🎯 The Uncertainty Principle in Relational Terms

Our Relational Ontology

• Ontology: Experience is construed as instances of potentials, always relational.

• Space and time: Not absolute, but relational dimensions of instances.

• Quantum mechanics: The observer collapses potential into instance.

• Measurement: Observation actualises one potential among many.

• Wavefunction: A construal of potential (i.e., probabilistic structure of potential instances).

• Uncertainty: Conventionally, a principle of limits in simultaneously knowing (measuring) conjugate variables like position and momentum.

1 From Determinate Quantities to Relational Potentials

In classical physics, position and momentum are inherent properties of a particle — they exist independently of observation.

In our ontology, however:

• There is no “position” or “momentum” without an instance — and instances are actualised only through observation.

• Prior to observation, we’re in the domain of potential — a relational structure describing possible instances, not actual values.

Thus:

The Uncertainty Principle is not a constraint on what is, but a condition on what can be actualised from potential in relation to observation.

2 Wavefunction as Relational Potential

The wavefunction is not a description of a particle “in itself,” but of the relational field of potentialities — a field that is observer-dependent in the sense that its actualisation requires the observer.

• The spread in position (∆x) and momentum (∆p) in the wavefunction reflects a structure of co-varying potentialities.

• These are not properties the particle “has,” but dimensions of possibility for instantiation.

So uncertainty reflects the structure of potential, not a lack of knowledge about pre-existing properties.

3 Collapse as Actualisation

Observation collapses this potential into an instance: a measured position, say.

• But that actualisation destroys the complementary potential — actualising one dimension (like position) renders its conjugate (like momentum) indeterminate in the instant.

• Not because momentum doesn’t exist — but because the relation constituting “momentum” is no longer defined for the instantiated relation that gave us position.

So uncertainty is not epistemic (a limit of knowledge), but ontological and relational:

The actualisation of one relation excludes the concurrent actualisation of its complementary relation.

This is a special case of a more general principle in our model:

The instantiation of a potential involves the transformation of a relational system, not the revelation of pre-existing values.

4 Time and Process

Because time is the unfolding of processes in our ontology:

• The wavefunction is a potential that unfolds — and is transformed — over time.

• A measurement at t₁ instantiates a relation; what is potential at t₂ is now a new structure, transformed by the earlier actualisation.

Thus:

• Uncertainty reflects the mutual exclusivity of certain instantiations at a given point in the unfolding of time.

• And the act of instantiation is always a temporal, material, and relational event.

🌀 5 Modality: Probability vs Potential

In conventional quantum theory:

• The wavefunction’s squared amplitude gives a probability distribution — a statistical account of outcomes.

But in our relational ontology:

• Probability is already modalised experience — a reconstruction of previous instances into abstract distributions.

• By contrast, potential is not yet modalised; it is the structured space of what may become actual.

Thus:

The wavefunction does not describe probability until the observer interprets it retrospectively, through a series of past instances.

Prior to that, it encodes relational potential, not statistical expectation.

So:

• When we interpret ∆x and ∆p as uncertainties, we're interpreting potential through the lens of probability.

• But from our view, these deltas are dimensionalities of potential in relation to the observer’s mode of engagement.

🤝 6 Observer and Apparatus as Relational Fields

In our ontology:

• The observer collapses potential into instance, but the observer is never isolated.

• They are always situated within a relational field, including:

  • the material apparatus,

  • the conceptual frame,

  • the epistemic commitments (what counts as an ‘observation’).

So:

What becomes actual is a relation between observer and observed — not a property of the observed.

And the conjugate variable (e.g., momentum if position is measured) loses its definitional frame in that instantiation, because:

• That relation was never actualised — its potential was excluded by the relational constraints of the measuring configuration.

• The apparatus constrains what relation can be instantiated. It does not uncover a pre-existing value, but participates in actualising one dimension of potential.

This is an extension of our principle:

Meaning (or value, in this case) is instantiated through systems of relation — never inherent in isolated entities.

🧭 7 Time, Uncertainty, and the Transformation of Potential

In our model, time is not an axis but the unfolding of processes — the ordering of actualisations.

So:

• A measurement event at time 
  $t_1$

• This event transforms the structure of potential for future instantiations.

• The uncertainty relation is not just a limit between simultaneous measures, but a temporal process of mutual exclusion in the unfolding of instances.

And crucially:

The uncertainty principle expresses the non-commutativity of certain instantiations in time:

The sequence of actualisations matters, because each one restructures the relational potential that follows.

This aligns naturally with our broader view of systems (semiotic or not):

• A feature, once instantiated, modifies the probabilities (or resonances) of future co-selections.

• But in quantum mechanics, the structure of potential itself changes — not just the statistical profile.

—

🚪 Summary: A Relational Ontology of Uncertainty

Conventional QM	Relational Ontology Interpretation
A particle has indeterminate properties	There are no inherent properties — only relational potential
Measurement reveals a value	Measurement actualises a relational instance
Uncertainty is a limit on knowledge	Uncertainty is a mutual exclusivity of possible relations
Probability as statistical modality	Potential as relational structure, probability as retrospective
Time is a parameter	Time is the unfolding of processes (ordered actualisations)