Bridging Across Scales: Emergence and Effective Theories

This project addresses the problem of modeling behaviors of systems at widely separated scales. Top-down, continuum modeling is safe and successful. Bottom-up atomic scale modeling is also appropriate and necessary. However, questions arise about why the continuum strategies are safe and successful and about how they relate to bottom-up atomic scale strategies. What explains the relative autonomy of continuum modeling? This autonomy is, we believe, a key feature of emergence. These questions are intimately connected with understanding how effective (field) theories are constructed and how they characterize emergent phenomena. Similar questions arise in new work on synthesis at the nanoscale. The construction of nanoparticles with specific properties involve attempts to fit atomic lattice properties with nanoscale features that often require continuum-like concepts such as surfaces and boundaries. The aim is to understand emergence and the relative autonomy of emergent effective theories in terms of mixed scale methods. These methods, involving homogenization theory and renormalization group theory, allow for a sophisticated and precise understanding of phenomena and theories that have been characterized, sometimes rather uncritically, using the term "emergent". The project is important because the term "emergent" is employed in various incompatible ways. This has led to considerable confusion. By focusing on the means for explaining the autonomy and safety of various modeling strategies and theories that characterize systems at relatively large scales, the project will settle a number of philosophical questions relating to issues about emergence and reduction. Specific activities include workshops and a conference bringing together applied mathematicians, physicists, and philosophers. Outputs include peer reviewed papers and conference proceedings. The project should radically change our philosophical understanding of scientific methodology.