Spinor geometry

TL;DR

This paper explores the deep connections between spinor geometry, spacetime, string theory, and quantum mechanics, proposing that logical structures underpin fundamental physical theories and geometries.

Contribution

It introduces a spinor-based framework linking quantum mechanics, string geometry, and spacetime, supporting Wheeler's pregeometry hypothesis.

Findings

Minkowski spacetime emerges from spinor composition.

String constraints are represented by real spinors matching minimal surface parametrization.

A spinorial analysis reveals a Hopf fibration in AdS3 spacetime.

Abstract

It has been proposed that quantum mechanics and string theory share a common inner syntax, the relational logic of C. S. Peirce. Along this line of thought we consider the relations represented by spinors. Spinor composition leads to the emergence of Minkowski spacetime. Inversely the Minkowski spacetime is istantiated by the Weyl spinors, while the merge of two Weyl spinors gives rise to a Dirac spinor. Our analysis is applied also to the string geometry. The string constraints are represented by real spinors, which create a parametrization of the string worldsheet identical to the Enneper-Weierstass representation of minimal surfaces. Further, a spinorial study of the AdS3 spacetime reveals a Hopf fibration AdS3 \rightarrow AdS2. The conformal symmetry inherent in AdS3 is pointed out. Our work indicates the hidden ties between logic-quantum mechanics-string theory-geometry and vindicates the Wheeler's proposal of pregeometry as a large network of logical propositions.