Quantum correlations are weaved by the spinors of the Euclidean primitives

TL;DR

This paper presents a geometric framework using Euclidean primitives and Clifford algebras to explain quantum correlations locally, extending Bell's bounds and overcoming Bell's theorem.

Contribution

It introduces an associative algebraic structure from Euclidean primitives that models quantum correlations within a local and deterministic framework.

Findings

Quantum correlations are modeled as points on a 7-sphere within a Clifford algebraic framework.

The framework extends Bell's bounds to the algebraic maximum of ±2√2 for strong correlations.

It provides a local, realistic explanation of quantum correlations without invoking nonlocality or contextuality.

Abstract

The exceptional Lie group E8 plays a prominent role in both mathematics and theoretical physics. It is the largest symmetry group associated with the most general possible normed division algebra, namely, that of the non-associative real octonions, which --- thanks to their non-associativity --- form the only possible closed set of spinors (or rotors) that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes, and volumes, which characterize the three-dimensional conformal geometry of the ambient physical space, set within its eight-dimensional Clifford-algebraic representation. Remarkably, the resulting algebra remains associative, and allows us to understand the origins and strengths of all quantum correlations locally, in terms of the geometry of the compactified physical space, namely, that of a quaternionic 3-sphere, S3, with S7 being its algebraic representation space. Every quantum correlation can thus be understood as a correlation among a set of points of this S7, computed using manifestly local spinors within S3, thereby extending the stringent bounds of +/-2 set by Bell inequalities to the bounds of +/-2\/2 on the strengths of all possible strong correlations, in the same quantitatively precise manner as that predicted within quantum mechanics. The resulting geometrical framework thus overcomes Bell's theorem by producing a strictly deterministic and realistic framework that allows a locally causal understanding of all quantum correlations, without requiring either remote contextuality or backward causation.