1 From Potential to Instance: A Relational Epistemology of the Quantum
In the history of quantum theory, much ink has been spilled over the status of particles and waves. Are they real? Are they mathematical conveniences? Are they contradictory? But from a relational epistemology, the question is not what they are “in themselves” — the question is: how do they function within a construal of experience?
We begin, then, not with things, but with relations — and more specifically, with instantiation.
The Cline of Instantiation
In the model we’ve been building, all meaning can be understood as emerging along a cline of instantiation: a semiotic spectrum stretching from potential to instance. This is the deep structure of how language works, but also — we propose — of how science itself construes experience.
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Potential is the structured field of possibilities: the meaning potential of a language, the genetic potential of a species, or the dynamical potential of a physical system.
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Instance is a singular realisation: a spoken utterance, a phenotypic trait, or a particle detection.
But the cline is not binary. Between potential and instance lies an intermediary: subpotential — the unfolding of particularised probabilities within the field. Subpotential is no longer universal possibility, but it is not yet fully instantiated. It is oriented toward actualisation.
This middle ground is where we locate the quantum wavefunction.
Field, Wavefunction, Particle
Quantum theory is often framed as a mystery of identity: is the electron a particle or a wave? Is the field real or just a bookkeeping device? But in our view, these are all perspectives on participation — each situated at a different point on the cline of instantiation.
Let’s map them:
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Quantum Field → PotentialA field is not an object. It is a system of potential relations — a structured topology of interaction. Fields do not occupy space; they construe it, offering a semantic map of what kinds of interactions are possible.
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Wavefunction → SubpotentialThe wavefunction is not a particle smeared out in space. It is a construal of what is probable, given a specific context. It is not universal potential, but conditioned potential: a subpotential. It represents the tendency of the system to actualise certain states over others.
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Particle (Detection) → InstanceA particle is not the “real thing” hiding behind the wavefunction. It is an event — an instantiation of a potential relation. What we call a “particle” is not a tiny object but a commitment: the moment at which potential becomes particular.
This framework shifts our focus from ontology to participation. Instead of asking “What is a wavefunction made of?”, we ask “What role does the wavefunction play in mediating participation between field and instance?”
Climate and Weather: A Relational Analogy
To ground this further, consider a familiar analogy: climate and weather.
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The climate is a system of potentials — a field of structured possibility: it defines what kinds of weather can occur, and how likely they are.
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A weather forecast is a probability distribution: a subpotential informed by particular conditions — it constrains which instantiations are likely here and now.
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A weather event (a storm, a heatwave) is an instance: the actual unfolding of a potential.
Crucially, these are not three different things, but three perspectives on the same phenomenon — a single process viewed from different points along the cline of instantiation.
Just so in quantum theory: field, wavefunction, and particle are construals of the same underlying participation, each representing a different vantage point.
Why This Matters
This model doesn’t claim to resolve all quantum paradoxes. But it reframes them in a more coherent semantic architecture:
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The double-slit experiment doesn’t require a particle to “decide” whether to act like a wave. Rather, it’s a matter of when and how a potential becomes an instance.
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The wavefunction doesn’t “collapse” because it was unreal; it collapses because meaning actualises. Like meaning in language, quantum events do not pre-exist their realisation.
In other words, the quantum world is not made of things. It is made of potential relations that instantiate through participation.
We’ll explore the semiotic logic of subpotential, show how the wavefunction fits this role, and consider how meaning is shaped when potential is already in motion.
2 Subpotentiality and the Wavefunction: Construals of Conditioned Probability
In our previous post, we proposed a relational mapping of the quantum field (as potential), the wavefunction (as subpotential), and the particle (as instance). This gives us a semantic cline: potential → subpotential → instance. But what exactly is subpotential, and why is it the right construal for the wavefunction?
To answer that, we need to understand what it means to move from undifferentiated potential to context-sensitive probability.
From Potential to Subpotential
In systemic functional linguistics, the concept of meaning potential refers to the full set of meanings available within a semiotic system. It is a highly structured field of possibility — but it is not the same as what will be said in any given situation.
To move from what could be meant to what is likely to be meant, we must construe a subpotential: a partial, conditioned potential that reflects the constraints of context. Subpotential represents the system’s orientation toward instantiation in a particular setting.
In physics, this is the role played by the wavefunction.
The Wavefunction as Subpotential
The wavefunction is not a thing. It is a semantic construal of constrained potential — a probabilistic map of possible instances, given certain conditions.
Importantly:
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The wavefunction is not the total potential of the quantum field (which is context-free).
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The wavefunction is not yet an instance (a particle or detection event).
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Rather, it is a midpoint: the potential pole, already shaped by participation.
In this sense, it is subpotential: it encodes tendencies, likelihoods, and orientations toward instantiation — a field of meaning that is on the verge of actualisation.
The subpotential does not pre-exist the context. It is co-emergent with it. Just as a speaker’s likely choices depend on the discourse situation, the wavefunction depends on boundary conditions, measurement configurations, and prior interactions.
The Power of Probability
Subpotential is not vagueness — it is structured uncertainty. This is not a bug in the model; it’s a feature of how the world becomes actual.
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In language, subpotential is probabilistic because context doesn't force meaning — it favours it.
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In physics, subpotential is probabilistic because the field doesn't force instances — it conditions them.
The wavefunction is precisely this: a probabilistic construal of conditioned potential. It allows us to calculate the probabilities of different instantiations, but it does not determine them. Just like a weather forecast, it is context-sensitive subpotential, not destiny.
Perspective Is Everything
Let’s return to our earlier example of climate and weather:
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Climate is a field of structured possibility (potential).
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Forecast is a context-conditioned construal (subpotential).
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Storm is an event that actualises potential (instance).
The wavefunction is like the forecast. It is not reality, but a structured interpretation of where and how reality is likely to emerge. And just as the same forecast can lead to different outcomes, the same wavefunction can lead to different measurement results — because instantiation is contingent.
A Relational Summary
So how should we think of the wavefunction, in relational terms?
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It is not a substitute for the field, nor a placeholder for the particle.
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It is a semiotic construal of the field’s tendencies, from within a particular relational context.
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It is oriented potential — shaped by participation, but not yet instantiated.
In short: the wavefunction is the subpotential through which the field leans toward instance.
We will now explore what it means for potential (or subpotential) to become instance. What does it mean to say a particle is an “event of commitment”? How does the quantum field participate in its own realisation?
3 Participation and Actualisation — What Makes a Particle?
In our last post, we introduced the wavefunction as a construal of subpotential — a context-sensitive shaping of potential, situated between the abstract possibility of the field and the concrete event of a particle.
But what happens when this subpotential is actualised? What does it mean to say that a particle emerges — or, more carefully, that a particle is instantiated?
In this post, we explore instantiation as an act of participation: the movement from possibility to event, from potential to instance. We will argue that a particle is not a thing that exists in a field, but an actualisation of the field’s capacity to participate.
A Particle Is Not a Pebble
We are used to thinking of particles as tiny marbles or points with properties like position and momentum. But in a relational ontology, this is misleading.
In quantum field theory, particles are better understood as discrete excitations of a field. And in a relational construal, this means they are:
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Events, not substances
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Instantiations, not pre-existing entities
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Committals, not mere fluctuations
When a field actualises, it participates — and the particle is the name we give to that participation.
Instantiation as Commitment
Let’s return to the cline of instantiation:
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Field: potential — what could happen
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Wavefunction: subpotential — what is likely to happen, given constraints
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Particle: instance — what actually happens
From a relational viewpoint, this is not a sequence in time, but a semantic cline — a shift in perspective on the same underlying process.
When a field participates in its own potential — when it commits to a possible configuration — we observe an event: a detection, a measurement, a particle. But the particle is not independent of the process that gives rise to it. It is the process, momentarily crystallised.
This is why some quantum theorists speak of particles as “quanta of action.” They are events of instantiation, not little objects moving through space.
Participation Requires Relation
What triggers this actualisation?
Not measurement in the simplistic sense of a human observer, but relation: an interaction that constrains possibility to the point of commitment. In technical terms, this might be a coupling with another field, a detection apparatus, or an environmental condition that collapses the range of potential.
But the principle is always the same:
Participation happens when potential meets constraint in a way that requires a decision.
This is the moment of instantiation — and the particle is what we call the outcome of that decision.
The Field Doesn’t Emit the Particle — It Becomes It
Here’s the radical shift: in a relational model, the field doesn’t produce the particle as something separate. Rather, it instantiates itself in a form that we construe as a particle.
This is not just a semantic point — it reorients the metaphysics:
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Not: “The field emits a particle.”
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But: “The field participates in its potential through this event.”
The particle is not a travelling entity, but an actualisation of relational capacity.
Actuality Is Not Absolute
Just as the wavefunction is shaped by context, so is the particle. Its “properties” are not carried with it from some inner core — they are emergent outcomes of the relational situation in which it is actualised.
This is why no particle is ever just “a particle.” It is always a particle-in-context, a specific instantiation of potential in a particular relational web.
This also means that:
A single field may instantiate in multiple, even contradictory, ways — because instantiation is not about expressing a hidden essence, but responding to a relational demand.
A Relational Summary
So what makes a particle?
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A particle is not a tiny object floating in a field.
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It is the instantiated event of the field’s participation in itself, shaped by constraints.
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It is a realised configuration of potential — the outcome of a relation, not a precondition.
In relational terms:
A particle is the semantic commitment of a field to a specific, context-bound instance.
Now that we’ve traversed the cline from field to wavefunction to particle, we turn our attention back to the field itself. What kind of “thing” is potential, and how should we think of the field not as substance but as structure? We’ll reinterpret the quantum field as a systemic constraint space — a grammar of participation.
4 The Field Revisited — Structured Potential and the System Pole
In our earlier posts, we described the quantum field as a domain of potential — the furthest point on the cline of instantiation from the actual event we call a particle.
But potential is not chaos. It is not an unstructured soup of possibilities. Rather, it is structured potential — a patterned space of constraints, affordances, and relational capacities. And that structured potential is what we call a field.
In this post, we revisit the quantum field from a systemic perspective: not as a physical substance, nor a mathematical backdrop, but as a semiotic structure — the grammar of quantum participation.
From Stuff to Structure
The classical intuition wants to picture a field as a kind of invisible substance that fills space and carries force — like an ocean in which particles swim.
But in a relational framework, the field is not a substance, and it does not occupy space. Rather:
The field is a relational structure that makes space possible.
This is a profound shift. The field is not embedded in spacetime; it is a semantic topology — a set of constraints that allows spacetime configurations to be actualised. It is not in the world; it is the structure that makes the world meaningful.
The System Pole of Instantiation
Let’s bring back our cline of instantiation:
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System → Subpotential → Instance
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Field → Wavefunction → Particle
Here, the field sits at the system pole: the pole of structured potential. Just as a grammar constrains what can be said in a language, the field constrains what can be instantiated in a given domain of reality.
And just as a speaker draws on their grammatical system to produce a sentence, the universe draws on the field’s structure to produce events.
This means:
The field is not what causes the particle, but what makes it possible.
It is the total potential for participation, from which subpotentials like wavefunctions are drawn.
Constraint Is Not Limitation — It’s Meaning
In ordinary language, to say something is “constrained” might sound like it’s being held back. But in relational semiotics, constraint is what makes meaning possible.
In this light:
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The gravitational field is not just a pull — it’s the structuring of spatial participation via mass.
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The electromagnetic field is not just a vector field — it’s the structuring of charged interaction.
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The quantum field is not an invisible fluid — it’s a domain of potential relational events, grammatically shaped.
This means a field is best understood as a map of allowable co-instantiations — a topology of potential configurations that are internally coherent and relationally viable.
The Field as a Grammar of Becoming
To call a field “structured potential” is to say it has an internal architecture. Not a blueprint of things, but a grammar of relations. This grammar governs:
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Which participatory events are possible
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How those events relate to one another
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What constraints guide actualisation
In this view:
A quantum field is not an object in space, but a semiotic system that governs how space (and the things in it) come to be.
This may sound abstract, but it has powerful implications. It tells us that what we call “reality” is not built from particles that preexist their interactions, but from fields whose structure defines the possibility of interaction.
Fields Are Not Flat — They Are Dynamic Constraint Spaces
Fields are often treated mathematically as continuous, uniform structures. But even classical fields (like the gravitational field near Earth) have gradients — structured variations that guide behaviour.
In relational terms, this means fields are internally differentiated: they contain zones, tendencies, and symmetries. They are not homogeneous backdrops, but richly contoured maps of possibility.
This is where wavefunctions come in: they are contextual slices of this total potential — local grammars shaped by global structure.
Summary: The Field as Structured Potential
Let’s bring it all together:
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A field is the system pole of the cline of instantiation.
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It is not a thing or a substance, but a structured domain of potential participation.
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It provides the semantic grammar from which wavefunctions (subpotentials) and particles (instances) emerge.
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It is relational, not objective — it does not “exist” independently, but constrains and enables relation.
In short: A field is not a thing you’re in. It’s a structured capacity for becoming-with.
Now that we’ve clarified the role of the field as structured potential, we’ll revisit the wavefunction. What does it mean to treat it as subpotential — as a partial actualisation of field potential? How does probability relate to meaning? And what are the implications for understanding quantum behaviour?
5 Subpotential in Practice — Reading the Wavefunction as Meaning Potential
In our last post, we redefined the quantum field as a structured potential — a semantic system, not a substance. This systemic view helps us see the field not as a thing in space, but as what makes spacetime configurations possible.
Now we turn to the wavefunction.
If the field is the system pole — the total structured potential — then the wavefunction is a subpotential: a context-specific narrowing of that total potential.
In this post, we explore the wavefunction not as a literal wave, nor as a cloud of possibilities in physical space, but as meaning potential — the field viewed from a particular standpoint of relevance.
The Wavefunction as Subpotential
Recall our cline of instantiation:
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System → Subpotential → Instance
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Field → Wavefunction → Particle
A subpotential is not a separate layer or thing, but a shift in perspective. It represents the field’s constraints as they apply in a particular situation — a conditional narrowing of what is possible.
The wavefunction is how the field constrains potential in context.
It carries structure (like the field), but it is probabilistic — tuned to a specific configuration of meaning, purpose, or participation.
In relational terms, it is a structure-for: not a complete system, but a conditional expression of system potential in response to relevant factors (such as boundary conditions, prior observations, or apparatus settings).
Wavefunction as Probability, not Prediction
It is tempting to treat the wavefunction as a predictive tool — a mathematical trick for guessing what comes next. But that’s a misreading.
From a relational perspective:
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The wavefunction is not a forecast; it is a map of structured affordances.
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It does not predict what will happen; it outlines what can happen, and how likely those options are under certain constraints.
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It does not exist apart from a context of interaction. It is an expression of potential meaning shaped by co-participation.
In this light, the wavefunction does not describe a particle’s location in space — it describes the meaning potential for an event of localisation.
Meaning Potential and the Subpotential Perspective
In Systemic Functional Linguistics (SFL), meaning potential refers to the range of meanings a speaker can draw on in a given context. Not all meanings in the grammar are relevant at once; the context of situation narrows what is likely or possible.
Likewise:
The wavefunction is the subpotential of the field: the meaning potential of the quantum system in context.
It is relationally conditioned:
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By how the system has interacted
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By what has been measured
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By which constraints have been imposed
So we do not treat it as a universal entity — a thing with a privileged status in reality — but as a temporary, contextual narrowing of potential, shaped by the relational conditions of observation.
Subpotential as a Middle Perspective
Most discussions of instantiation oscillate between the poles:
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Potential (field)
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Instance (particle)
But the wavefunction sits in the middle of the cline — and that’s where the most action happens.
This midpoint — the subpotential — reflects:
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The conditioned perspective of the observer
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The partial actualisation of system potential in preparation for further specification
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The probabilistic grammar of what might be instantiated next
It’s not halfway in time — it’s halfway in perspective. It expresses how the system pole appears when viewed through the lens of an emerging instance.
In short:
The wavefunction is the field-as-relevant — the system as conditionally available for instantiation.
No Ontology of the In-Between
It is important to note: we are not inventing a new class of objects between field and particle. Subpotential is not a third entity — it is a perspectival shift.
We move:
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From the systemic perspective (structured, timeless potential)
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Through the subpotential perspective (contextual, probabilistic potential)
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To the instantial perspective (eventual actualisation)
This shift does not represent different things, but different ways of construing the same unfolding phenomenon.
The wavefunction is not a half-formed particle, or a smeared-out object. It is a conditional construal of field potential — a grammar of meaning before meaning becomes text.
Summary: Wavefunction as Contextual Meaning Potential
To summarise:
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The wavefunction is a subpotential — a constrained view of the field in a specific context.
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It represents meaning potential: the available affordances for participation in a given situation.
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It is probabilistic, not because the world is fuzzy, but because instantiation is a process, and subpotential is a stage within it.
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It is not a thing, but a relational construal — a structure-for, shaped by co-participation and anticipation.
To read the wavefunction rightly is to read potential through the lens of relevance.
Having followed the arc from field to subpotential, we now arrive at the instance: the particle event. What does it mean to treat the particle not as a thing that persists, but as a semiotic actualisation — a transient event of meaning? We’ll explore collapse, actualisation, and what it means to be “real” in a relational universe.
6 The Particle as Instantial Actualisation — Meaning Event and the Collapse of Potential
Having traced the field as structured potential and the wavefunction as subpotential — a contextual narrowing of that potential — we now reach the instantial pole: the particle.
In this post, we reframe the particle not as a persistent object but as an event of actualisation — the momentary specification of meaning from potential. In the relational ontology we’ve been building, the particle is not the basic unit of the world, but a semiotic accomplishment: a meaningful event that arises in participation.
The Particle as Instance
Let’s return to our cline of instantiation:
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Field → Wavefunction → Particle
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System → Subpotential → Instance
Each point on this cline represents a shift in perspective on the same underlying relational phenomenon.
Where the field is the total potential, and the wavefunction a context-conditioned narrowing of that potential, the particle is the instantial actualisation: the event in which potential becomes specific — an act of meaning made material.
It’s not a marble-like thing flitting through space. It’s not even a smeared-out cloud waiting to collapse. It is the semiotic endpoint of a trajectory of relevance.
A particle is not a thing that is; it is an event that happens.
Collapse as Specification
This leads us to the idea of wavefunction collapse.
Traditionally, collapse is treated as a mystery — a sudden jump from indeterminacy to determinacy. But from a relational semiotic view, collapse is not a mysterious process but a natural stage in meaning-making:
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The wavefunction represents structured potential.
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The particle event specifies a particular value from that potential.
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Collapse is not a physical snap; it is an act of specification — the selection of one pathway among many.
This is just what happens in language and meaning more broadly: a general structure (grammar) is narrowed by context (subpotential) and finally actualised as a particular utterance (instance).
In this light:
Collapse is instantiation. The particle is the text.
The Particle as a Meaningful Event
To make this concrete, let’s draw from Systemic Functional Linguistics (SFL), where:
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The grammar is a meaning potential (like the field),
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A context narrows the range of meanings (like the wavefunction),
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A text instantiates meaning (like the particle).
The particle is thus the meaning event — the outcome of potential made actual in a specific configuration. It is a semiotic event, not an independently existing thing.
This perspective lets us avoid paradoxes like:
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How can a particle go through two slits at once?
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How can it be both here and there?
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How can it interfere with itself?
These aren’t problems once we stop treating the particle as an object and start treating it as the endpoint of a relational unfolding.
Actualisation is Not Persistence
Another common misunderstanding is to treat the particle as a persistent entity — a thing that is just temporarily hidden.
But this view emerges from object-based metaphysics. In relational epistemology, we focus on events, not things.
A particle is not a small object moving around. It is a point of interaction — a specification of potential into actual, just as a word in a sentence is a specification of grammatical potential into meaning.
So rather than asking:
“Where is the particle?”
We ask:
“When and how was the particle actualised?”
This is a temporal, not spatial, question — a question about instantiation, not trajectory.
The Role of Participation
Who or what performs the act of actualisation?
In quantum mechanics, this is often chalked up to the “observer.” But if we treat the observer as a detached external agent, we fall back into a representational model of knowledge.
Instead, we say:
Actualisation is co-emergent.
The particle becomes actual not because it is watched, but because a relational configuration brings it forth. The apparatus and the field participate in this co-specification. The meaning event arises within a web of conditions — just as a word only makes sense within a clause, and a clause within a context.
There is no pre-existing “thing” waiting to be seen. There is only potential becoming instance — with all participants jointly constituting the event.
Summary: The Particle as Meaning Made Actual
To summarise:
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The particle is the instantial pole of the field–wavefunction–particle triad.
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It is not an object but a semiotic event — the moment a potential is specified in context.
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Wavefunction collapse is not a physical process but a perspectival shift: the field seen as structure-for, giving rise to an instance.
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Actualisation is relational, not representational: it arises from participation, not perception.
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The particle is not what the world is made of — it is how meaning appears in the world.
In the quantum view, the real is not what endures, but what emerges.
To conclude the series, we’ll draw the full arc of instantiation — from field to subpotential to instance — and return to the idea of meaning not as possession, but as participation. What becomes possible when we read the quantum not as a puzzle, but as a grammar of co-specification?
7: Completing the Arc — From Field to Particle and Back Again
We’ve journeyed through the quantum triad: field, wavefunction, and particle — reframing each through the lens of relational epistemology and the cline of instantiation.
In this final post, we step back to trace the arc as a whole. What emerges is a view of reality not as a collection of things, but as a dynamic unfolding of potential into actual — a world of meaning not possessed, but co-specified.
Recalling the Cline of Instantiation
Let’s recall the full cline we’ve developed:
| Quantum Domain | Instantiation Perspective |
|---|---|
| Field | Structured potential |
| Wavefunction | Subpotential |
| Particle | Instantial actualisation |
Each stage corresponds to a different perspective on the same phenomenon. These are not separate entities, but different levels of abstraction in how meaning emerges from structure.
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The field is potential construed as a system — the full space of possibility.
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The wavefunction is a narrowing of that potential — structured by context, conditioning what might happen.
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The particle is what does happen — an instance of meaning, actualised within and through participation.
From Potential to Instance — And Back Again
A crucial insight from systemic functional linguistics (SFL) is that instantiation is not a one-way process. It is not simply that potential gives rise to instances. Every instance, once actualised, re-enters the system, contributing to its potential.
This means:
The particle, once actualised, becomes part of the evolving field.
Just as texts shape grammar over time, particle-events shape the conditioning of the field.
There is no ultimate separation between potential and instance. The cline of instantiation is cyclical:
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From field to wavefunction to particle — meaning narrowed and specified
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From particle back to field — meaning reabsorbed into potential, altering the probabilities of future actualisations
This cycle is not mechanical but semiotic: a pattern of meaning becoming actual, then re-entering the potential.
Relational Ontology Revisited
This view challenges traditional metaphysics in a decisive way.
Where classical physics posited entities that endure and act, quantum mechanics — reframed relationally — suggests that being is always becoming. There are no self-contained objects, only relational events of actualisation.
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A field is not a thing that contains particles. It is a space of structured potential.
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A wavefunction is not a blurry particle. It is a conditional narrowing of potential.
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A particle is not a hidden object revealed. It is a semiotic event, actualised through participation.
This is not to deny the material order, but to reinterpret it as the product of semiotic processes — processes of instantiating meaning in context.
The real is what is made actual — not what lies behind the veil of appearance, but what is brought forth in relation.
Knowledge as Participation
In this light, knowing is not discovering what is already there, but participating in what comes to be.
This reframes the role of the observer:
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Not as a detached recorder of facts
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But as a co-instantiator of meaning
In observing, measuring, interacting — we are not uncovering a pre-existing world. We are helping to shape its actualisation. This is not solipsism. It is relational co-specification: a world that emerges not from the subject or the object, but from the relation between them.
Why It Matters
This reframing of the quantum through instantiation does more than offer a philosophical lens. It provides:
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A coherent way to understand quantum concepts without falling into contradiction
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A path beyond dualisms: wave/particle, subject/object, observer/observed
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A model of reality that is dynamic, participatory, and meaningful
And perhaps most importantly, it invites us to reimagine science itself — not as the uncovering of fixed truths, but as an evolving grammar for meaning-in-the-world.
Closing Thought: A New Kind of Realism
The world, in this view, is not a puzzle of hidden parts but a dialogue of unfolding relations. Reality is not a stockpile of objects but a flow of meaning-in-relation.
The cline of instantiation — from field to wavefunction to particle — gives us a grammar for this unfolding.
And with it, we may say:
Reality is not what is there; it is what becomes actual in the dance between potential and participation.
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