Hidden indeterminacies of (classical) dynamics

Dr Mike Jeffrey, University of Bristol. Part of the Leeds Applied Nonlinear Dynamics seminar series.

Since Newton set out the fundamental laws of mechanics, our ideal picture of classical physics has been of a deterministic world, each moment uniquely set in motion by the last. Even chaotic or other emergent phenomena are deterministic. But in fact this picture is a mirage.

There are already numerous static situations where Newton's laws do not uniquely determine all of the forces involved. There are likewise many dynamics situations where determinacy is lost, and here the effect is extreme. It seems that a potential indeterminacy tends to become a physical instability, resulting in highly erratic and volatile behaviour, extremely unpredictable and impossible to model deterministically.

Here we look at how such situations are derived and modelled. They arise due to discontinuities, often due to rigid body contact, switches, or decision making, looking particularly at some proposed applications to how decisions affect dynamically evolving systems.