Microscopic Laws vs. Macroscopic Laws: Perspectives from Kinetic Theory and Hydrodynamics

Abstract

Reductionism is a prevalent viewpoint in science according to which all physical phenomena can be understood from fundamental laws of physics. Anderson (Science 177:393 1972), Laughlin and Pines (PNAS 97:28 2000), and others have countered this viewpoint and argued in favour of hierarchical structure of the universe and laws. In this paper, we advance the latter perspective by showing that some of the complex flow properties—Kolmogorov’s theory of turbulence, turbulence dissipation and diffusion, and dynamic pressure—derived using hydrodynamic equations (macroscopic laws) are very difficult, if not impossible, to describe in microscopic framework, e.g. kinetic theory. We also provide several other examples of hierarchical description.