Einstein’s general theory of relativity transformed gravity from a force into geometry. No longer a pull between masses, gravity became the curvature of spacetime itself — a manifestation of the shape of the universe. But if we follow this move to its relational conclusion, we arrive at something even more radical: curvature not as an entity or field, but as a construal of potentiality.
From a relational standpoint, gravity is not something that “is” — it is something that happens, and only ever in relation.
What Is Curvature, Really?
In differential geometry, curvature is a measure of how a space deviates from being flat. In general relativity, the presence of mass-energy alters the curvature of spacetime, and that curvature in turn guides the motion of bodies. This elegant feedback loop is often described as a kind of mutual determination: matter tells space how to curve, space tells matter how to move.
But there is a quiet assumption embedded here: that “space” is something that can be curved. That it has an ontological status apart from the bodies within it.
Relational ontology challenges this head-on.
Curvature as Systemic Potential
Curvature, in a relational view, is not a property of a background medium — it is a systemic regularity in the construal of motion. When we describe trajectories as “geodesics in curved spacetime,” we are not uncovering the shape of an entity, but articulating a theory of meaningful relations among potential paths.
Think of it this way: gravity is not the deformation of a substance, but the deformation of expectation. It is a pattern in the way potential trajectories become actualised — a systemic bias in the field of what can happen. This bias is not objective in the classical sense; it is invariant across construals.
In this sense, curvature is a relational affordance — a way of coordinating perspectives on motion without postulating any underlying “stuff” that is being bent.
No Empty Stage, No Background Dance
Relational ontology discards the stage. There is no container, no void that curves. Instead, curvature is a higher-order meaning potential: a configuration of construals that makes sense of how systems of interaction unfold in relation to mass-energy distributions.
This move reconfigures the field equations themselves. What Einstein took as an identity between geometry and energy becomes, from our standpoint, a mapping between orders of relational constraint: a dynamic coordination of the potential to distinguish, cut, and orient motion within a construed topology of possibility.
The Horizon as Relational Boundary
One of the most striking consequences of curvature is the emergence of horizons: boundaries beyond which events cannot affect a given observer. In a substance ontology, horizons raise paradoxes — information loss, singularities, firewall hypotheses. But in a relational ontology, a horizon is not a place; it is a limit of potential coordination. It is the boundary of a system’s ability to construe — a semiotic horizon, not a spatial one.
This reframing neutralises many of the metaphysical puzzles associated with black holes and cosmological horizons. There is no “inside” or “outside” in absolute terms — only systems of construal, each with their own domain of actualisable relation.
Gravity as the Tendency to Construe Together
Gravity, in this light, is not simply “geometry” — it is the relational skew of the universe’s meaning potential. It is the tendency for trajectories to cohere, for systems to orient toward mutual construal. We might say: gravity is not what holds matter together; it is what holds meaning together at the scale of mass and motion.
Seen this way, the Einstein field equations are not a description of objective reality. They are a grammar of curvature: a systemic theory of how possibilities coordinate under conditions of mass, energy, and construal.