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

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