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The conceptual and practical challenges in defining "realistic" are a consequence of the fact that we're trying to talk about the system and the interfaces to that system as if these are separate things.
By separating the system in this way, we see experiments to be the act of making inputs to that system, collecting outputs from that that system, and then evaluating the information with mathematical models. We're asking: does our mathematical model of what's inside produce the same outputs as Nature when given the same inputs?
But, the veracity of what we infer from this process depends critically on the veracity of our understanding of what are the inputs and outputs.
The decades long process of recognizing, defining, and experimentally ruling out, the various loopholes in EPR experiments shows the significant challenges of this process.
In CHSH, we assume that we are inputing two particles into two measuring apparatuses. Well, more precisely, we assume that if two particles are detected sufficiently coincidentally, then we have input two particles into the measuring apparatuses. We don't know this, however.
This is an assumption that, it would seem, we cannot experimentally prove due to Heisenberg. Why? If we are to detect the presence of the particles prior to their entry into the measuring apparatuses, we break their presumed entanglement and thus lose the correlations of measurements.
So, we are precluded from experimentally confirming the veracity of our understanding of the inputs and the outputs to this experiment. Just like we cannot measure, with arbitrary precision, both the momentum and location of a particle, we cannot know with conclusive precision the inputs and outputs to this experiment.
This is, at least conceptually, the essence of the challenge of performing a "loophole free" CHSH experiment.
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