Structure, scale and emergence

Abstract

In this paper I consider the structures that chemists and physicists attribute at the molecular scale to substances and materials of various kinds, and how they relate to structures and processes at other scales. I argue that the structure of a substance is the set of properties and relations which are preserved across all the conditions in which it can be said to exist. In short, structure is abstraction. On the basis of this view, and using concrete examples, I argue that structures, and therefore the chemical substances and other materials to which they are essential, are emergent. Firstly, structures themselves are scale-dependent because they can only exist within certain physical conditions, and a single substance may have different structures at different scales (of length, time and energy). Secondly, the distinctness of both substances and structures is a scale-dependent relationship: above a certain point, two distinct possibilities may become one. Thirdly, the necessary conditions for composition, for both substances and molecular species, are scale-dependent. To know whether a group of nuclei and electrons form a molecule it is not enough to consider energy alone: one also has to know about their environment and the lifetime over which the group robustly hangs together.