Gravity Without Things: I. Gravity Without a Gravitational Force

We are accustomed to thinking of gravity as a force. General relativity asks us to think differently: massive bodies do not pull objects through space; rather, mass-energy changes the geometry in which motion occurs.

But even this formulation can leave us imagining space as a thing—an arena that can somehow be bent or distorted.

A relational ontology suggests a further step.

Space need not be understood as a substance at all. What we call spatial extension is constituted by relations between instances. A distance is not something that exists between things; it is the relation itself.

Gravity can then be conceived as a differential change in those relations.

Consider a sequence of spatial intervals extending toward a concentration of mass. If the intervals in the radial direction progressively contract relative to intervals in orthogonal directions, the geometry becomes increasingly differentiated. A trajectory that would otherwise be geodesic in an approximately flat relational structure follows a different path.

What general relativity describes as the curvature of spacetime can therefore be given a relational reading: curvature is not the bending of a spatial substance, but the consequence of the changing relations that constitute spatial geometry.

The important word is differential. Uniform change would not produce the gravitational geometry we observe. It is the progressive difference in the relations that matters.

This gives us a different order of explanation:

mass-energy → differential relational change → geometry → geodesic motion

rather than:

mass-energy → force → motion

The distinction is more than verbal. Nothing has to pull an object toward the centre, and nothing has to bend a pre-existing space. The changing relations themselves constitute the geometry through which objects move.

Gravity, on this view, is not something that happens in space.

It is something that happens to the relations by which space exists.

And if that is so, the black hole presents a particularly interesting case.

What happens when this progressive differentiation of relations is followed all the way to the event horizon—and beyond it?

That is where the geometry becomes strange.

And perhaps the strangest thing about it is that there may be no "space" there, in the ordinary sense, through which anything is falling.