On a new mode of description in physics

Abstract

We explore the possibilities of a new informal language, applicable to the microdomain, which enables such characteristics as superposition and discreteness to be introduced without recourse to the quantum algorithm. In terms of new notions that are introduced (e.g. 'potentiation' and 'ensemblation'), we show that an experiment need no longer be thought of as a procedure designed to investigate a property of a 'separately existing system'. Thus, the necessity of a sharp separation between the 'system under observation' and the 'apparatus' is avoided. Although the new language is very different from that of classical physics, classical notions appear as a special limiting case. This new informal language leads to a mathematical formalism which employs the descriptive terms of a cohomology theory with values in the integers. Thus our theory is not based on the use of a space-time description, continuous or otherwise. In the appropriate limit, the mathematical formalism contains certain features similar to those of classical field theories. It is therefore suggested that all the field equations of physics can be re-expressed in terms of our theory in a way that is independent of their spacetime description. This point is illustrated by Maxwell's equations, which are understood in terms of cohomology on a discrete complex. In this description, the electromagnetic four-vector potential and the four-current can be discussed in terms of an 'ensemblation' of discontinuous hypersurfaces or varieties. Since the cohomology is defined on the integers the charge is naturally discrete. © 1970 Plenum Publishing Company Limited.