Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives
 Citation data:

Royal Society Open Science
 Publication Year:
 2017
 Repository URL:
 http://philsciarchive.pitt.edu/id/eprint/13019
 Author(s):
 Most Recent Tweet View All Tweets
preprint description
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 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, 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 EPRBohm 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.