Physics Commons^™

Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Complex numbers are ubiquitous in physics, they lead to a natural description of different physical processes and to efficient algorithms for solving the corresponding problems. But why this seemingly counterintuitive mathematical construction is so natural here? In this paper, we provide a possible explanation of this phenomenon: namely, we show that complex numbers appear if take into account that some physical system are described by derivatives of fractional order and that a physically meaningful analysis of such derivatives naturally leads to complex numbers.