ALTERNATIVE FORMULATION OF BELL'S INEQUALITY SUPPORTED BY LINEAR PROGRAMMING PROVING THE EXISTENCE OF HIDDEN VARIABLES PROVING EINSTEIN VS. BELL RIGHT IN HISTORICAL DEBATE
Creators: name: Sandoval Rodríguez, Alfredo José
Publisher: name: Zenodo
Year: 2025
Subjects: Desigualdad de Bell: Bell's inequality Bell's theorem Quantum entanglement Hidden variables Local realism Non-locality EPR paradox (Einstein-Podolsky-Rosen paradox) Correlation inequalities Crítica y reformulación: Reformulation of Bell's inequality Misinterpretation of Bell's theorem Incorrect formulation Experimental violation Frame of reference Theoretical framework Logical inconsistency Mecánica cuántica y variables ocultas: Quantum mechanics completeness Hidden variable theory Determinism vs. indeterminism Quantum correlations Superdeterminism Statistical interpretation Enfoque matemático y programación lineal: Linear programming Optimization theory Feasible solutions Variable constraints Mathematical modeling Algorithmic approach System of inequalities Computational methods

description: Written by:

Alfredo José Sandoval Rodríguez, M.S.

alfredosandovalr@gmail.com

Whatsapp (Mexico): 011-52-551-134-8900

 

ALTERNATIVE FORMULATION SUPPORTED BY LINEAR PROGRAMMING PROVING THE EXISTENCE OF HIDDEN VARIABLES PROVING EINSTEIN VS. BELL RIGHT IN THE HISTORICAL DEBATE

 

INTRODUCTION

 

This paper is a continuation of an article I published previously. For purposes of clarity and to go directly into the subject I will not talk about the background for this paper but I invite those who would like to know a little about it to check the last article I published at the following link: https://zenodo.org/records/14934126

 

BELL'S INEQUALITY

 

I constantly read statements regarding Bell's inequality in which it is said that the inequality was violated in practice. I have devoted myself to studying the formulation and have come to the conclusion that the inequality is not correctly formulated. This is in the aspect that it does not represent what was originally intended, that is, not to provide a frame of reference of what we should expect as a result of the experiments as to be able to conclude that hidden variables exist or not.

 

Clearly, if the inequality is not correctly formulated, the frame of reference would not be correct and therefore the fact that the inequality is not fulfilled as it is formulated in my opinion does not imply the non-existence of hidden variables.

 

NEW APPROACH TO DEMONSTRATE THAT THE THEORY OF QUANTUM MECHANICS CAN BE CONSIDERED COMPLETE SUPPORTED BY LINEAR PROGRAMMING TO FIND POSSIBLE VALUES OF THE HIDDEN VARIABLES THAT EXPLAIN THE RESULTS OF THE VARIOUS EXPERIMENTS.

 

I consider that among the reasons for the confusion and why the proposed objective was not achieved with Bell's inequality is among them that in its approach based on John Bell's inequality it was not considered that 2 sample spaces were being involved to which they refer indistinctly and as a consequence this leads to incorrect conclusions.

 

I describe next which are these 2 sample spaces which are 2 sets with the same number of elements with a biunivocal relation, that is to say, each element of one of them corresponds to one and only one of the other space. In addition the probability of occurrence of one of these elements is therefore the same probability of occurrence of the corresponding one.

 

For this case we will define the first sample space as all the possible occurrences of 2 particles correlated with 2 observers A and B where each one can in turn decide between 2 different configurations on different axes and expressing the results in terms of +1's and -1's, i.e. the observer A (A1, A2) and B (B1, B2) expressing each result as a single vector (A1,A2,B1,B2).

 

The second sample space we express it as the set composed by all the possible results in each event which results from all the possible combinations in which A and B can observe and that is obtained as the multiplication of the values 1 or -1, being this space represented in each event as a single vector composed by the product of each possible joint observation of A and B. That is, it is the set of possible outcomes (A1B1,A1B2,A2B1,A2B2). This is shown in the following diagram where the events listed in the left table or the corresponding event in the same row of the second table can occur with the same probability stated in the middle column.