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 nonassociative real octonions, which  thanks to their nonassociativity  form the only possible closed set of spinors that can parallelize the 7sphere. By contrast, here we show how a
similar 7sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes, and volumes, characterizing the threedimensional conformal geometry of the physical space, set within its eightdimensional Cliffordalgebraic 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 3sphere, 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 BellCHSH 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 EPRBohm 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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Keywords:  Quantum Correlations, Local Realism, Local Causality, E_8, Normed Division Algebra, Octonions, Spinors, Euclidean Primitives, Conformal Geometry, Clifford Algebra, Quaternions, 3sphere, 7sphere, S^3, S^7, EPRBohm 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://philsciarchive.pitt.edu/id/eprint/14305 
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Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives. (deposited 04 May 2017 22:54)
 Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives. (deposited 19 Jan 2018 13:43) [Currently Displayed]
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