Quantum Effects Through a Fractal Theory of Motion

Scale Relativity Theory (SRT) affirms that the laws of physics apply in all reference systems, whatever its state of motion and its scale. In consequence, SRT imply [1-3] the followings: i. Particle movement on continuous and non-differentiable curve (or almost nowhere differentiable), that is explicitly scale dependent and its length tends to infinity, when the scale interval tends to zero. ii. Physical quantities will be expressed through fractal functions, namely through functions that are dependent both on coordinate field and resolution scale. The invariance of the physical quantities in relation with the resolution scale generates special types of transformations, called resolution scale transformations. In what follows we will explain the above statement. Let F (x) be a fractal function in the interval x∈ a, b and let the sequence of values for x be: