Models and Theories at the Nano-scale

Abstract

One of the most interesting things about science and engineering at the nanoscale, from the point of view of the philosophy of science, is the frequent use they make of models constructed out of theories belonging to different levels of description. We usually take it for granted that every level of description falls under the domain of its own theory. For example, we generally presume there is some fundamental level of description. And with that presumption comes the hope that we will be able to find a general theory of how things work at that level. But we also often take it for granted that at every other level of description that interests us—whether it be at the level of subatomic particles, atoms, fundamental theory molecules, fluids or mechanical solids— there will be some non‐fundamental theory available to us that will be practically serviceable for explaining, predicting, and controlling the various phenomena that live at that level of description. Nano‐science challenges this assumption. And in so doing, it challenges the idea that theory is where the action is for philosophers. Much of nano‐science involves the study of phenomena that exhibit themselves on a scale too large to be studied practicably using the resources of our best microscopic theories, and too small to be studied, with a reasonable degree of accuracy, using any of our standard higher‐level, non‐fundamental macroscopic theories. Many of the so‐ called " multiscale " approaches to studying phenomena at the nanoscale are predicated on a certain degree of scepticism that a coherent, unified theory of these phenomena exists to be found. Take, for example, the field of nano‐mechanics. " Nano‐mechanics " is the study of solid‐state materials that are too large to be manageably modelled with atomic physics, and too small to be studied using the physics of continua. Consequently, nano‐sized solid‐state materials are studied with hybrid models constructed out of theories from a variety of levels (Nakano et al. 2001). As such, they create models that bear interestingly novel relationships to their theoretical ancestors. So a close look at simulation methods in the nano‐sciences could offer novel insights into the kinds of relationships that exist between different