In Newtonian mechanics, acceleration is defined as the rate of change of velocity over time. It marks the effect of a force acting on a mass, causing it to change direction or speed. It plays a central role in classical dynamics and remains essential to relativistic and quantum accounts of motion.
But like velocity and momentum, acceleration presupposes entities — things with position, speed, and mass. In relational terms, this foundation collapses: without substances or trajectories, we must redefine acceleration not as something experienced by an object, but as a second-order shift in the dynamics of relational actualisation.
1. The Classical View: Change in Change
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Acceleration is conventionally a second derivative: the rate at which velocity changes with respect to time,
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It measures how quickly a particle is speeding up, slowing down, or changing direction,
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But this view assumes particles, trajectories, and a continuous spatial background — all of which a relational ontology dissolves.
2. Acceleration Without Entities
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If there are no entities moving through space, there can be no literal “change in speed,”
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Instead, we consider how configurations of potential unfold — and how that unfolding itself can shift,
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Acceleration becomes: a change in the rate at which actualisation proceeds through a relational field.
3. Second-Order Actualisation
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We can think of a relational system as traversing a topology of constraints — unfolding from one configuration to the next,
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The rate at which this unfolding occurs corresponds to momentum or transition pressure,
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But if the rate of that rate changes — if the system speeds up or slows down in its transformation — this is relational acceleration.
4. Acceleration as Constraint Dynamics
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Forces don’t “act on bodies” — they are shifts in the structure of constraints that reshape what’s possible,
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From a relational perspective, forces are modulations in systemic affordances, and acceleration is the system’s reconfiguration in response,
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Thus, acceleration is not the result of an external push, but the internal realignment of potential in a field responding to altered coherence conditions.
5. Non-Uniform Actualisation
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In a static relational topology, actualisation might proceed at a steady pace (analogous to constant velocity),
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But when the topology itself is curved, compressed, or destabilised, the system reorganises more rapidly or more slowly,
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Acceleration, then, is an index of curvature in potential space — a second-order derivative of actualisation constrained by systemic structure.
Relational Definition
We might say:
Acceleration is the second-order modulation of actualisation within a relational field — the changing rate at which a system reconfigures under evolving constraints.
In this view, acceleration does not describe the behaviour of a body, but the increasing or decreasing coherence pressure across a field of constrained potential.
Closing
In the object-based model, acceleration describes how things change speed. In the relational model, it reveals how systems shift their unfolding pathways — a deeper measure of transformation. It is not a force applied to a thing, but a symptom of relational instability and emergent reorganisation.
In the next post, we’ll take up the concept of force itself — the apparent cause of acceleration — and explore how a relational ontology reframes it as gradient tension in the fabric of potential.
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