Time-like Extra Dimensions: Quantum Nonlocality, Spin, and Tsirelson Bound

The $E_8 \otimes E_8$ octonionic theory of unification suggests that our universe is six-dimensional and that the two extra dimensions are time-like. These time-like extra dimensions, in principle, offer an explanation of the quantum nonlocality puzzle, also known as the EPR paradox. Quantum systems access all six dimensions, whereas classical systems such as detectors experience only four dimensions. Therefore, correlated quantum events that are time-like separated in 6D can appear to be space-like separated and, hence, nonlocal, when projected to 4D. Our lack of awareness of the extra time-like dimensions creates the illusion of nonlocality, whereas, in reality, the communication obeys special relativity and is local. Bell inequalities continue to be violated because quantum correlations continue to hold. In principle, this idea can be tested experimentally. We develop our analysis after first constructing the Dirac equation in 6D using quaternions and using the equation to derive spin matrices in 6D and then in 4D. We also show that the Tsirelson bound of the CHSH inequality can in principle be violated in 6D.