Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives

Christian, Joy (2017) Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives. [Preprint]

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Official URL: https://www.academia.edu/32804179/Quantum_Correlat...

Abstract

The exceptional Lie group E_8 plays a prominent role both in mathematics and theoretical physics. It is the largest symmetry group connected to the most general possible normed division algebra, that of the non-associative real octonions, which — thanks to their non-associativity — form the only possible closed set of spinors 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, characterizing the three-dimensional conformal geometry of the 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, S^3, with S^7 being the corresponding algebraic representation space. Every quantum correlation can thus be understood as a correlation among a set of points of this S^7, computed using manifestly local spinors in S^3 , thereby setting the geometrical upper bound of 2√2 on the strengths of all quantifiable correlations. We demonstrate this by first proving a comprehensive theorem about the geometrical origins of the correlations predicted by any arbitrary quantum state, and then explicitly reproducing the strong correlations predicted by the EPR-Bohm and GHZ states. The raison d'etre of strong correlations turns out to be the twist in the Hopf bundle of S^3 within S^7.

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Item Type:

Preprint

Creators:

Creators	Email	ORCID
Christian, Joy	jjc@alum.bu.edu

Keywords:

Quantum Correlations, Local Realism, Local Causality, E_8 Normed Division Algebra, Octonions, Spinors, Euclidean Primitives, Conformal Geometry, Clifford Algebra, Quaternions, 3-sphere, 7-sphere, S^3, S^7, EPR-Bohm State, GHZ State, Hopf fibration

Subjects:

Specific Sciences > Physics
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Symmetries/Invariances

Depositing User:

Dr. Joy Christian

Date Deposited:

04 May 2017 22:54

Last Modified:

04 May 2017 22:54

Item ID:

13019

Official URL:

https://www.academia.edu/32804179/Quantum_Correlat...