In mainstream discussions of general relativity, it is common to hear that “spacetime is curved.” The language is seductive: we picture a stretched sheet bending under the weight of mass, or lines curving through a warped container. But careful reflection — especially from the perspective of relational ontology — reveals a crucial distinction: a curved geodesic is not curved spacetime.
Geodesics Are Instances, Not Properties
A geodesic is the path that an object follows under the influence of mass-energy, according to the constraints of general relativity. It is an instance, a sequence of events actualised in a relational pattern. The curvature of the geodesic describes how that sequence of events is shaped, not the bending of an underlying “space.”
From a relational perspective, it is a mistake to conflate the geodesic with the space it traverses. The geodesic emerges from the relational constraints imposed by mass and energy; it is the outcome of those constraints, not a manifestation of a curved container.
Space Is Not Curved, Constraints Are
One way to visualise this, which avoids the pitfalls of the container metaphor, is to think in terms of directional contraction relative to mass:
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A geodesic curves not because space itself bends, but because the relational structure of possible events is locally contracted in the direction of the mass.
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The curvature we observe is a readout of these constraints on pathways — the pattern of allowed instances — rather than a property of space itself.
In other words, what we call curvature is a formal description of the relational configuration of events, not a feature of an underlying substance called spacetime.
Why the Distinction Matters
Saying “spacetime is curved” can be useful shorthand, but it carries metaphysical baggage:
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It suggests a background container that bends — a thing in itself — which the relational perspective rejects.
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It invites intuitive but misleading pictures, like rubber sheets or warped grids, that obscure the true nature of geodesics as events constrained by relational potentials.
By contrast, reading geodesics relationally keeps things clean:
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The wavefunction of GR is the system of constraints imposed by mass-energy.
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Geodesics are actualised pathways, first-order instances shaped by those constraints.
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Curvature is formal, relational, and perspectival, not physical or material.
Conclusion
From a relational perspective, curved geodesics do not imply curved spacetime. They are patterns of constrained events, actualised in accordance with the system of relational potentials defined by mass-energy. The curvature we read off a geodesic is a description of the pathway — the pattern of the instance — not of space itself.
This distinction frees us from the container metaphor and keeps general relativity firmly in the domain of relations and instances, rather than hidden substances. It aligns beautifully with relational ontology: paths are actual, potentials are relational, and spacetime, as a “thing,” is simply not part of the story.
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