Few features of quantum theory have provoked more discomfort than probability. Unlike classical probabilities — which typically reflect ignorance about an underlying certainty — quantum probabilities appear to be intrinsic. The world does not seem merely unknown before measurement; it seems indefinite.
This has led to decades of debate. Is the wavefunction real or epistemic? Is quantum randomness fundamental or apparent? Does collapse reflect knowledge or ontology?
A relational perspective reframes these questions entirely.
Quantum probability is not a statement about ignorance or chance. It is a measure of structured potential — the system’s internal landscape of affordance.
Let us explore how this differs from classical and standard quantum views.
1. From Ignorance to Indeterminacy
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In classical systems, probability arises when we lack information: we don’t know which side the coin will land on, but the outcome is determined,
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In quantum theory, even with complete knowledge of the system’s wavefunction, outcomes are only probabilistically determined,
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This is often framed as fundamental randomness — an irreducible gap between potential and actual,
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But in relational terms:
What we call randomness is a structured ambiguity — a condition of possibility, not arbitrariness.
The system is not hiding a value. It is not constituted until constrained into an actualisation.
2. The Wavefunction as Potential, Not State
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Quantum mechanics uses the wavefunction to assign amplitudes to different outcomes,
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These amplitudes yield probabilities through the Born rule,
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But what is the wavefunction “of”? A system? A particle?
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Relational view:
The wavefunction is not a description of a thing, but a structured map of what can happen under specific constraints.
It encodes the relational topology of the system’s potential — not the properties of an entity.
3. Probability as Systemic Affordance
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When we measure a system, we actualise one possibility among many,
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The probability of a given outcome is not an expression of chance,
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It is:
A reflection of how the system's structure — its internal constraints and couplings — biases certain actualisations over others.
Probability, in this sense, is affordance-weighted resolution. Not ignorance. Not randomness. Not mere likelihood.
4. Collapse as Reconfiguration
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Standard interpretations speak of wavefunction collapse: an abrupt reduction to one outcome,
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This is often treated as an ontological event, or a projection of knowledge,
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In relational terms:
Collapse is not a reduction. It is a reorganisation — the system’s potential being punctualised under constraint into a new topology of affordance.
Measurement does not destroy possibilities; it reconfigures what’s possible from a new relational perspective.
5. Decoherence and the Myth of Branching
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In decoherence theory, the apparent collapse of probability is explained by entanglement with the environment,
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This leads to many-worlds interpretations, where all possibilities occur, and the universe “branches”,
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But this presumes a reality of outcomes independently of construal,
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Relationally:
There are no branches. There is only one system, continuously reorganising its affordances under evolving constraints.
Probability does not reflect unseen alternatives — only the modal structure of this system, here, now.
Relational Definition
We might say:
Quantum probability is the expression of a system’s internal tension — a distribution of affordances constrained by relational structure and experimental context.
It is not a sign of incompleteness. It is how a structured potential becomes legible in a world where nothing is determined in advance.
Closing
Where classical physics saw probability as a veil over certainty, and standard quantum mechanics reified it into ontological randomness, the relational view locates probability where it belongs:
In the structure of the system’s potential itself — not as uncertainty about a hidden state, but as a measure of what the system makes possible.
In the next post, we will explore measurement not as an intervention by an observer, but as a systemic transition — the punctualisation of coherence under constraint.
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