2015/12/14 by Brandon Fogel, Fogel, Brandon
Arts and Humanities · Physics and Astronomy · Psychology · #Data Analysis #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Mathematical Physics (math-ph) #Philosophy and History of Science #Philosophy and Theoretical Science #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.1512.04974
openalex publication_date 2015/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open problem. Here I provide a new set of tools, which I refer to as "multideviations", for finding and analyzing these inequalities for the fully general case. In Part I, I introduce the multideviation framework and then use it to prove an important theorem: the Bell distributions can be generated from the set of joint distributions over all observables by deeming specific degrees of freedom unobservable. In Part II, I show how the theorem provides a new method for finding tight Bell inequalities. I then specify a set of new tight Bell inequalities for arbitrary event spaces -- the "even/odd" inequalities -- which have a straightforward interpretation when expressed in terms of multideviations. The even/odd inequalities concern degrees of freedom that are independent of those involved in parameter independence, raising the possibility of a new Bell's theorem with stronger philosophical implications. Also, contrary to expectations, the violation of the inequalities by quantum mechanics increases in size with the number of systems.