If the previous discussion is correct, the quantum wavepacket should not be understood as an ontic object but as a theory of possible instances associated with a physical configuration. In systemic terms, it behaves like a system: a structured potential from which instances may be actualised.
This observation invites a further step. If the wavepacket is a theory of possible instances, then it must sit somewhere on the cline of instantiation — the perspectival continuum between potential and event.
Once placed on that cline, the formal behaviour of quantum states becomes unexpectedly transparent.
1. The cline itself
Relational ontology treats potential and instance not as separate ontological categories but as poles of a perspectival cline.
Between these poles lies a continuous spectrum of intermediate construals: increasingly specific configurations of potential approaching actualisation.
Quantum theory appears, in retrospect, to have written down an explicit mathematical structure that occupies precisely this intermediate territory.
2. The wavepacket as intermediate potential
A pure system in SFL describes the complete potential of selections. But language users rarely operate at that maximal level. Instead they work within registers — subpotentials defined by particular contexts.
Something strikingly similar occurs in quantum mechanics.
A wavepacket is rarely a completely unconstrained superposition of all possible states. Instead it is already shaped by boundary conditions, experimental arrangements, and interaction histories. Its amplitude distribution therefore defines a restricted potential: a structured subset of possible events.
From the pole of potential, the wavepacket therefore appears as:
a subpotential within the larger space of physically possible instances.
From the pole of instance, however, the same structure appears differently. It looks like a distribution of possible outcomes for a forthcoming event.
In other words, the same object shifts interpretation depending on which pole of the cline we adopt.
3. Probability amplitudes as gradients of potential
Within this perspective the role of probability amplitudes becomes clearer.
They are not probabilities in the everyday sense. Nor are they physical waves carrying energy through space.
Instead they encode the gradient of potential across the instance space.
Regions of high amplitude correspond to regions where potential is strongly configured toward actualisation. Regions of low amplitude correspond to weakly configured potential.
The familiar probability rule then emerges as a mapping from potential gradients to frequencies of instantiated events.
Nothing collapses; rather, the event simply actualises at some point within the structured potential.
4. Decoherence as contraction of the cline
Environmental interaction introduces further constraints on the potential structure.
In orthodox terms this produces decoherence: the suppression of interference between alternative branches of the wavefunction.
On the cline of instantiation this phenomenon has a simpler interpretation.
The interaction progressively contracts the available potential, narrowing the space of instances that remain viable. The system moves closer to the instance pole.
By the time an event is construed, the potential space has already been so tightly constrained that only a small cluster of instances remains accessible.
The apparent “classical world” therefore emerges not because quantum potential disappears but because the cline has become extremely steep.
5. The illusion of collapse
The famous collapse appears dramatic only because the formalism jumps directly from the potential description to the instantiated event.
But this jump is not ontological; it is perspectival.
The mathematics does not track the entire construal process between these poles, so the shift appears abrupt.
In reality it is simply the system–instance cut.
6. Entanglement on the cline
Entangled systems occupy a particularly interesting position.
Their potentials are not separable; the relevant system describes joint instances across multiple loci.
On the cline this means the potential space is defined at a higher level of relational organisation. Individual subsystems cannot be assigned independent instance spaces.
When an event occurs, the relational cut therefore selects a joint instance across the entire entangled configuration.
The famous nonlocal correlations follow immediately from this fact.
Nothing travels between the particles because the relevant potential was never localised to them individually.
7. Quantum theory as an explicit theory of potential
The remarkable thing about this reconstruction is how little of the formalism needs to change.
Quantum mechanics already provides:
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a structured space of potential states (Hilbert space),
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rules governing the deformation of that potential (unitary evolution),
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and a mapping from potential to instantiated events (Born probabilities).
What it lacks is an ontology that recognises potential itself as fundamental.
Relational ontology supplies precisely that missing step.
Once potential is understood as a system — a theory of possible instances — the wavepacket becomes entirely ordinary. It is simply the structured potential associated with a particular physical configuration.
The supposed mysteries of quantum mechanics then turn out to be nothing more exotic than the consequences of moving along the cline of instantiation.
8. The next question
If this reconstruction is correct, an obvious question follows.
Hilbert space appears to function as the geometry of potential — the structure within which possible instances are organised.
But geometry is only one way to represent relational structure.
Category theory suggests another.
In the next post we will explore the possibility that quantum states are better understood not as vectors in a space but as objects in a category of potential relations — and that quantum evolution corresponds to the morphisms that transform one structure of potential into another.
If so, the wavepacket may turn out to be something even more interesting:
not merely a system of possibilities,
but a relational object whose very identity is defined by the transformations it can undergo.
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