, density and smooth velocity fields.
At sufficiently small scales, those variables cease to provide the most fundamental description.
The fluid does not suddenly become a “quantum fluid” in the sense that pressure itself becomes a microscopic object.
Rather, the continuum description stops being fundamental.
The underlying molecular structure becomes relevant.
Likewise, perhaps spacetime does not become a bizarre quantum object at the Planck scale.
Perhaps the smooth geometric description simply reaches the limit of its domain of applicability.
The question then becomes:
What lies beneath the geometry?
The danger of quantising the description
This brings us back to the problem raised in the first essay.
Suppose the metric is fundamentally a representation of relations.
We then write down a quantum theory in which the metric itself fluctuates.
That may be perfectly legitimate.
But we should ask what the fluctuating metric represents.
If the metric is not an independent physical substance, then a “superposition of metrics” may not mean what our ordinary language suggests.
It might represent a superposition of possible relational structures.
That is quite different from imagining spacetime itself as being literally in two geometries at once.
The distinction mirrors our earlier treatment of the wavefunction.
A quantum superposition describes structured potential.
It need not describe multiple incompatible actualities existing simultaneously as physical things.
Likewise, a quantum description of geometry need not imply that a physical fabric called spacetime is literally fluctuating between alternative shapes.
It may represent potential relational structures.
Once again:
potential is not actuality.
A geometry of possibilities?
This suggests a fascinating possibility.
Perhaps quantum theory and general relativity are not as far apart as they appear.
Quantum theory gives us a structured field of potential actualisations.
General relativity gives us the relational geometry of actual physical events and their causal possibilities.
Perhaps a deeper theory would describe the transition between them.
Not:
quantum matter + quantum spacetime
but:
quantum potential → actual events → relational geometry.
In this picture, geometry is not imposed on quantum events from outside.
It emerges from the organisation of their relations.
And the resulting geometry then constrains which further actualisations are possible.
This gives us a feedback structure:
potential
↓
actualisation
↓
relations
↓
geometry
↓
new constraints on potential
↓
further actualisation
The universe would then be understood not as objects moving through spacetime, but as a process in which possibility, actualisation and relational structure continually generate one another.
That is a very different ontology.
Why general relativity looks so geometric
If spacetime is emergent, why does general relativity work so extraordinarily well?
Because an emergent description can be exact at the level at which it applies.
Temperature is not an approximation in the sense that it becomes meaningless because molecules exist.
Thermodynamics works.
Fluid mechanics works.
Elasticity works.
None requires us to know the microscopic ontology every time we calculate a macroscopic phenomenon.
Likewise, if spacetime geometry is emergent, general relativity can remain an extraordinarily accurate theory of the large-scale relational structure of physical events.
Its equations describe the emergent geometry.
They need not describe the fundamental ontology beneath it.
This distinction allows us to respect the enormous empirical success of general relativity without assuming that its fundamental variables must remain fundamental at every scale.
The geometry may be an achievement
This leads to a striking possibility.
Perhaps spacetime is not the starting point of physical reality.
Perhaps it is an achievement.
The universe does not begin with events sitting inside a pre-existing geometric arena.
Rather, physical processes generate increasingly stable patterns of relation.
At large scales, those patterns become smooth enough to be represented as geometry.
Spacetime is then what the relational structure looks like when viewed at the appropriate scale.
This would make geometry analogous to temperature.
Temperature is not imposed upon molecules.
It is what their collective behaviour looks like under a particular description.
Likewise, spacetime might be what a deeper relational dynamics looks like when its possibilities become organised into sufficiently stable causal structures.
The geometry is real.
But it is real as a pattern.
This changes what “fundamental” means
We should be careful with the word fundamental.
It does not necessarily mean:
“the only thing that is really real.”
It means something closer to:
that upon which other structures depend without itself depending upon them in the same way.
An emergent phenomenon can therefore be ontologically significant without being fundamental.
A human organism depends upon cells.
Cells depend upon molecular processes.
Molecules depend upon atoms and fields.
This does not make organisms unreal.
It gives their reality a different structure.
Perhaps spacetime is similar.
Perhaps it is a high-level physical structure whose existence depends upon deeper relational processes.
Then the question is not whether spacetime exists.
It is:
What does spacetime depend upon?
And what might lie beneath it?
Here we must resist another temptation.
Once we decide that spacetime is emergent, it is very easy to replace it with another thing.
Perhaps the universe is made of tiny loops.
Or networks.
Or strings.
Or causal sets.
Or some other fundamental object.
But this would simply reproduce the problem at another level.
We would have abandoned spacetime-as-thing only to invent a new thing underneath it.
The relational ontology demands something more radical.
It asks whether the fundamental level itself might be structural rather than object-like.
Perhaps what is fundamental is not a new kind of thing.
Perhaps it is a space of possibilities together with rules governing actualisation and transformation.
Perhaps the primitive ontology is relational all the way down.
If so, there may be no microscopic spacetime waiting underneath the macroscopic spacetime.
There may be no tiny geometric pieces at all.
Relation without relata?
This raises an obvious philosophical difficulty.
If relations are fundamental, what are they relations between?
Can there be relations without things?
We should not rush to answer.
The question itself may assume too much.
At the macroscopic level, relations are naturally described between objects and events.
But if objects themselves are emergent patterns of relations, then the fundamental level may not contain fully formed relata in the ordinary sense.
This sounds paradoxical only if we assume that relations must always be secondary to the things they relate.
A relational ontology reverses that priority.
The objects may be stable patterns within a more fundamental relational process.
A particle would then be something like a persistent node or pattern.
An event would be an actualisation.
A spacetime geometry would be a large-scale organisation of relations among such events.
The relata are not abolished.
They are derived.
The black hole gave us a clue
Our previous investigation now looks rather different.
The black-hole information paradox seemed to involve three mysterious things:
a quantum state;
spacetime;
information.
But each became less mysterious when treated relationally.
The wavefunction became potential structure.
Information became distinctions and correlations.
Spacetime became relational geometry.
The horizon became causal structure.
The black hole became a gravitational regime.
The apparent paradox weakened because the ontology became less crowded.
Perhaps this was not an accident.
Perhaps the black hole was giving us a glimpse of a more general principle:
The closer physics gets to its foundations, the less useful an ontology of independent things may become.
If so, the quantum-gravity problem may be another manifestation of the same difficulty.
What if spacetime is an affordance?
There is another way to describe the possibility.
We have previously used the idea of affordance to describe how a structure of possibilities makes some actualisations more available than others.
Perhaps spacetime itself is an extraordinarily rich system of affordances.
Its geometry tells physical systems what trajectories are possible.
Its causal structure determines which events can influence which others.
Its gravitational structure alters the relative possibilities of motion and measurement.
In this sense, spacetime is not merely where things happen.
It is part of the structure that determines what can happen.
That makes its relationship to quantum potential especially interesting.
Quantum theory describes potential actualisations.
Spacetime geometry constrains the relations among actualisations and the possibilities available for subsequent events.
Perhaps the deeper theory is therefore not about combining two substances.
It is about understanding how potential and affordance interact.
That may be much closer to the conceptual structure we actually need.
The possibility of a wrong question
We can now state the challenge more sharply.
The conventional programme asks:
How can spacetime be made quantum?
Our investigation asks:
Why assume spacetime is fundamental enough to require quantisation?
Perhaps the more fundamental problem is:
How does a quantum relational structure give rise to the stable geometry we call spacetime?
If that question is right, then quantum gravity is not primarily a problem of quantisation.
It is a problem of emergence.
And if it is a problem of emergence, then the appropriate mathematical tools may be very different from those suggested by the phrase “quantum gravity”.
We may need to understand:
how relational structures become stable;
how causal order emerges;
how metric relations arise;
how dimensionality becomes meaningful;
how smooth geometry appears from a deeper structure;
and how the classical limit is produced.
The problem would not be:
“How do we make spacetime quantum?”
It would be:
“How does spacetime become possible?”
We have not solved anything yet
It is important to be honest about the status of this argument.
We have not demonstrated that spacetime is emergent.
We have not shown that quantum gravity is unnecessary.
We have not derived Einstein's equations from a relational quantum ontology.
We have not identified the fundamental relational structure.
We have done something earlier and more modest.
We have shown that the assumption of fundamental spacetime is not forced merely by the success of general relativity.
And that is enough to justify asking the question.
Perhaps spacetime is fundamental.
Perhaps it is emergent.
Perhaps the distinction itself will need to be reformulated.
But now the burden is on the ontology, not merely the mathematics.
Before asking how to quantise spacetime, we should know what spacetime is.
A new direction
The first essay asked:
What are we trying to quantise?
This essay has led us to:
Is spacetime fundamental?
And the answer is not yet “yes” or “no”.
But the question has changed.
If spacetime is fundamental, we need to understand what kind of fundamental entity it is.
If spacetime is emergent, we need to understand what generates its relational structure.
Either way, we have moved one level deeper.
And this suggests the next question.
Suppose relations really are fundamental.
Suppose physical reality is not fundamentally composed of independent objects possessing intrinsic properties, but of a structured field of possibilities and actualisations in which relations are primary.
Then we must confront a much more difficult question:
Can relations themselves be quantum?
That is where the investigation must go next.
Because perhaps the real object of quantisation was never spacetime.
Perhaps it was never gravity.
Perhaps what we need to understand is the quantum structure of possibility and relation themselves.
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