El Naschie’s ε(∞) theory and an alternative to gauged spacetime scale relativity theory

An alternative to the Nottales’s scale relativity theory using the concept of transfinite discreet space is established. Subsequently, quantum vacuum fluctuations, arise naturally from the model and the connection with El Naschie’s ε(∞) spacetime is given by means of the movements with uniform acceleration in a Minkowskian vacuum.