Abstract

A fractal particle is a three-dimensional (3D) standing wave (SW) superimposed on much smaller fractal particles, which comprise the finite substrate of one universe within a hierarchical series of fractal universes, or a fractal cosmos.  In this presentation, units of absolute time and length are defined with respect to the fram or a fractal cosmos.  In this presentation, units of absolute time and length are defined with respect to the frame of reference of a fractal universe.  It is then shown that, for a fractal particle in motion, the frequency of vibration decreases (clock retardation) and the wavelength decreases in the direction of motion (length contraction) as the velocity of the particle increases with respect to the rest frame of (i.e., zero-velocity in) the fractal universe.  Predications are in agreement with experimental results, yet the equations of "fractal mechanics" are derived without recorse to the controversial two principles of Einstein's special relativity theory (SRT).  The present derivation is based on Newtonian mechanics as applied to the built-in clocks and rulers of a fractal particle.  It is indicated that Einstein's ad hoc derivation is preposterous and superfluous in the context of the fractal cosmos and leads to unnecessary paradoxes.  In conclusion, the fractal cosmos hypothesis is compatible with experimental results relating to clock retardation and length contraction, suggesting that it is a robust theory worth examining in greater detail.