TOWARD A CONSTRUCTIVE PHYSICS
H. Pierre Noyes, Christoffer Gefwert, Michael J. Manthey · University of North Texas Digital Library (University of North Texas) · 1983
We argue that the discretization of physics which has occurred thanks to the advent of quantum mechanics has replaced the continuum standards of time, length and mass which brought physics to maturity by counting. The (arbitrary in the sense of conventional dimensional analysis) standards have been replaced by three dimensional constants: the limiting velocity c, the unit of action h, and either a reference mass (eg m/sub p/) or a coupling constant (eg G related to the mass scale by hc/(2..pi..Gm/sub p//sup 2/) approx. = 1.7 x 10/sup 38/). Once these physical and experimental reference standards are accepted, the conventional approach is to connect physics to mathematics by means of dimensionless ratios. But these standards now rest on counting rather than ratios, and allow us to think of a fourth dimensionless mathematical concept, which is counting integers. According to constructive mathematics, counting has to be understood before engaging in the practice of mathematics in order to avoid redundancy. In its strict form constructive mathematics allows no completed infinities, and must provide finite algorithms for the computation of any acceptable concept. This finite requirement in constructive mathematics is in keeping with the practice of physics when that practice is restricted to hypotheses which are testable in a finite time. In this paper we attempt to outline a program for physics which will meet these rigid criteria while preserving, in so far as possible, the successes that conventional physics has already achieved.