On the Need for Fractal Logic in High Energy Quantum Physics

Modern advances in pure mathematics and particularly in transfinite set theory have introduced into the fundamentals of theoretical physics many novel concepts and devices such as fractal quasi manifolds with non-integer (Hausdorff) dimension for its geometry as well as infinite dimensional wild topology and non classical fuzzy logic. In the present work transfinite fractal sets and fuzzy logic are combined to enable the introduction of a new theory termed fractal logic to the foundation of high energy particle physics. This leads naturally to a new look at quantum gravity. In particular we will show that to understand and develop quantum gravity we have to bring various fields together, particularly fractals and nonlinear dynamics as well as sphere packing, fuzzy set theory, number theory and quantum entanglement and irrationally q-deformed algebra.