On macroscopic spatial averaging of contact and long-range microscopic forces

Abstract

Even though ensemble averages are sometimes equivalent, or even preferable, to spatial averages, the latter have incontestable significance. Spatial averaging, which has been restricted until now to basic electromagnetic equations, is applied here to the Cauchy equation of movement. Spatial filtration of microscopic properties is especially useful in the case of continuous media subjected to long-range forces, for which no intuitive macroscopic reasoning is possible.