Quantum mechanics, more than any other domain, reveals how a model’s internal architecture can seduce its practitioners into metaphysics. Nowhere is this clearer than in the treatment of the wavefunction.
For a century, the ψ-function has been read as a physical state of the world, a literal resident of reality’s backstage. Whether “living” in configuration space, Hilbert space, or the mind of God, the wavefunction is imagined to be the thing that is—until, of course, it suddenly isn’t, because measurement “collapses” it.
But all of this arises from a category mistake: linear algebra treated as ontology.
Where Posts 3 and 4 identified errors of over-openness and under-openness, the wavefunction reveals the complementary pathology: over-closure. A construal compresses the phenomenon into a particular representational form and then treats that compression as the phenomenon itself. The model’s orientation stabilises too sharply, fixing distinctions that belong to the calculus, not the world.
Let us track how this over-closure happens, and how the relational frame dissolves the paradoxes that have haunted quantum foundations for a century.
1. The wavefunction as generator, not inhabitant
The formal role of the wavefunction is straightforward:
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it encodes dispositions for measurement outcomes,
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it represents the model’s orientation relative to a chosen basis,
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and it generates probability amplitudes through well-defined transformations.
Nothing in this role requires or even suggests that ψ is the physical state of a system. It is a model-generative device, a representational stance, a way of inclining the mathematics toward particular patterns of expectation.
Yet physics routinely reifies it, as if the quantum world were a literal vector in Hilbert space awaiting collapse.
2. Collapse: the artefact of a frozen construal
If ψ is treated as the “real” state of the system, collapse instantly becomes a metaphysical mystery: How can something evolve smoothly under Schrödinger’s equation and then instantaneously jump?
The paradox arises only because physics confuses:
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change in the model’s orientationwith
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change in the world’s being.
Thus collapse is simply the most dramatic symptom of over-closure: the cost of treating ψ as a thing rather than a projection.
3. Coherence: the shadow of the same mistake
Quantum coherence, too, is often loaded with unnecessary metaphysics. Interference phenomena are treated as evidence that systems “really are” in superpositions, with each term in the expansion representing an ontically real branch or component.
But coherence is not a feature of the world’s interior structure; it is a feature of the linear relations the model imposes in order to generate predictions.
To call it “real” is to confuse the geometry of Hilbert space with the geometry of phenomena. This is again over-closure: the construal prematurely crystallises and then naturalises its own internal relationships.
4. Over-closure as the quantum pathology
Let us mark this pathology clearly:
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Over-openness (Post 3) lets the model expand beyond the phenomenon → divergence.
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Under-openness (Post 4) leaves orientation insufficiently cut → gauge freedom.
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Over-closure (Post 5) fixes the construal too rigidly → wavefunction metaphysics.
In quantum mechanics, over-closure works like this:
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Choose a representational apparatus (Hilbert space).
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Select an orientation (basis, dynamical law, observable algebra).
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Encapsulate this orientation into a single object (ψ).
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Forget that this encapsulation reflects a cut.
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Reinterpret ψ as a physical state of affairs.
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Spend decades trying to explain “collapse,” “superposition,” “measurement,” and “nonlocality.”
5. What quantum foundations look like after the relational cut
In the relational frame, the wavefunction is not an ontological entity; it is an expression of the model’s inclination—a selective, constrained encoding of how the model maps potentialities to expectations.
This view yields immediate clarity:
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Collapse is a re-inclination, not a cosmic event.
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Superposition is a perspective-dependence, not a physical blending.
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Coherence is a modelling relation, not a ghostly interference between “actual” branches.
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The measurement problem dissolves, because the problem was never in the world—it was in treating the construal as the world.
6. Releasing quantum theory from its metaphysical burden
Seen correctly, quantum mechanics is not weird; the interpretations are.
Once we re-locate the wavefunction as a modelling device, not a metaphysical inhabitant, the foundational problems lose their bite. They remain fascinating, but no longer paradoxical.
Next: Post 6 — The Shape of Spacetime and the Shape of Equations
With the quantum side of over-closure clarified, we turn next to general relativity. There, the issue is not collapse but geometric overcommitment: the conflation of the representational machinery of differential geometry with the nature of spacetime itself.
The cuts continue.
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