We’re accustomed to thinking of spacetime as a four-dimensional stage — a geometric arena in which physical events unfold. This picture, inherited from general relativity, portrays spacetime as curved, but still somehow there: an objective container with fixed topological properties.
But what if spacetime is not a container at all?
What if it is the geometry of possibility — not an object in the world, but a relational configuration of meaning?
The Geometry Isn’t There — It’s Enacted
General relativity teaches us that mass and energy curve spacetime, and that this curvature tells matter how to move. But the curvature is not an object in itself. It is a differential in constraints — a structural variation in the field of possible relations.
From a relational perspective, the metric field does not describe an external geometry. It configures meaning potential — not semantic content in the linguistic sense, but the structuring of temporal, spatial, and causal possibilities through a particular cut in the field.
This cut is not drawn onto spacetime. It is spacetime.
From Manifold to Meaning Potential
The “spacetime manifold” is often treated as a neutral mathematical canvas. But it only becomes meaningful through specific construals — the selection of coordinate systems, the choice of metric, the delineation of events.
These are not arbitrary conventions. They are semantic acts: selections from a system of structured potential that actualise a specific configuration of relations.
Thus, what is commonly called “spacetime” is not a pre-existing manifold, but an enacted configuration of possibility. Geometry, in this model, is not found — it is brought forth.
Curvature as Differential Meaning Potential
In general relativity, curvature is encoded in the Riemann tensor — a differential structure that varies from point to point. But in relational terms, curvature is not a hidden property of a physical fabric. It is a gradient in semantic topology: a locally variant field of possible construals of time and space.
In regions of high curvature (e.g. near a massive object), the system of meaning potentials is more tightly constrained — temporal paths diverge or converge, simultaneity fractures, and causal access narrows.
This isn’t merely an abstract metaphor. It is a reframing of geometry itself: from metric structure to semantic configuration.
Spacetime Events as Relational Instantiations
In the relational model, an “event” is not a point in spacetime but a cut that enacts a local configuration of meaning. These events are not embedded in spacetime — they constitute it.
The network of such events does not “trace out” a path through a pre-given geometry. Rather, the coherence among construals — the system of compatibility relations across cuts — is what we call geometry.
Spacetime, then, is not the background against which meaning occurs. It is the field of mutual intelligibility among different enactments of meaning.
Geometric Structures as Higher-Order Constraints
Finally, the geodesic equation — which governs the paths of free-falling objects — becomes, in this view, a meta-semantic constraint: a second-order principle that limits how construals can coherently evolve in relation to one another.
The Einstein field equations are not equations for the dynamics of a physical substance. They are constraints on the evolution of a system of meaning potential. They tell us not how “the universe moves,” but how cuts can cohere across a relational field.
To reconceive geometry as meaning potential is to dissolve the boundary between physics and metaphysics. Spacetime is no longer a passive stage. It is the grammar of construal, the systemic ground upon which all instances of experience — and their coordination — become possible.
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