I propose a reformulation of the Bohm-Bell Gedanken Experiment that is in the spirit of Leibniz. Instead of assuming Newton’s absolute space as a container of the experimental setup, I presuppose that space is composed of the relations encountered in a Bell-type experiment. In this approach, outcomes of spin component measurements can be explained causally, and Bell’s conclusion becomes invalid. As an offshoot, the maximum degree to which Bell’s inequality is violated is shown to be indicative of the number of spatial dimensions.
This program accompanies an article with the same title. The program produces the data that in the article is treated as coming from an ideal Bell-Bohm experiment. Both Alice and Bob have many more than two settings to choose between. Settings are disguised as 'keys'. Shared hidden variable explain the actual outcomes. The statistical correlations agree with those predicted by Quantum Mechanics.
This can be done because it is not assumed that Alice and Bob share a system of reference, contrary to what Bell does. To compensate, Alice and Bob must each have many more than two choices.
The program takes as input: number of spatial dimensions number of keys on Alice's apparatus number of keys on Bob's apparatus number of trials
For example:
./belldata 3 30 30 30000000
The program produces data that violate the Clauser-Horne-Shimony-Holt inequality if the number of dimensions is >2, up to the super-quantum limit of 4 for very high dimenions. For 3 dimensions, the limit is the Tsirelson's bound, the same as the limit according to QM.