Current Research in Statistics & Mathematics(CRSM)
ISSN: 2994-9459 | DOI: 10.33140/CRSM
Research Article - (2026) Volume 5, Issue 1
J. S. Bell’s Inequality Postulate Reviewed by Direct Comparison of Expectation Formulae
Received Date: Mar 16, 2026 / Accepted Date: Apr 16, 2026 / Published Date: Apr 21, 2026
Copyright: ©2026 Roger L. Mc Murtrie. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation: Murtrie, R. L. M. (2026). J. S. Bell
Abstract
This paper identifies inconsistencies between the expression for the Kolmogorov expectation value of the product of two discrete random variables A (ð??â??, λ) B (ð?â??, λ) and the incorporation of such expectation values in Bell-type inequalities. Calculations related to Bell and Horne-Clauser-Shinomy-Holt inequalities are included.
Introduction
Expectation Analysis
Comparison
Consideration of Bells 1964 Inequality
Consideration of the HCSH Inequality
Conclusion
Acknowledgements
This work was assisted by chatGPT and is the culmination of over a decade’s collaboration with Gordon Watson.
Appendices
A Lemma
References
- Aspect, A. (1991). Testing Bell’s inequalities. Europhysics News, 22(4), 73-75.
- Bell, J. S. (1964). On the einstein podolsky rosen paradox. Physics Physique Fizika, 1(3), 195.
- Bell, J. S., & d'Espagnat, B. (1971). Introduction to the hidden-variable question. John S. Bell on the Foundations of QuantumMechanics, 22-32.