On El Naschie’s Fractal-Cantorian Space-Time and Dark Energy—A Tutorial Review

Abstract

This tutorial review is dedicated to the work of the outstanding Egyptian theoretical physicist and engineering scientist Prof. Mohamed El Naschie. Every physics student knows the well-known Einstein’s mass-energy equation, E=mc 2 , but unfortunately for physics, few know El Naschie’s modification, E(O)=mc 2 /22, and El Naschie’s dark energy equation E(D)= mc 2 (21/22) although this new insight has truly far reaching implications. This paper gives a short tutorial review of El Naschie’s fractal-Cantorian space-time as well as dark energy. Emphasis is put on the fundamental concept of Cantor set, fractal dimensions, zero set, empty set, and Casimir effect.