I was reading a little just now about Bell's Theorem on Wiki and soon became confused and cross eyed. According to Wiki, Bell's theorem is essentially:
So I Googled "local hidden variables" but am still not sure what the term means. Does "local hidden variable" mean some sort of particle or mechanism that is as yet unknown?
Yeah, it tends to have that effect.
"Local hidden variables" are a hypothetical mechanism for avoiding faster than light transmission of information. They are a means to avoiding a flaw in "objective reality."
Take a particle. We assign various properties to particles. It has a location. It has a momentum (possibly zero). It is spinning in some fashion (possibly including not). It has a charge (which may be zero). We devise experiments to measure these properties. However, there is no process of measurement that does not affect the particle. If we measure its location, and then measure its momentum, we do not know if the result of our measurement of momentum is the same as it would have been had we not measured the location first, because our measuring of location has affected the particle. So in assigning all these properties to particles, we in affect are acknowledging that we can really only measure one of them, which calls into question whether the properties we are not measuring objectively exist, or if they are just potentially existing until they are actually measured.
So, we conduct experiments, and we find that unless we measure these properties they in fact do not exist. Our "particle" exhibits ALL of the possible values for the properties expressed as probabilities, until we actually measure it and "collapse" all the probabilities into a "reality"...at which point the particle begins exhibiting all the possible values for other properties expressed as probabilities...and we are still stuck with the fact that when we measure one property it affects the others so our particle can have, at most, ONE "experimentally real" property at a time.
BUT...the properties themselves ARE real, even when we aren't measuring them...right? There is an objective reality to things...right??? Please?
So, an experiment is called for. The subject of the experiment is
pairs of particles. There are processes that create particles that are in fact identical in at least one characteristic. If we measure ONE of the particles we then KNOW that the other particle will have that value for that property
and we have not done any disturbing measurement of it.
So, now we can predict how this particle will act, and there are experiments that have demonstrated that these predictions are valid. But until we measured one, both particles behaved as if they had all possible values expressed as probabilities. We measured ONE so it "collapsed" to a single reality, but what actually changed the behavior of the other particle?
One explanation is that some sort of "entanglement" between the two particles exists such that despite the distance between them what happens to one will affect the other. Unfortunately, for this to work (based on experiments that examine both particles simultaneously) this "entanglement" somehow conveys information between the particles instantaneously regardless of distance (uh oh, faster than the speed of light

).
In order to protect the speed of light, we introduce the "hidden variable". There is
some unobserved characteristic in the pair of particles that controls how each of them will react. Since it is the same in both they react the same, without entanglement. We call this "plan." Particles that interact with each other, even if that interaction is not their simultaneous creation, affect each other. When we measure this one, it tells us something about the other one. For this "plan" to work as a way to avoid "entanglement" with the attendant failure of the speed of light being inviolate there has to be, in EVERY particle, an aspect of
plan to cover every eventuality of every interaction it has ever had with ANY particle. All of this plan must be contained in local hidden variables in the particle.
Bell basically demonstrated that there is a limit on how much plan there can be, and it is insufficient to account for experimentally verified entanglement.
If you are cross eyed at this point, I apparently did not do any better than Wiki. If you are a physicist and you are furious about my gross oversimplifications, feel free to clarify.