A Spacetime Model with Macroscopic Torsion Twist: A Two-Component Geometric Conjecture of Revolution and Rotation

By Zhang Suhang, Luoyang, Henan

General relativity describes gravity by spacetime curvature and can effectively explain orbital motions such as celestial revolution and the deflection of light. But its geometric foundation rests on the torsion-free assumption. Whether curvature exhausts all dimensions of spacetime geometry remains open to discussion.

There exist in the universe two essentially different rotational motions: revolution and rotation.

Revolution is orbital motion and corresponds to the curvature deformation of spacetime. Curvature is a holistic, large-scale bending and governs all orbiting motion.

Rotation is local motion and corresponds to the twist deformation of spacetime. Twist is a local, axial-vector vortical curling and governs all rotational motion.

An intuitive analogy may be made: spacetime is like a curved shell surface, which has both an overall arc-like curvature and local helical twists. The two are two independent geometric deformations and should not be conflated.

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 contains no independent twist 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 twist dimension should also be introduced.

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. The concept of twist in this article echoes the direction of torsion, but emphasizes its macroscopic celestial correspondence, rather than being limited to microscopic spin.

I. Macroscopic Torsion Field Equation: A Formal Generalization of the Cartan Equation

In Einstein-Cartan theory, torsion couples with microscopic spin density, and its equation form is:

T^\alpha_{\ \mu\nu}+\delta^\alpha_\mu T_\nu-\delta^\alpha_\nu T_\mu=-\kappa S^\alpha_{\ \mu\nu}

where S^\alpha_{\ \mu\nu} is the microscopic spin density.

This article generalizes this equation to the macroscopic setting: replacing the microscopic spin source with a macroscopic rotational angular momentum source \mathcal{J}^\alpha_{\ \mu\nu}, we obtain the form of the macroscopic torsion field equation:

T^\alpha_{\ \mu\nu}+\delta^\alpha_\mu T_\nu-\delta^\alpha_\nu T_\mu=-\kappa \mathcal{J}^\alpha_{\ \mu\nu}

It should be noted that this equation formally draws on the Cartan equation, but replaces the source term from microscopic spin with macroscopic angular momentum. This step is a conjectural generalization, not a rigorous derivation. The definition of its source term, its dimensional self-consistency, and its physical viability still await rigorous argumentation. This article does not claim that the equation is already established, but presents it only as a formal framework for further exploration.

II. Rotational Dynamics Equation: The Intermediate Link from the Field Equation to Rotational Motion

In general relativity, the derivation chain for orbital motion is:

G_{\mu\nu}=\kappa T_{\mu\nu}

\quad \rightarrow \quad

\text{solve the metric}

\quad \rightarrow \quad

\text{geodesic equation}

\quad \rightarrow \quad

\text{orbital trajectory}

This article imitates this chain and supplies the intermediate link from the torsion field to rotational motion:

\frac{D \mathcal{J}^{\mu\nu}}{d\tau} = \lambda \cdot T^{\alpha}_{\ \mu\nu} \cdot \mathcal{J}_{\alpha}

where \lambda is a coupling constant.

It should be noted that this equation imitates the derivation paradigm in general relativity—“field equation → geodesic equation → orbital motion”—and supplies the intermediate link “torsion field → rotational motion.” It is likewise a conjectural construct, and its index consistency, dimensional correctness, and physical meaning still await rigorous argumentation. This article does not claim that the equation is already established, but presents it only as a formal analogical framework.

III. Conjectural Correspondence of the Complete Derivation Chains

Revolution system (standard general relativity) Rotation system (this article’s conjecture)

Energy-momentum tensor Macroscopic rotational angular momentum tensor

Curvature field equation Macroscopic torsion field equation

Spacetime curvature Spacetime twist

Geodesic equation Rotational dynamics equation

Celestial revolution Celestial rotation

The table above displays the symmetrical structure of this article’s conjecture: the revolution system is completely described by standard general relativity, while the rotation system corresponds to a formally analogous geometric framework of rotation. The two systems are formally symmetric, but the physical legitimacy of the rotation system remains to be rigorously demonstrated.

IV. Distinction from the Former Soviet Union’s “Torsion Field” Theory

It must be clearly distinguished that the macroscopic twist discussed in this article is strictly limited to an extension of the boundaries of spacetime geometry, and does not involve any pseudoscientific assumptions related to a “fifth force,” superluminal propagation, or consciousness.

The former Soviet-era “torsion field” theory overextended geometric concepts induced by microscopic spin into a new interaction, and its core claims have never been confirmed by mainstream experiments. The macroscopic torsion field equation in this article formally derives from the Cartan equation and discusses the boundary problem of spacetime geometry; it does not involve any new-force hypothesis beyond the geometric framework of general relativity.

V. Positioning and Boundaries

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

The core proposition of this article is: macroscopic spacetime geometry may simultaneously contain two components, curvature and twist; curvature governs orbital revolution, and twist governs local rotation. If this conjecture holds, the geometric mechanism of macroscopic rotation may correspond to a torsion-type component independent of curvature.

Both sets of equations are formal conjectural constructs, and their physical legitimacy remains to be rigorously demonstrated. This article does not claim that these equations are already established, but presents them only as a formal framework for further exploration.