Relational Mass — Inertia, Gravitation, and the Potentiality of Matter: 2 Inertia as Stability Under Relational Cut

1. Introduction: Why Inertia Has Always Been a Problem

Classically, inertia is treated as a primitive: objects “resist acceleration.”

In Newton’s formulation it is a property without explanation; in Einstein’s, inertia is absorbed into geometry but still presupposed as a basic disposition of matter.

The metaphysical residue is unmistakable:

inertia is taken to be a brute fact about objects.

In a relational ontology this position is untenable.

There are no inert objects, only patterns whose stability varies with the structuring of potentiality.

Thus inertia must be derived, not assumed.

2. Instantiation and the Horizon of Potentiality

Recall the relational structure:

• A system is a structured potential — a theory of its possible instantiations.

• An instantiation (cut) is a perspectival actualisation within that potential.

• A trajectory is a pattern in the ordering of cuts.

The stability of such a trajectory cannot be attributed to any intrinsic property of an “object” moving through space.

It must instead be read off the coherence of potentiality that constrains how successive cuts may unfold.

Thus we replace the classical notion of “the same object continuing in motion” with:

pattern-consistency across successive instantiations.

3. The Relational Definition of Inertia

Inertia is the stability of a construal pattern across successive cuts.

When the potentiality field remains unmodulated, the same pattern is the easiest to instantiate again; it becomes the path of least reconfiguration.

This yields the relational analogue of Newton’s first law:

A system will instantiate the same pattern across successive cuts

when the potential horizon is stable.

There is no “tendency” to maintain velocity.

There is only the coherence of the system’s potentiality, which constrains instantiations to follow a consistent rhythm.

4. Why ‘Uniform Motion’ Seems Simple

Traditional mechanics treats constant velocity as the default, the “natural state.”

Relationally, uniform motion is simply the case where:

• the potentiality field is stable,

• the relational horizons are unmodulated,

• and the construal of successive cuts reproduces the same pattern with minimal tension.

Nothing moves “through space.”

There is only pattern recurrence, constraining the ordering of instantiations.

Uniform motion = minimal modulation of relational potentiality.

This dissolves the metaphysical distinction between “being at rest” and “being in uniform motion.”

Both are stable patterns, distinguished only by the construal of separation across cuts.

5. Why Acceleration Breaks the Pattern

Acceleration is not “changing velocity.”

It is modulating the potential horizon so that the most stable pattern becomes a different one.

From the perspective of the system, this modulation appears as:

• instability in the previously stable pattern,

• a shift in the construal of successive cuts,

• a “force-like” deviation from the expected rhythm.

The classical idea that a “force causes acceleration” is replaced by:

acceleration is the reconfiguration of relational potentiality.

When the potential horizon is perturbed, the system’s pattern of instantiation must shift accordingly.

6. Why Inertia Feels Like Resistance

The phenomenology of inertia — the felt resistance during acceleration — also receives a clean relational account.

Acceleration induces tension in the horizon of potentiality, because:

• the construal pattern that was stable is now being suppressed,

• competing patterns demand reconfiguration,

• coherence must be maintained across the entire relational field.

This coherence requirement manifests in experience as “inertial force.”

It is not an internal property of a body but a response to horizon modulation.

7. Inertial Frames as Emergent, Not Given

In a representational ontology, inertial frames are chosen, defined, or privileged.

Relationally, an inertial frame is simply:

a perspective in which the potential horizon is locally unmodulated.

Such frames are not fundamental; they arise when the relational structure allows stable patterning with minimal reconfiguration.

They persist only so long as that structure remains coherent.

Thus inertial frames are contingent manifestations of relational stability — not metaphysical absolutes.

8. Summary and Transition

Inertia, classically a brute property, emerges here as:

• coherence of potential,

• stability of pattern,

• constraint on the ordering of cuts,

• and a perspectival effect of an unmodulated horizon.

This sets the foundation for the next development.

In Post 3 — Gravitation as Horizon Curvature, we show that “gravity” is not a force or a geometric field, but a deformation of relational potentiality that guides the construal of successive instantiations.