Barbour–Bertotti Best Matching

Barbour and Bertotti’s Mach–Poincaré Principle can be realized in classical mechanics with a mathematical procedure which was beyond the grasp of Leibniz or Newton, and turns out to be equivalent to modern gauge theory. This is the formulation of a variational principle based on ‘best matching’: one transforms subsequent configurations of the system with the Euclidean group, and by minimizing a certain functional a notion of ‘equilocality’ is established: now it makes sense to say that a particle comes back to the same point at different times.