General relativity is usually presented in terms of a “curved spacetime,” where mass-energy bends the background and objects follow geodesics. From a relational perspective, this picture is misleading. A geodesic is not evidence of a bent container; it is an instance of a relationally constrained pathway. The true content of GR can be expressed entirely in terms of relational potential and actualised events.
1. Mass-Energy Defines Potential
Instead of asking how spacetime bends, we ask: what relational constraints does mass-energy impose?
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Mass-energy defines the system of potential pathways for objects and light.
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These potentials specify which sequences of events are possible under the system’s relational constraints.
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Nothing is bending; no container exists. The “geometry” is simply the structure of potential relations.
Formally, this is analogous to the wavefunction in quantum mechanics: the system encodes all that could occur, without presupposing a physical medium.
2. Geodesics as Actualised Pathways
A geodesic is an instance:
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It is an actualised sequence of events that satisfies the relational constraints defined by mass-energy.
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Each object, photon, or particle traces one pathway through the system of potentials.
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“Curvature” is a shorthand description of how these pathways are patterned relative to one another, not a property of anything underlying the events.
The geodesic emerges from the system, not in it. Its shape is a readout of relational constraints, not the bending of space.
3. Sub-Potentials and Local Constraints
Within this system of potential pathways, local configurations impose sub-potentials:
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A planet’s mass, for example, locally constrains nearby pathways.
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Light near the planet has a restricted set of possible trajectories.
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These sub-potentials explain why events cluster along particular geodesics without requiring additional “curvature” of a background.
The sub-potentials are relational structures: they shape events, but they are not separate entities.
4. Perspective: Potential vs. Instance
We can now see the perspectival structure:
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From the potential pole, the system of mass-energy specifies which pathways are possible.
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From the instance pole, each object’s trajectory is an actualised sequence of events within those constraints.
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There is no process in which potential becomes actual; actualisation is simply the selection of a pathway within the relational system.
This mirrors the wavefunction vs. two-slit events distinction: potential constrains, instance manifests, but neither is a substance.
5. Horizon: Emergent Novelty
Even within GR, relational potential is dynamic:
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The horizon is the edge of what could occur next, given the history of actualised events.
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Each new event slightly reshapes the relational constraints on subsequent instances.
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This captures the emergence of novelty — bending light near a massive object, orbital precession — without invoking hidden curvature or physical deformation.
6. Historical Evolution
Relational potential evolves historically:
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Prior events shape what future events are possible.
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Orbital dynamics, gravitational lensing, and the structure of planetary systems emerge as accumulated relational constraints.
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The “geometry” we infer is a stable pattern across actualised instances, not a property of space itself.
7. Rejecting Container Metaphors
Throughout:
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There is no spacetime substance that curves.
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Geodesics are not “rivers flowing through curved space.”
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Curvature is not a force, nor is it a medium.
What remains is pattern, potential, and actualisation. GR is entirely about how mass-energy structures relational possibilities and how instances emerge within that system.
8. The Relational Summary
In fully relational terms:
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Potential: the system of pathways constrained by mass-energy.
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Instance: a realised trajectory through that system.
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Sub-potential: local constraints that shape clusters of instances.
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Horizon: the evolving edge of possibility as instances accumulate.
Curvature, geodesics, and gravitational effects are descriptions of relational structure, not of “space” itself.
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