Author(s)

F. P. Eblen¹, A. F. Barghouty²

¹Advanced Communications and Navigation Technology Division, Space Communications and Navigation (SCaN) Program, Human Exploration and Operations Mission Directorate, NASA Headquarters, Washington DC, USA.
²Astrophysics Division, Science Mission Directorate, NASA Headquarters, Washington DC, USA.

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.

Measurement Theory, Bell’s Theorem, Bell’s Inequality, Interval-Based Analysis, Interval-Based Physical Measures

Eblen, F. and Barghouty, A. (2019) Interval Based Analysis of Bell’s Theorem. Journal of Modern Physics, 10, 585-600. doi: 10.4236/jmp.2019.106041.