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.

Relational Mass — Inertia, Gravitation, and the Potentiality of Matter: 1 Mass as the Depth of Potentiality

1. Introduction: The Problem of Mass as Substance

Classical and modern physics alike treat mass as an intrinsic property: a scalar quantity attached to an object, a measure of “how much matter” or “how much resistance to acceleration” or “how strong the gravitational pull.”

These descriptions differ in emphasis but share a foundational metaphysics: mass is something objects have.

From the standpoint of relational ontology, this commits the same category error that once animated representational accounts of motion, light, and geometry. It presumes an object whose identity and capacities are prior to relation, and whose “mass” is a private attribute that relations merely reveal.

This post develops the opposite stance:

Mass is not a substance, quantity, or property.

Mass is the depth of relational potentiality.

2. Potentiality as System, Instantiation as Cut

In this ontology, a system is understood as a structured potential — a theory of possible instantiations.

Actualisations are cuts: perspectival selections that bring part of the system’s potential into the order of phenomenon.

Thus, “having mass” cannot be an intrinsic state. It must instead be a feature of the system-level structuring of potentiality actualised across successive cuts.

The metaphysical continuity once attributed to a substance of mass is replaced by the coherence and stability of an ontological horizon.

3. Depth of Potentiality: The Relational Definition of Mass

To speak of “depth” is to speak of the resilience of patterning under perturbation.

A system exhibits deeper potential when:

• its patterning persists across a wider range of possible cuts,

• perturbations lead to less dramatic reconfiguration,

• and its horizon of potentiality constrains neighbouring systems more strongly.

In this frame, mass is the relational signature of stable coherence.

What classical mechanics calls “inertia” is simply this stability construed along a temporal axis; what gravitation calls “mass” is this same stability construed as curvature of the potential horizon.

The old distinction between “inertial mass” and “gravitational mass” dissolves.

Both are construals of the same relational topological depth.

4. Why ‘More Mass’ Means ‘More Stability’

Systems with “more mass,” in classical terms, are those that resist acceleration and generate gravitational influence.

Relationally:

• Resistance to acceleration = stability of pattern across successive instantiations.
  A deeper potential well requires greater modulation to shift its construal.

• Gravitational influence = deformation of neighbouring potential horizons.
  A deeper well modulates the structure of possible construals around it.

Nothing here is mysterious or field-like.

There are no forces acting, no hidden substances transmitted.

There is only the topology of potentiality: deeper wells produce more stable trajectories and stronger horizon curvature.

5. Mass Without Matter

In this account, mass is not tied to the presence of “stuff.”

A system has depth not because it is made of matter, but because:

• its construals exhibit strong coherence,

• its potential horizon is tightly structured,

• and it participates in relational networks that reinforce that structure.

This is why fields, particles, and continuous media can all be “massive” or “massless” in classical representation — mass is a signature of pattern depth, not a property of substance.

6. The Relational Resolution of the Classical Puzzle

The so-called “mystery” of why inertial and gravitational mass are equal collapses at once.

They were never distinct quantities to begin with.

Classical physics created the distinction by splitting the construal:

• inertia = pattern stability under successive cuts

• gravitation = horizon curvature induced by potential depth

Relationally, these are two ways of describing the same topological feature.

Thus the equivalence principle becomes not a profound fact about nature, but a reminder that a representational ontology has double-counted a single relational dynamic.

7. Consequences for the Series

This reconstrual opens a structured pathway forward:

• Post 2 will examine inertia as the persistence of pattern across successive cuts.

• Post 3 will show gravitation as horizon curvature, not force or field.

• Post 4 will reinterpret energy as the tension of reconfiguration potential.

• Subsequent posts will integrate massless systems, the equivalence principle, and relational gravitational waves.

Mass, once demoted from substance to potentiality, becomes the unifying hinge for a relational rewrite of mechanics, gravitation, and cosmology.

Synthesis: Relational Physics — Geodesics, Motion, and Light

Over the past three series, we have systematically reconstructed classical physics within a fully relational ontology. The three threads — geodesics, motion, and light — form a unified framework in which all phenomena emerge from patterns of actualisation within relational fields of potentiality.

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1. Geodesics: Trajectories as Emergent Patterns

• Classical trajectories are replaced by geodesics of relational coherence.

• Paths are not traced through a pre-existing space; they emerge from the interplay of constraints between systems.

• Geodesic analysis provides the global structure for relational patterning, defining the landscape in which dynamics and light unfold.

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2. Relational Motion: Local Dynamics Without Forces

• Motion is successive actualisation, not displacement.

• Velocity = relational rhythm (pattern stability across cuts).

• Acceleration = modulation of potentiality constraints (change in rhythm).

• Momentum = tension of pattern coherence across cuts (consistency under perturbation).

• This framework reproduces classical dynamics without invoking objects moving in space, forces, or intrinsic properties.

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3. Relational Light: Photons, Frequency, and EM Phenomena

• Photons = sequences of null cuts at the limit of potentiality.

• Frequency = rhythm of cuts as construed across relational horizons.

• Redshift/blueshift = horizon dynamics (perspectival reordering of cuts).

• Electromagnetism = emergent relational coherence (fields are descriptions, not substances).

• Light phenomena naturally integrate with geodesics and dynamics, producing classical observables without classical metaphysics.

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4. Unified Relational Ontology

Across all three domains, we observe consistent principles:

1. No intrinsic objects or properties: Everything emerges from relational patterns.

2. No background space or time: Apparent motion and propagation are perspectival orderings of actualisations.

3. Constraints and horizons: Relational fields define potentiality; coherence of patterns produces observable phenomena.

4. Patterns, rhythms, and tensions: The fundamental primitives are pattern stability, modulation, and tension across successive cuts.

Classical concepts — motion, acceleration, momentum, frequency, electromagnetic fields — are all relationally emergent descriptions, not metaphysical entities.

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5. Implications and Future Directions

• This framework provides a complete relational replacement for classical kinematics, dynamics, and electromagnetism.

• It unifies massive-body motion and photon behaviour in a single ontology of patterned actualisation.

• It sets the stage for future relational reconstructions of quantum phenomena, where potentiality, coherence, and horizon constraints play a central role.

• Observables are now understood as construals of relational patterns, rather than intrinsic measurements of pre-existing objects or fields.

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6. Concluding Perspective

Relational physics shifts our perspective:

• From objects in space experiencing forces

• To patterns in potentiality fields experiencing modulation

In doing so, it preserves all predictive and explanatory power of classical physics while eliminating representational metaphysics.

What remains is a world of emergent coherence, where motion, light, and electromagnetic phenomena are all expressions of relational ordering at multiple scales. The universe, in essence, is the becoming of possibility, actualised and construed through the interplay of constraints and horizons.