The wavefunction is often treated as the archetype of potential in quantum mechanics. Within the relational ontology, it can also serve as a mirror for the conceptual evolution of potential itself. As our construal of potential has shifted — from readiness to structured, perspectival, and historically evolving possibility — so too does our understanding of what the wavefunction represents.
1. Readiness: Inclination and Ability
In the earliest phase, the wavefunction could be understood as a system poised to realise outcomes. Its amplitudes suggested two complementary aspects of readiness: inclination, the tendency toward particular measurement results, and ability, the structural capacity of the system to realise those outcomes. The wavefunction felt like a mechanism waiting to be triggered: some states were “more ready” than others.
This reading was intuitive but carried temporal and causal overtones. The wavefunction seemed to wait for measurement, a latent store of potentiality. Although this captured an immediate sense of differentiated availability, it also blurred the line between the system itself and any imagined “inner” property of readiness.
2. Latent Structure: The Space of Possibilities
Next, we abandoned the notion of readiness as stored propensity and reframed the wavefunction as a space of constrained possibilities. The amplitudes no longer described readiness to trigger, but formal relational weightings across potential outcomes.
In this view, the wavefunction is a structured map: a landscape of what could occur under the system’s rules. Potential is no longer dispositional or temporal. We can see the shape of possibilities without imagining the system “waiting” for an event. The wavefunction, as a latent structure, becomes the field of formal potential rather than a store of propensity.
3. System as Theory of Instances
The next conceptual leap fully aligns the wavefunction with relational potential: the wavefunction is the system. It is the theory of instances. Measurement outcomes are contingent events that satisfy the system’s constraints; the system itself is the ensemble of potential.
There is no latent “stuff” waiting to collapse. The wavefunction’s structure embodies all possibilities: specifying it is specifying potential. Novel outcomes can still arise, but they do so within the relationally defined system rather than as a pre-existing, hidden content.
4. Perspective: Potential vs. Instance
With the perspectival cut, the wavefunction’s dual role becomes clear. From one orientation, it is entirely potential: a relational description of possible measurement outcomes. From another orientation, a particular measurement outcome is an instance. There is no process in which potential “becomes” actual; the wavefunction does not collapse as a physical process but is re-described relationally under a different cut.
This move eliminates the classical illusion of becoming, while preserving explanatory power. The wavefunction is now a mirror of relational potential, coexisting with its instances under perspectival shifts.
5. Sub-Potentials: Localised Constraints
Within the wavefunction, certain modes, eigenstates, or subspaces can be seen as sub-potentials: restricted sets of possibilities under the same system. These local constraints explain why particular transitions or interactions dominate, without introducing new ontological layers. Sub-potentials make patterned structure intelligible, showing how the relational shape of potential governs observed outcomes.
6. Horizon: The Edge of Possibility
The notion of horizon highlights the forward-facing, emergent character of potential. For the wavefunction, the horizon represents the edge of what could happen in the next measurement or interaction, given the relational constraints of the system. It captures novelty: states that have not yet been actualised but could plausibly emerge. Horizons shift with each measurement and construal, allowing the wavefunction to retain a sense of openness without implying latent content or stored readiness.
7. Evolution of Potential
Finally, potential itself can evolve. The wavefunction’s potential is historically shaped: prior actualisations, stabilisations, and interactions influence which states are available for future consideration. This evolution is relational and non-teleological; it does not imply inherent direction or purpose. Each measurement or interaction reshapes the landscape of potential, creating new constraints and new edges for future possibilities. The wavefunction becomes a living record of relational potential, evolving alongside the system it describes.
8. Explicitly Rejected Conceptions
In parallel, several misleading readings of the wavefunction are consciously rejected:
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It is not a causal power waiting to act.
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It is not latent content stored in the system.
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It is not value-laden, pre-meaning substrate, or probabilistic in a classical sense.
Each of these would violate the relational, perspectival nature of potential. The wavefunction, properly understood, is a relational system of possibilities actualised under different cuts, evolving through history.
9. Deep Continuity
Through this lineage, we see how the wavefunction mirrors the evolution of our concept of potential: from intuitive readiness to structured possibility, from perspectival relationality to emergent horizons and historically evolving systems. At each stage, it retains coherence, yet its meaning shifts as the relational ontology matures.
The wavefunction thus becomes both an illustration and a laboratory: it embodies the same transitions we made conceptually in understanding potential, providing a bridge between formal physics and the relational perspective on possibility.
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