Against the Curvature of Spacetime

Einstein’s equations are elegant: mass and energy tell spacetime how to curve, and curved spacetime tells matter how to move. A neat reciprocity, expressed in a geometric metaphor. But somewhere along the way, the metaphor hardened into ontology: space itself is imagined as a pliable fabric, bending and warping under the weight of planets and stars.

This is a sleight of hand. The equations describe relations of motion and potential, not the contortions of an invisible sheet. To picture spacetime as a thing that curves is to confuse description with substance — to mistake the geometry of our models for the dynamics of reality.

Relationally, the problem is stark. There is no “fabric” to be curved, no background medium awaiting deformation. What exists are the lawful correlations between events — how motions align, constrain, and open possibilities. To speak of curvature is shorthand for those relational constraints, not the bending of an ether we have already abandoned.

The metaphor comforts because it offers a picture. We can imagine a marble rolling on a trampoline, gravity made visible. But this picture misleads: it reintroduces a medium in order to explain what requires none, and disguises relational necessity as geometric surface.

The alternative is cleaner: gravity is not the sagging of a fabric, but the pattern of lawful alignment in the becoming of events.

So let us cut through the metaphor:

There is no curvature of spacetime — only the relational order of motion.