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.