In classical mechanics, acceleration is defined as the rate of change of velocity with respect to time. This definition brings with it the full representational apparatus of classical thought: velocity as a property of an object, time as an external parameter, and motion as passage through a spatial manifold.
In a relational ontology, none of these structures exist independently of construal. Velocity, as the previous post established, is not an intrinsic state but a rhythm: a stability of patterning across successive actualisations. Acceleration, consequently, cannot be a derivative of that rhythm. It is not a change of a quantity, but a shift in the underlying relational potentiality that allows certain rhythms to stabilise.
This reframing eliminates forces, fields, and intrinsic “changes of motion” while retaining the explanatory content of dynamics. It positions acceleration as a property of the relational field, not of the object construed within it.
1. Why Acceleration Cannot Be “Change of Velocity”
Velocity, relationally understood, is already derivative:
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It is not a quantity in the system.
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It is a construed pattern of the system’s successive actualisations.
To define acceleration as “change of velocity” therefore presupposes:
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that velocity is an object-level property;
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that time is an independent parameter;
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that change is measured against a background that remains fixed.
Acceleration must therefore be reconceived without appeal to representational structures. What remains is the relational field itself—the constraints that shape the coherence of actualisations.
2. Stable Potentiality Fields and the Relational Analogue of Inertia
From the perspective of relational ontology, what classical mechanics calls “uniform motion” is simply the persistence of a stable pattern of actualisation. This stability arises because the system’s field of relational potentiality is coherent, unperturbed, and locally uniform.
Thus the relational analogue of inertial motion is:
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a rhythm sustained by a stable constraint field.
No force is required to maintain it, because no “motion” in the classical sense is being maintained. What persists is pattern, not momentum as a quantity.
3. Acceleration as Modulation, Not Derivative
Acceleration, relationally construed, occurs when:
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the constraints that shape successive actualisations shift,
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producing a different coherence pattern across cuts,
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which construal organises as a change of motion.
But importantly:
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Nothing “changes” within the object.
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There is no “state of motion” that is being altered.
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There is no intrinsic vector being updated.
Thus:
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Acceleration = modulation of relational potentiality.
This modulation may be smooth (producing what classical mechanics calls constant acceleration) or irregular (producing complex motion), but in every case, the acceleration is a property of the relational structure, not the object.
4. Why Acceleration Feels “Force-like”
The classical picture treats force as the cause of changes in motion. From a relational perspective, what is felt or observed as “force” is simply the experiential mark of constraint modulation.
When the field of potentiality shifts:
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patterns that were coherent become unstable,
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new patterns become viable,
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successive actualisations no longer fit the old rhythm,
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and construal organises this as an “acceleration.”
This is why acceleration is perceptible in a way that inertial motion is not. When the relational field is stable, patterning flows smoothly; when it modulates, the system experiences the shift. There is no separate force acting on an object—only the relational structure changing around it.
This is why forces do not exist in this ontology. They are metaphors for constraint modulation.
5. Gravity as the Paradigm Case
The geodesics series already reframed gravity not as a force but as a relational horizon effect: systems actualise patterns that maximise coherence within a potentiality gradient. That analysis allows us to see gravitational acceleration as:
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not attraction,
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not a field interaction,
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but a modulation of the relational potentiality structuresuch that the stable rhythm of a system’s actualisation aligns with what classical theory calls “free fall.”
In Einsteinian terms, free fall is inertial motion; in relational terms, it is unmodulated rhythm within a structured potentiality horizon. The “acceleration” is not experienced because it is not a perturbation of pattern; it is the pattern itself.
This gives the relational ontology a natural integration of gravitational acceleration without invoking spacetime curvature or force.
6. Non-Gravitational Acceleration Without Forces
What about accelerations in laboratory settings—pushes, pulls, collisions?
From the relational perspective, these are simply cases where:
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one system modulates the constraint field of another,
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altering the coherence of its successive actualisations,
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generating a new rhythm construed as a change of velocity.
There is no quantity of momentum transferred, because momentum (as the next post will show) is not a substance but a measure of pattern consistency. Instead, what is “transferred” is the reconfiguration of the relational horizon so that different patterns become stable.
Collisions are therefore events in which two systems mutually reconfigure each other’s potentiality fields.
7. What Acceleration Ultimately Becomes
Acceleration, under this ontology, is:
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not a vector quantity;
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not a derivative of velocity;
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not a response to force;
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not a change in the motion of an object.
It signals that the patterning available to a system has shifted. Nothing else is required.
This reconceptualisation preserves every observable feature of classical dynamics while removing its metaphysical commitments.
8. Transition to Momentum: Tension Across Cuts
With motion reconceived as pattern and velocity as rhythm, and with acceleration reconceived as constraint modulation, we are ready to reinterpret momentum.
This will be the focus of the next post.
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