Christian, Joy (2018) Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives. Royal Society Open Science, 5 (180526). pp. 140. ISSN 20545703
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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 nonassociative real octonions, which  thanks to their nonassociativity  form the only possible closed set of spinors (or rotors) 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, which characterize the three dimensional conformal geometry of the ambient physical space, set within its eightdimensional 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 3sphere, 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 EPRBohm and the GHZ states. The raison d’être of strong correlations turns out to be the Möbiuslike twists in the Hopf bundles of S3 and S7.
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Item Type:  Published Article or Volume  

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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 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:  https://doi.org/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. 140  
Volume:  5  
Number:  180526  
ISSN:  20545703  
URI:  https://philsciarchivedev.library.pitt.edu/id/eprint/14759 
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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)
 Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives. (deposited 08 Jun 2018 17:35) [Currently Displayed]

Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives. (deposited 19 Jan 2018 13:43)
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