Soft matter (such as biomaterials, polymers, sediments, oil, emulsions, etc) has become an important bridge between theoretical physics and a range of applied disciplines. Its fundamental physical mechanism, however, is largely obscure. This study makes a first attempt to connect the fractional Schrodinger equation and soft matter physics within a consistent framework from empirical power scaling to phenomenological kinetics and macromechanics to mesoscopic quantum mechanics. The new perspectives of this study are the fractional quantum relationships in soft matter, which show that Lévy statistics and fractional Brownian motion are essentially related to momentum and energy, respectively. Fractional quantum theory has been conjectured as underlying fractal mesostructures and many-body interactions of macromolecules in soft matter, and is experimentally testable.
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