Fractional Brownian Motion in Biomedical Signal Processing, Physiology, and Modern Physics

Fractional Brownian motion (FBM) is an important tool in biomedical signal processing. Recently, it has been used to explain the synergic/cooperative co-activations of physiological functions and mechanism of acupuncture in traditional Chinese medicine via its scaling and self-similar properties. In this paper, its essential ideas are further used to derive a more general uncertainty principle. By combining it with a newly derived spectral density formula for blackbody radiation, we can readily account for the emission and absorption of light and laser in terms of an undulatory, not quantum, picture. Hence, the theory of optics from emission, transmission, to absorption can be described completely by the classical wave theory without invoking the quantum hypothesis. It is believed that many of the phase transition phenomena in physiology and modern physics can also be unified under the same notion of FBM.