Interval Based Analysis of Bell’s Theorem

Abstract

This paper introduces the concept and motivates the use of finite-interval based measures for physically realizable and measurable quantities, which we call D -measures. We demonstrate the utility and power of D -measures by illustrating their use in an interval-based analysis of a prototypical Bell’s inequality in the measurement of the polarization states of an entangled pair of photons. We show that the use of finite intervals in place of real-numbered values in the Bell inequality leads to reduced violations. We demonstrate that, under some conditions, an interval-based but otherwise classically calculated probability measure can be made to arbitrarily closely approximate its quantal counterpart. More generally, we claim by heuristic arguments and by formal analogy with finite-state machines that D -measures can provide a more accurate model of both classical and quantal physical property values than point-like, real numbers—as originally proposed by Tuero Sunaga in 1958.