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Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives

Christian, Joy (2018) Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives. Royal Society Open Science, 5 (180526). pp. 1-40. ISSN 2054-5703

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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. We demonstrate this by first proving a general theorem concerning the geometrical origins of the correlations predicted by arbitrarily entangled quantum states, and then reproducing the correlations predicted by the EPR-Bohm and the GHZ states. The raison d’être of strong correlations turns out to be the Möbius-like twists in the Hopf bundles of S3 and S7.

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Item Type: Published Article or Volume
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
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: 08 Jun 2018 17:35
Last Modified: 08 Jun 2018 17:35
Item ID: 14759
Journal or Publication Title: Royal Society Open Science
Publisher: The Royal Society of London
Official URL: http://rsos.royalsocietypublishing.org/content/5/5...
DOI or Unique Handle: 10.1098/rsos.180526
Subjects: Specific Sciences > Physics
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Relativity Theory
Specific Sciences > Physics > Symmetries/Invariances
Date: 30 May 2018
Page Range: pp. 1-40
Volume: 5
Number: 180526
ISSN: 2054-5703
URI: https://philsci-archive.pitt.edu/id/eprint/14759

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