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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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Abstract

The exceptional Lie group E8 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, S3, with S7 being the corresponding 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 the Bell-CHSH inequalities to the bounds of +/-2\/2 on the strengths of all possible correlations, in the same quantitatively precise manner as that predicted within quantum mechanics. The resulting geometrical framework thus circumvents Bell's theorem by producing a deterministic and realistic framework that allows a locally causal understanding of all quantum correlations, without requiring either remote contextuality or backward causation. We demonstrate this by first proving a general
theorem about the geometrical origins of the correlations predicted by arbitrarily entangled states, 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 S3 within S7.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Christian, Joyjjc@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 > Quantum Gravity
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Dr. Joy Christian
Date Deposited: 19 Jan 2018 13:43
Last Modified: 19 Jan 2018 13:43
Item ID: 14305
Subjects: Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
Date: 3 May 2017
URI: http://philsci-archive.pitt.edu/id/eprint/14305

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