Sunday, 14 December 2025

Rethinking the Wavefunction: Not a Thing, but a Theory of Potential

The wavefunction, ψ, is central to quantum mechanics. It encodes all that can be said about a system, evolves according to Schrödinger’s equation, and (somehow) yields probabilities upon measurement.

But what is the wavefunction?

Is it a real, physical field? A statistical tool? A representation of knowledge? A disposition? Interpretations diverge wildly, and each stumbles on the same obstacle: how to explain a formal structure that behaves like a thing, but doesn’t correspond to anything directly observable.

In a relational ontology, this confusion is diagnostic.

The wavefunction is not a hidden reality or a wave in space. It is a relational encoding of constrained potential — a theory of what may be, not a statement of what is.

It is not an entity. It is the shape of affordance across a field of relation.


1. From Substance to Structure

  • In realist interpretations, the wavefunction is a field over configuration space — a highly abstract multidimensional object,

  • But this reifies the formalism, making it into a thing-in-itself,

  • A relational approach reframes it:

The wavefunction is not a physical object but a formal articulation of systemic constraint — a structured encoding of possible actualisations.

It does not describe what exists, but what is afforded by the topology of relation.


2. Probability and Potential

  • ψ is often said to yield probabilities via the Born rule: |ψ|² gives the likelihood of outcomes,

  • But what kind of probability is this? Not classical ignorance, and not frequentist chance,

  • Relationally:

It encodes the relative stability of different construals under current constraints.

It is not uncertainty about a hidden state, but a distribution over the field’s modal profile — how potential is shaped.


3. No Configuration Space, No Collapse

  • The formal structure of ψ often implies a reality in configuration space — not physical space,

  • But this leads to ontological problems: is the universe a wavefunction in 3N dimensions?

  • In relational terms:

ψ is not spatial at all. It does not live in a place, because it is not a thing — it’s a theory of where and how construals can be resolved.

The "collapse" of ψ is not physical discontinuity. It is the selection of one construal path within the system’s potential.


4. Dynamics Without Ontology

  • Schrödinger’s equation gives ψ’s evolution. But what is evolving?

  • If ψ is not a physical object, then there is no need to picture it "changing in time",

  • Instead:

ψ evolves as a shifting theory of potential — a relational recalibration of what affordances are possible under the system’s unfolding constraints.

The evolution is not of a wave, but of a structure of coherence within the system.


5. Interpretive Impasse Dissolved

  • The multiplicity of quantum interpretations (Copenhagen, many-worlds, Bohmian, epistemic) each assigns a different ontological status to ψ,

  • But all assume ψ must refer to something that exists in a familiar sense,

  • The relational approach reframes this entirely:

ψ refers not to a thing but to a modal architecture — a second-order field of constraint within which events may become.

It is not a veil over hidden variables. It is the map of what may be made actual under constraint.


Relational Definition

We might say:

The wavefunction is a systemic encoding of structured potential — a construal of what transitions are possible, given the constraints of the current field.

It is not a description of being, but a dynamic theory of affordance.


Closing

The wavefunction has long been the symbol of quantum mystery — a ghostly field, both present and elusive. But its paradoxes only arise when we assume it must be a thing.

Reimagined relationally, ψ becomes clear: not a picture of what is, but a system’s internal model of what it may become. Not a wave in space, but a logic of transition — a coherence across potential.

In the next post, we’ll examine the role of the observer — not as a subject separate from the system, but as an instance of perspective within a relational cut.

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