Noether's theorem: past, present, and a possible future

Silvio Capobianco

Institute of Cybernetics

Thursday, 7 April 2011, 14:00
Cybernetica Bldg (Akadeemia tee 21), room B101

Slides from the talk [pdf]

Abstract: Noether's theorem is one of the key results of classical physics, establishing a twofold link between the dynamical properties of a physical system to the geometry of its phase space. Its classical statement in terms of groups of transformations and constants of the motion often makes the reader overlook its additional conditions. However, it might well be that suitable versions of the theorem hold for discrete systems, provided the right hypotheses are given.

In this talk, we will go through the history of the theorem and its meaning for classical systems. We will then go through more recent work by Boykett and others, as well as our own with Tommaso Toffoli about applying similar ideas to discrete systems. We are particularly interested into general definitions of energy and momentum for cellular automata. We will illustrate the outcome of some of our experiments, both conceptual and practical, with some generalizations of the Ising spin glass model. We will see how, for this class of systems, the quantity which is usually called "energy" is in fact the "right" one according to Noether's theorem.

(Joint work with Tommaso Toffoli.)

Tarmo Uustalu
Last update 7.4.2011