The Wavefunction as Subpotential: A Relational Perspective

In the relational model we’ve been developing, we view a quantum field not as a substance or a background entity, but as a system of potential participation — a structured semantic space that constrains what kinds of interactions are possible.

In this framing, a particle is not a thing in the field, but an instantiation of that potential — a commitment to one of the possibilities latent in the field’s structure. It is an instance, not an entity.

But between these two — the field as potential and the particle as instance — lies a third construal that is central to quantum theory: the wavefunction.

What is the wavefunction, in this framework?

We suggest it is best understood as a subpotential — that is, a partial construal of potential, one that has been constrained but not yet actualised. It sits at the midpoint of the cline of instantiation, not as an ontological hybrid, but as a perspectival construal of the field: more specific than the system as a whole, but still fundamentally a potential.

The wavefunction is a region of the field’s possibility space that has been shaped by context, entanglement, and prior interactions.

It is the field viewed under constraints — a focused subpotential that carries a structured probability distribution over possible instances. It tells us where and how a particle could emerge, given the current configuration of the system.

The cline of instantiation is perspectival

This distinction hinges on an important clarification:

The cline of instantiation — from potential to instance — does not describe a temporal process or ontological layering. It represents different perspectives on the same phenomenon, distinguished by level of generality.

For example, in climate science:

• Climate is the potential: the long-term structured conditions

• Weather is the instance: the actualisation of those conditions in a particular moment

Likewise, in quantum theory:

• Field is the potential: the general space of possibilities

• Wavefunction is the subpotential: the constrained shape of that space for a specific context

• Particle is the instance: the fully committed realisation of that shape

Each is a semiotic construal of the same system, not a separate layer of reality.

Why this matters

Reframing the wavefunction as subpotential helps clarify its dual nature:

• It is not a particle, because it is not an instance.

• It is not a field, because it is already conditioned by a specific configuration.

• It is a way of viewing the field: potential viewed through the lens of contextual probability.

This construal also allows us to treat wavefunction collapse not as a physical event, but as a semiotic shift — a change in construal from potential to instance.

In this light, quantum theory becomes a richly relational semiotics of possibility, where reality is not built from things, but from commitments — and the wavefunction is a map of uncommitted possibility shaped by context.