Bell's Inequalities, Superquantum Correlations, and String Theory

Abstract

We offer an interpretation of super-quantum correlations in terms of a "doubly" quantum theory. We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tension α ′ and the string coupling constant gs, is such a super-quantum theory, one that transgresses the usual quantum violations of Bell's inequalities. We also discuss the → ∞ limit of quantum mechanics in this context. As a super-quantum theory, string theory should display distinct experimentally observable super-correlations of entangled stringy states.

Galois Field Quantum Mechanics

“…We conjectured in Ref. 24 that a super-quantum theory may exist in the → ∞ limit of canonical QM. Recalling that 1/ is effectively the curvature of CP N −1 , this complex projective space would degenerate to C N −1 in the → ∞ limit.…”

Spin and rotations in Galois field quantum mechanics

“…The underlying vector space in the present 'spin' system has no inner product, a key element in the derivation of the Cirel'son bound [4], and the symmetry group in this context is not equivalent to SU (2). The entangled states have parallels to those of SU (2), but have an independent existence and structure.…”

“…Both canonical QM and our variant quantum description make crucial use of the underlying linear properties, and the CHSH bound for both is predicated upon properties of the vector space. In [4] we point out the importance of the inner product in deriving the conventional CHSH bound. The vector spaces on which our variants are constructed do not support an inner product because of the cyclicity of Galois fields.…”

Is Quantum Gravity a Super-Quantum Theory?

“…The third avenue starts from a theory defined by and G N , a non-relativistic quantum theory of gravity [3]. One version of this unconventional, yet logically viable, option was advocated by us in Ref.…”