4-Spinors and a Projection onto 3+1 Spacetime

TL;DR

This paper introduces an explicit projection from 4-spinors to 3+1 spacetime that preserves Lorentz invariance, revealing a natural spinor-based formulation of spacetime and extending to a five-dimensional interpretation.

Contribution

It provides a new Lorentz-invariant projection from 4-spinors to spacetime, offering a novel spinor-centric perspective on spacetime structure.

Findings

A projection commuting with Lorentz transformations is constructed.

The projection maps 4-spinors to points in 3+1 spacetime.

Real components of 4-spinors relate to a five-dimensional spacetime.

Abstract

We write down an explicit projection that maps any given 4-spinor to a point in 3+1 spacetime while commuting with the Lorentz action. This suggests that a Lorentz invariant theory - including spacetime itself - has a more natural expression in terms of these primitive spinor variables, while an ordinary spacetime interpretation may be obtained by projecting solutions. Using this projection, we show how the real components of a given 4-spinor reference a point in a five dimensional spacetime.