Quantum mechanics is not weird, unless presented as such

[Jilang]

Bell discussed a toy model for EPR correlations in which the "hidden variable" was a hemisphere, and Alice measured spin-up if she chose an axis in that hemisphere, and spin-down if she chose an axis not in that hemisphere. That model does not replicate the predictions of QM.

Agreed, I have come across this too. I believe that the toy model assumes a direction that is predetermined in all three directions. My toy model assumes that it is only predetermined in one.

 

[wle]

Well, it misses the point of Bell's theorem, because it is supposed to miss the point of Bell's theorem. Bell wants to exclude deterministic hidden variables and the violation of the inequality shows that he was successful. It's not about finding a loophole in Bell's argument, I happily reject deterministic hidden variables. The point of the contextual model is to offer an alternative explanation to deterministic hidden variables, while still maintaining locality. The question is: Is there an apriori reason to exclude contextual probabilistic models like the one I described in post #530? If not, then either we can show that these models are incompatible with QM as well (which I doubt), or we are unable to claim that QM violates locality.

As far as I'm concerned, the way Bell defined locality excludes the sort of contextual hidden variables you're describing: the point is to be able to explain correlations in terms of some common origin or past interaction, described by variables $\lambda$, and variables that don't have a value independently of the choice of measurement aren't useful for this purpose. But if you define locality differently than Bell did then of course the result can be different.

If you want to argue that we should be OK with a type of contextual local model that is more general than Bell then you need to consider why one might want an alternative model to quantum physics in the first place. If you look at Bell's reasons, he criticised quantum physics for being too vague and badly defined, specifically describing what we would nowadays call the measurement problem. From this perspective I think contextuality doesn't even qualify as a well-defined physical concept since, for me, if you call a model "contextual" you're basically admitting it will have the same sort of measurement problem as quantum physics does.

 

[Point Conception]

No, I wasn't arguing for that. What I assumed, as I said in an earlier post, was:

1. There is a single random variable, $\lambda$, associated with the twin pair. This is chosen according to some probability distribution, $P(\lambda)$.
2. When a particle reaches Alice, she has already picked a measurement setting $\vec{a}$, and her device is already in some state $\alpha$. Then she will get result $+1$ according to some probability $P_A(\vec{a}, \alpha, \lambda)$ that depends on $\vec{a}$, $\alpha$ and $\lambda$.
3. Similarly, when the other particle reaches Bob, he will get result $+1$ according to some probability $P_B(\vec{b}, \beta, \lambda)$ that depends on $\vec{b}$, $\beta$ and $\lambda$, where $\vec{b}$ is his detector's setting, and $\beta$ is other facts about his detector.

There is no assumption of determinism here. But there is no way to reproduce the perfect anti-correlations predicted by QM unless Alice's and Bob's results are deterministic functions of $\lambda, \vec{a}$ and $\vec{b}$, or unless there are nonlocal interactions (so that $P_A$ may depend on facts about Bob, or $P_B$ may depend on facts about Alice).

In this paper by C.S. Unnikrishnan http://arxiv.org/pdf/quant-ph/0407041.pdf
" If both analyzers were set to the same direction a=b the (anti) correlation is perfect according
to the conservation of angular momentum "
And later he shows that P (a,b)_c = - a⋅b = P(a,b)_QM = -cos (θ)

 

[stevendaryl]

Agreed, I have come across this too. I believe that the toy model assumes a direction that is predetermined in all three directions. My toy model assumes that it is only predetermined in one.

Well, I don't see how that could possibly work. It would be nice to see you work out the mathematics to show what such a model predicts for correlations.

 

[Dale]

Closed pending moderation

Edit: the thread has outlived its usefulness and will remain closed