Self-Organization and Emergence

Heinz von Foerster 100

Organizing Institutions:

Heinz von Foerster Gesellschaft / Wien

ASC – American Society for Cybernetics

WISDOM – Wiener Institut für

sozialwissenschaftliche Dokumentation und Methodik

Institut für Zeitgeschichte | Universität Wien

AINS – Austrian Institute for Nonlinear Studies

Heinz von Foerster Gesellschaft / Wien

ASC – American Society for Cybernetics

WISDOM – Wiener Institut für

sozialwissenschaftliche Dokumentation und Methodik

Institut für Zeitgeschichte | Universität Wien

AINS – Austrian Institute for Nonlinear Studies

Louis H Kauffman

Discrete Physics and the Emergence of Quantum Mechanics

Math, UIC

University of Illinois at Chicago

Chicago, Illinois 60607-7045

USA

We show how taking a discrete stance from the very beginning for
physical processes and physical measurements leads to the
non-commutativity of position and momentum in physical observation. Thus
discrete physics, viewed in this way, yields a framework for quantum
mechanics. We then discuss the role of i where i^2 = -1, and its
appearance in the commutator of position and momentum.

In order to bring i into this structure we analyze the nature of i
in relation to discrete time and identify i as standing for a fundamental
temporal process. We take the dictum inspired by special relativity and replace
t by it, interpreting this substitution in terms of i as a discrete dynamical
system. With this identification we can write pq - qp = i hbar in our
discrete model and thus arrive at the elements of quantum mechanics.

We will elaborate on the foundations of discrete physics in terms of
non-commutativity and the view of i as the recursion i -> -1/i.

The symbolic i is a solution to i = -1/i. The temporal i is the simplest
alternating iterant +1,-1,+1,-1,... The purpose of this talk is to discuss
the possibilities in new ways to view quantum echanics as emergent from
discrete and non-commutative measurement.