Relational Mass — Inertia, Gravitation, and the Potentiality of Matter: 3 Gravitation as Horizon Curvature

1. Introduction: Gravity Without Forces, Fields, or Background Geometry

Classical physics casts gravity as a force; general relativity reinterprets it as curvature of spacetime.

Both inherit a representational assumption: a background—whether force-field or manifold—acts on massive bodies.

A relational ontology cannot accept this metaphysics.

There is no background, no pre-given geometry, and no external field exerting influence.

There are only structured potentials and the cuts that actualise them.

Thus gravity must be reconceived not as something a system experiences or responds to, but as the topology of the horizon of potentiality itself.

2. Potential Horizons as the Architecture of Constraint

Recall:

• A system is its organised potential for instantiation.

• A cut is a perspectival actualisation within that potential.

• A trajectory is the patterned ordering of such cuts.

The horizon of a system is the boundary within which possible construals maintain coherence.

This horizon is not spatial but relational; it circumscribes the limits of potential modulation without pattern collapse.

The topology of this horizon determines the constraints on successive instantiations — what classical mechanics mistakes for “forces” or “fields.”

3. Gravitation as Curvature of the Potential Horizon

Gravitation is the curvature of the relational horizon generated by systems with deep potential wells.

A deep potential well:

• tightly structures its own possible instantiations,

• modulates the construal potentials of neighbouring systems,

• and deforms the coherence landscape across which trajectories are patterned.

This curvature is not curvature in space; it is curvature of constraint, of potential, of coherence structure.

When construals occur in this curved relational topology, the most stable succession of cuts corresponds exactly to what classical physics calls free fall.

Thus free fall is inertial motion — not because gravity is “really geometry,” but because in curved horizons, stable construals appear as accelerated trajectories from the outside view.

4. Why Free Fall Is Inertial: The Relational Explanation

In representational physics, the equivalence principle bridges inertia and gravitation but leaves their relationship obscure.

Relationally:

• inertia = pattern stability across cuts

• gravitation = curvature of the relational horizon that structures those cuts

The two are simply the same phenomenon described differently.

Free fall is inertial because:

• the system’s own potential horizon is not being actively modulated,

• the modulation originates in the curvature of the surrounding horizon,

• and the trajectory of successive cuts aligns with the most coherent construal possible.

Thus a falling system “feels weightless” because no intrinsic modulation of its own potential is occurring.

The constraint is relational, arising from horizon structure, not from any force acting on the system.

5. Gravity as Constraint, Not Cause

What looks like gravitational “attraction” is merely the structure of what it is possible to instantiate.

If the horizon of potentiality is curved:

• stable successions of cuts converge where the potential deepens,

• trajectories appear as if being “pulled,”

• but nothing draws or pushes anything.

This replaces causation with coherence.

The world does not pull bodies together; their relational potentialities make coherent actualisation patterns appear convergent.

6. Gravitational Time Dilation, Relationally Reinterpreted

In general relativity, clocks run slower near massive bodies because spacetime is curved.

Relationally:

• the depth of potentiality modulates the horizon’s structuring of possible cuts,

• deeper potentials restrict the spacing of stable construals,

• giving rise to what is construed as slower “time.”

“Time dilation” is simply perspectival variation in construal density across horizons.

No geometry is required; only relational topology.

7. Gravitational Redshift as a Horizon Effect

A photon actualised across horizons of different depth exhibits shifted frequency not because it “loses energy,” but because:

• frequency is a relational pattern across cuts,

• the horizon curvature changes the construal density,

• so the pattern is instantiated differently in each relational context.

Redshift = the re-slicing of pattern across non-uniform horizons.

It is not a change of the photon, but a shift in the relation that construes it.

8. Summary and Transition

Gravitation thus emerges as:

• curvature of relational potentiality,

• deformation of horizons,

• constraint on patterning,

• not force, not geometry, not intrinsic interaction.

With inertia (Post 2) and gravitation (Post 3) unified at the level of relational topology, the next step is to interpret energy in this same framework.

Post 4 — Energy as Pattern Tension Across Cuts

will show how the conservation of energy is a coherence requirement of relational patterning, not the persistence of a metaphysical substance.