Bell's Inequalities are a set of inequalities that establish that theories with "counterfactual definiteness" and "locality" require a set of inequalities (describing the probabilities of making any measurement) to hold. Since quantum mechanics violates these inequalities, it therefore rules out theories with these two properties.
Is Bell's Inequality still considered to rule out a significant amount of meaningful alternative "hidden-variable theories"?
Specifically, are there meaningful theories with both locality and "counterfactual definiteness" that are ruled out by Bell's Inequality?
The writers of this paper (which I wasn't able to completely follow) seem to think that the requirement of counter-factual definiteness "reduces the generality of the physics of Bell-type theories so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made."
Starting things off: what exactly is counterfactual definiteness? According to this source:
Let us define “counterfactual-definite” [14, 15] a theory whose experiments uncover properties that are pre-existing. In other words, in a counterfactual-definite theory it is meaningful to assign a property to a system (e.g. the position of an electron) independently of whether the measurement of such property is carried out.
Maybe I'm misunderstanding, but doesn't this rule out even "'classical' Heisenberg Uncertainty"? What I mean is that early students before they learn quantum mechanics are taught a sort of "classical intution" for Heisenberg's Uncertainty (People who understand QM know this is inaccurate, but it didn't even stop Feynman from using this analogy in his lectures for first year undergrads.)
Intution is: If you ever need to observe something sufficiently small, you must physically "hit it" to see it. This interaction imparts some energy and you end up changing the state.
Therefore isn't even a simple "billiard ball" model of the universe contained within "counter-factual definite" theories because measurements of "billiard balls" require collisions with other billiard balls (measurements therefore change the properties of the states that are being observed)?