Relational Geodesics: 3 Light, Lensing, and Relational Curvature

In the previous posts, we established that geodesics curve, not spacetime, and explored how mass modulates relational potentialities to produce curved trajectories for massive bodies. In this final post, we extend this relational perspective to photons and null geodesics, examining gravitational lensing and the ontological implications of relational curvature for light.

Light Trajectories as Relational Paths

Photons, like massive bodies, follow geodesics. However, they move along null trajectories, tracing paths at the limit of relational instantiation defined by the speed of light. From a relational-ontology perspective, the “bending” of light near a mass is not a property of spacetime itself but emerges from the modulation of relational potentialities by the mass. Each successive instantiation of the photon’s position is constrained by the relational field of nearby systems, producing the curved path we observe.

Gravitational Lensing

Gravitational lensing — the apparent deflection of light by a massive body — exemplifies relational curvature vividly:

• The central mass shapes the relational field, contracting radial possibilities.

• Photons, constrained by this field, follow curved geodesics.

• Observers perceive the deflection as lensing, a manifestation of relational emergence rather than a bending of an independent space.

In this way, lensing is a phenomenon of perspective and relational structure: the light’s trajectory emerges from the interaction of its potential instantiations with the surrounding mass’s relational field.

Implications for Observation and Measurement

Adopting a relational view reshapes our understanding of observation:

• The “distance” and “angle” of deflected light are properties of the relational system that includes the photon, the mass, and the observer.

• Measurements are not readings of pre-existing spacetime geometry; they are traces of instantiated relational patterns.

• Phenomena such as Einstein rings, arcs, and multiple images are expressions of the emergent geometry of geodesics, not of a bent spacetime substrate.

Ontological Reflection: Co-Actualisation Near Mass

Relational curvature highlights a profound ontological point: near mass, every instantiation — whether a planet, an asteroid, or a photon — is co-actualised within the relational field. The field is not a passive container; it is the pattern of constraints shaping what can actualise. Geodesics, in this sense, are the signature of relational emergence: they map the interaction of potentialities, constrained by the central mass, across time and space as these dimensions are perspectivally experienced.

Relational Gravity

Seen through this lens, gravity is not a force or a property of spacetime: it is the emergent modulation of relational potentialities by mass, shaping trajectories of all systems — massive or massless. Geodesics are the record of this relational shaping, the paths along which systems co-actualise, and phenomena such as light bending or planetary orbits are the visible expressions of the underlying relational patterns.

---

Series Conclusion:

Through this three-post series, we have traced a relational interpretation of gravity:

1. Geodesics curve, not spacetime — trajectories are emergent patterns of instantiation.

2. Mass modulates relational fields — producing radial contraction and curved geodesics for massive bodies.

3. Light follows relationally curved paths — gravitational lensing is an emergent phenomenon of relational constraints.

This perspective reframes relativity in relational-ontology terms: motion, causality, and trajectory are not properties of a pre-existing container but co-emergent features of systems interacting within relational fields. Understanding gravity in this way preserves the empirical predictions of relativity while illuminating the perspectival, emergent, and co-actualised nature of all trajectories in the vicinity of mass.