# Why does breaking Bell's inequality rule out all local hidden variables theories? [duplicate]

It seems that a hidden variables theory could reproduce Bell's experiments results, preserving locality, as long as it accepts that the superposition state(or at least a faux superposition) existed at $t=0$ of the creation of entangled pair. In this case, the question "where and how were the particles previous to the measurement?" makes sense, but only up to the moment they were defined to be opposites. It could be that, while movement over time for a entangled particle is also described by a wave function, its spin for each vector remains constant over time (when considering the same direction measured), only being uncertain at t=0. There's even a global vertical direction that could be responsible for this: gravity.

Bell, in fact, accepts that $\vec\lambda\cdot\vec p >0$ could properly describe the possibly states for a single particle in a local hidden variable theory. Why can't it be that when the entangled pair is created, this measurement is ran over in a particle, which defines every possible vector for this particle (respecting the probability), then the result is transferred and reversed in the other particle? That's all this local hidden theory would need to accept. In this case, the particles only communicate at $t=0$, and never again.

• Let $A,B,C,D$ be the results of measurement 1 on particle 1, measurement 2 on particle 1, measurement 1 on particle 2 and measurement 2 on particle 2. Then the correlations among $A,B,C,D$ violate Bell's inequality, so $A,B,C,D$ cannot be modeled as classical random variables. As a special case of this, your proposed model cannot account for the observed correlations. Feb 15, 2017 at 15:32
• Take the following case: $X$ and $Y$ are measurements on particle 1, $U$ and $V$ are measurements on particle 2, $X=U$ 100% of the time, $U=Y$ 100% of the time, $Y=V$ 100% of the time, and $X=V$ 0% of the time. This is a more extreme violation of Bell's inequality then you'll find in quantum mechanics, but it raises exactly the same issues and might be clearer for you to think about --- and if your model works in quantum mechanics, it should work here also. How exactly can you use your model to explain these correlations? Feb 15, 2017 at 15:39
• Feb 15, 2017 at 16:39

## 2 Answers

Ruling out local hidden variables sounds equivalent to proving non-locality of entanglement. If that is so then -

No, it does not. That is why experiments are still being done as recently as in 2015 to prove non-locality of entanglement.

There are loopholes that are claimed to be closed. But they are closed only to a certain extent, not fully.

For example, to close the memory loophole completely, the experimentalists claim that that would require a brand new equipment for each entangled pair generated and measured, thereby requiring billions of equipment and making it impossible to really perform such a test. That is actually not necessary. The trend/indications can be captured with multiple equipment, say dividing the experiment into 10 parts/equipment and then checking whether the results materially differ from those from a single equipment. The will to drill non-locality seems to be missing as far as I can tell.

There are two ways Bell's inequality would be violated -

1. Entanglement is really non-local.

2. The outcomes are steered to violate the inequality, by nature, to keep things in balance.

In both the cases, QM predictions remain quantitatively correct. But non-locality, Vs balancing still needs more checking.

Imagine Bob and Alice take a pair of red and blue marbles each to the opposite sides of the Earth.. They mix up the marbles behind their backs, hold out their hands, and at the same time ask a random bystander to pick a hand. What's going on with Entanglement is equivalent (take my word for it if you want) to the same color marble being picked more than 50% of the time. At the heart of the experiment is the idea of free will, the choice of hand is something that is not known before hand, and can't be incorporated into each marble's "hidden variable plan". That leaves us with two possibilities, the marbles (on some level, using a very broad definition of the term, are communicating faster than light), or the choice of hand by the bystander was actually not a choice, but a predetermined action that was planned by reality since the beginning of time.

Given all that, Bell's inequality is a mathematical theorem that says, this is the maximum amount of correlation two separate systems can have. If they are correlated more than Bell's inequality allows for, it means the systems are actually not separate or are "communicating" with each other at some level.