I'm studying Bell's theorem and the CHSH inequality for some time. Now it's clear to me that one cannot reproduce the correlations predicted by quantum mechanics by assuming that particles carry hidden variables with them, and measurements depend only on them.
But what about the case where we consider the most general scenario: the measurement outcome can depend on the entire past light cone. Why not?
This would mean more information are available when the detector "chooses" an outcome, than just the variables carried by the current particle: for example the measurement of the current particle can depend on previous measurements, past measurements on the other detector when they reached the past light cone of the current event, etc.
Is it possible to show that such assumptions are also ruled out Bell's theorem?