Does Bell's theorem include causal networks?

Question

I am not an expert, so by causal networks I mean whatever it is that Wolfram talks about in its book. Regardless of the official definition, it basically means that spacetime is an emergent property of a connected graph. At macroscopic scales this graph is connected in such a way that it looks like spacetime, in which you can define coordinates, distances and so on, but on a microscopic scale is not so well behaved. The smooth macroscopic properties are not exact, so it allows connections between nodes that are very far away in terms of what otherwise would be a macroscopic distance. For instance, two particles (however they are defined in such a network) can be "locally" connected (that is, one link away) even if the rest of the connections are "non local" (that is, they look to be far away according to the macroscopically defined "distance").

In such scenario, it seems that Bell inequalities can be violated, because what you consider non-local in the macroscopic description is actually local in the microscopic one.

Question: Is the argument above correct? Do the implicit or explicit hypotheses on Bell's theorem also exclude such scenario, or is Wolfram's claim of a possible "local" hidden variables theory possible? In other words, how much "local" means in Bell's theorem?

Answer 1

The point of Bell's theorem, explained nicely e.g. on Scholarpedia (http://dx.doi.org/10.4249/scholarpedia.8378), is that the measured violations of Bell's inequality are incompatible with a notion I would like to call EPR-locality, which always uses light-cones to define what is "close" and what not. One should not redefine the words like saying that something is now close in graph distance and therefore the network theory is local. No, EPR-local always means local in the every-day sense with distances measured in space-time as usual.

I would therefore say that the network you describe can provide an explicit mechanism of non-local connections between different particles. Such a model might be compatible with Bell, but I would have to look at the details.