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In reading Nick Herberts book, (1985), Quantum Reality, he states that local interaction = direct contact with mediation; non-local interaction = non-direct unmediated contact.

For example, in classical macroscopic view, the proton [P] and neutron [N], when they combine to form the deuteron [NP]--the interaction between the two is always "local" because the strong force is mediated by p-mesons (pions). In microscopic quark-gluon view the [P] is itself a local physical object of three quarks (uud) that are in local contact, and mediated by gluon color force.

Now, this view of "local" makes sense to me, I can grasp that things like pions and gluons mediate physical objects like nucleons and quarks to make the cybernetic system "local", e.g., holistic.

But, Bell Theorem tells me that the deuteron [NP] is a physical object where the [N] and [P] are held together by a "non-local" interaction (and by definition this cannot be pions otherwise it would be local), and same logic for [P] at quark level.

So, could someone please explain to me in mathematical formalism the physical nature of this "non-local" force or field or whatever it is that Bell Theorem claims to be holding together reality at both the macroscopic nucleon [NP] and microscopic quark (uud) spatial scales ? Thank you for any help on this confusing (for me) subject.