HUYGENS' PRINCIPLE, PHYSICS AND COMPUTERS

Abstract

We discuss the emergence of topology from a consideration of set extensions in General Systems Theory. Boundaries arise in a natural way, separating independent elements or regions of the system. Our aim is a unification of Etter theory, Kron's method of Tearing and Jessel's formulation of Huygens' Principle. This should make explicit the equivalence between the objective, structural, holographic and the subjective, relative definitions of information, sought in Bowden (1994b), reprinted in this Special Issue. It connects the abstract generalisations of Schrodinger's equation and Bom's rule derived in probabilistic Etter theory with the real world of electrical and other physical phenomena in General Physical Systems Theory. This paper can be considered as a continuation of Bowden (1990; 1994a) and as a response to Bowden (1994b), reprinted in this issue. We review the ideas behind Kron's Method of Tearing and Jessel's Principle of Secondary sources (both special cases of the above theory) and their equivalence. We follow Hiley's argument in Hiley (1996) to show how Schrodinger's equation can be thought of as specifying the evolution of (a series of) tearings in continuous space. These can be shown on a commutative diagram as a series of similarity transforms. We compare this with Etter's derivation (Etter, 1998). We describe briefly a recently published derivation of Maxwell's equations from a non-commutative algebra and show how they fit onto a related commutative diagram. Finally we make some comments on applications of the general theory to computer systems. This paper is a series of vignettes of work in progress. It is designed to point the direction of work to come in Constructive Physics.