Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime

Abstract

We show how Einstein’s four dimensionality of spacetime arises via a Hardy quantum entanglement form of compactification acting on Veneziano bosonic strings space. In turn this quantum entanglement mechanism is directly connected to the transfinite version of Heterotic string’s dimensional hierarchy, i.e. 26, 16, 10, 6, 4 and leads directly to ‘tHooft-Veltman-Wilson fractal spacetime of dimensional renormalization from which the missing 95.5% dark energy density of the cosmos may be accurately determined. Furthermore we predict the existence of a quasi dimensional regularization quasi particle with a topological mass charge equal to twice that of Hardy's entanglement.