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Doubts about the Geometric Model of Relativity

By Zhang Suhang, Luoyang, Henan

General relativity attributes gravity to spacetime curvature and uses curvature to describe the geometric deformation of spacetime. This model can effectively describe orbital motions such as celestial revolution and the deflection of light. But whether its geometric dimensions are complete remains open to discussion.

There exist in the universe two essentially different rotational motions: revolution and rotation. The two correspond to different forms of spacetime deformation and should not be conflated.

Spacetime curvature corresponds to revolution.

Spacetime twisting corresponds to rotation.

Curvature is a flexural deformation of spacetime as a whole; it produces orbital deflection and governs all orbiting motion.

Twisting is a local vortical deformation of spacetime; it produces spin structure and governs all rotational motion.

It should be clarified that general relativity does not fail to address rotation. The Kerr metric and the frame-dragging effect already describe, within the curvature framework, the geometric effects of rotating celestial bodies. The problem is not that “rotation is not described,” but that its geometric foundation rests on the torsion-free assumption and contains no independent torsion component. The curvature framework can encode complex rotational effects, but if the local vortical deformation corresponding to rotation requires an independent geometric quantity for its description, then beyond curvature, a torsion dimension should also be introduced.

A complete spacetime geometry may simultaneously contain two independent dimensions: curvature and twisting. Curvature governs orbital revolution; twisting governs local rotation. Only when the two coexist is the complete form of spacetime deformation present.

This line of thought does not overturn general relativity, but points out the boundary of its geometric assumptions. Einstein-Cartan theory has already shown that, if the spin of matter is taken into account, spacetime geometry can permit torsion to exist, and torsion couples directly with spin density. The intuitive direction of this article echoes this extended theory.

This article is only a philosophical discussion of a geometric model. It does not offer empirical conclusions and does not involve specific physical calculations. Local conservation remains valid within this framework.

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