Relational Geodesics: 2 Radial Contraction and the Relational Field

In the first post, we clarified a crucial point: in relativity, it is the geodesics that curve, not spacetime itself. From a relational perspective, geodesics are emergent trajectories, actualised through successive instantiations constrained by the relational field of nearby mass. Here, we develop the notion of radial contraction and show how mass shapes these relational trajectories.

Radial Contraction as Modulation of Potentialities

Radial contraction is often described in classical terms as the shortening of space intervals toward a massive body. Relationally, it is not a geometric compression but a constraining of relational potentialities. Near a central mass, the set of possible trajectories available to a system is modulated: radial directions toward the mass allow fewer variations, while tangential directions may remain comparatively unconstrained.

This modulation produces the apparent curvature of geodesics: what would be a “straight path” in the absence of mass becomes a curved path when relational constraints are applied. The curvature is emergent, arising from the interaction between the system’s potentialities and the field generated by the central mass.

Geodesics as Emergent Trajectories

Consider a planet orbiting a star. Its trajectory is not guided by a force transmitted through a bent spacetime but by the relational structure imposed by the star’s mass. Each successive instantiation of the planet’s position is constrained by:

1. The planet’s internal dynamics and potentialities

2. The relational field generated by the star

3. The combined influence of other nearby systems (e.g., other planets)

The geodesic is the pattern traced by these successive instantiations. In relational terms, curvature is the emergent shape of the trajectory, a record of how the system’s potentialities are modulated by the mass of the star.

Planetary Orbits and Free-Fall Paths

Planetary orbits offer a clear illustration:

• Radial contraction reduces the range of possible inward trajectories.

• Tangential motion allows a wider spread of instantiations.

• The interplay produces stable, curved orbits, which are the geodesics of the relational field.

Free-fall paths behave similarly: a body falling toward a central mass traces a curved geodesic, not because it is “falling through curved spacetime,” but because the relational field constrains its instantiations. The apparent acceleration is a reflection of the changing pattern of relational potentialities along the trajectory.

Relational Fields as Dynamic, Contextual Structures

Relational fields are not static. As systems move and actualise, they modify the field, producing feedback loops. For example:

• A massive planet perturbs the relational field of its star, subtly altering trajectories of nearby asteroids.

• Interactions among multiple bodies generate complex patterns of geodesics, all emergent from system-relative relational constraints.

This perspective allows us to see gravitational dynamics not as an external force or a geometric property of spacetime, but as the co-emergence of relational patterns of potentiality that shape trajectories.

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Next in the series: Light, Lensing, and Relational Curvature — we will extend the analysis to photons and null geodesics, exploring gravitational lensing and the apparent bending of light entirely from the perspective of relational emergence.