After the Reluctant Universe: Dialogue III — On Curvature (and the Error of Geometric Substance)

Characters:

Professor Quillibrace

Mr Blottisham

Miss Elowen Stray

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Blottisham:

Curvature, at least, must be real. Space bends. Time bends. We have diagrams.

Quillibrace:

We have diagrams, yes. Reality is not obliged to resemble them.

Elowen Stray:

So curvature isn’t something happening to space?

Quillibrace:

No. That is the error of geometric substance.

Blottisham:

But masses curve spacetime! That’s what we’re taught.

Quillibrace:

We are taught a shorthand that survives only because it usually works.

Elowen Stray:

Then what does curvature actually describe?

Quillibrace:

A systematic deviation in relational regularities.

Blottisham:

That sounds suspiciously abstract.

Quillibrace:

It is suspicious only if you insist that geometry must be a thing.

Elowen Stray:

So when light bends around a star…

Quillibrace:

…it is not sliding along a warped surface, but following a relational constraint that differs from flat expectation.

Blottisham:

But geodesics! The straightest possible paths!

Quillibrace:

Straightness is defined within a construal. Change the construal, and “straight” obediently follows.

Elowen Stray:

So curvature isn’t distortion, but bookkeeping?

Quillibrace:

Careful bookkeeping, yes—of how relations cohere.

Blottisham:

You make it sound as though geometry were optional.

Quillibrace:

Not optional—conditional.

Elowen Stray:

Conditional on what?

Quillibrace:

On the stability of the relational scheme you are using to describe phenomena.

Blottisham:

Then spacetime isn’t curved out there…

Quillibrace:

…it is curved within a particular way of making sense of relations.

Elowen Stray:

And when curvature becomes extreme?

Quillibrace:

We approach the edge of that construal’s coherence.

Blottisham:

You mean black holes again.

Quillibrace:

Among other things. They are not pits in space, but warnings.

Elowen Stray:

Warnings of what?

Quillibrace:

That you are insisting on treating geometry as substance rather than condition.

Blottisham:

Then Einstein didn’t reveal the fabric of reality?

Quillibrace:

He revealed the consequences of taking relations seriously—without abandoning substance entirely.

Elowen Stray:

So curvature is a relational symptom, not an ontological feature.

Quillibrace:

Exactly.

Blottisham:

I find this deeply disrespectful to the elegance of tensors.

Quillibrace:

On the contrary. It respects them enough not to turn them into furniture.

Elowen Stray:

And once we stop imagining spacetime as a thing…

Quillibrace:

…the universe stops tearing itself into knots at the edges of our diagrams.

Blottisham:

I am beginning to suspect that nothing is where I thought it was.

Quillibrace:

A promising suspicion.

(Elowen sits quietly, the notion settling: geometry as constraint, not canvas. Blottisham stares at the blackboard, its chalk curves suddenly looking less solid.)