From Pure Spinor Geometry to Quantum Physics: A Mathematical Way

TL;DR

This paper explores a mathematical foundation for quantum mechanics using pure spinor geometry, linking spinors to null vectors in Minkowski space and deriving quantum equations from geometric principles.

Contribution

It introduces a novel approach by constructing null vectors from pure spinors, connecting them to quantum and classical equations of motion, and proposes a mathematical basis for Planck's constant.

Findings

Pure spinors generate null vectors in Minkowski space.

Quantum and classical equations are derived from spinor geometry.

Potential mathematical foundation for Planck's constant.

Abstract

In the search of a mathematical basis for quantum mechanics, in order to render it self-consistent and rationally understandable, we find that the best approach is to adopt E. Cartan's way for discovering spinors; that is to start from 3-dimensional null vectors and then show how they may be represented by two dimensional spinors. We have now only to go along this path, however in the opposite direction; with these spinors (which are pure) construct bilinearly null vectors: and we find that they naturally generate null vectors of Minkowski momentum space, where Cartan equations defining pure spinors are identical to all equations of motion for massless systems: both the quantum (Weyl's) and the classical ones (Maxwell's), are determined by them. We have then the possibility of a new, purely mathematical, determination of h: the Planck's constant, and thus the possible mathematical starting point for the representation of quantum mechanics.