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While i don't know all the mathematical/experimental specifics i know enough about entanglement/bell's theorem to know the general ideas of what's going on. It's definitely interesting but i'm not sure how the "hidden variable" argument can ever be ruled out. I definitely understand why it is thought that bell's theorem says what people think it does but i still can't get around the idea that any possible result we find simply being a product of some sort of "preprogamming" if you will. Doesn't the concept of programming allow for any possible result?

Yogi DMT
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    You may want to post this on philosophy.stackexchange.com, where they don't take physical observations as seriously as around here. – CuriousOne May 10 '15 at 14:09
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    Bell's Theorem tells you precisely that (given simple background conditions) certain results can't result from what you call "preprogramming". Quantum mechanics tells you those results will occur. Observation confirms the quantum mechanical predictions. So a) if you believe in quantum mechanics, then Bell's theorem rules out your "preprogramming", and b) if you believe the observations, then Bell's theorem rules out your "preprogramming". Do you doubt both quantum mechanics and the observations? – WillO May 10 '15 at 14:14
  • @curious Yea i figured. I'm not sure if that was a slight towards philosophy or whatever but isn't the concept of physical observation still a very much debatable topic in either field? On topic though, i understand spin, i understand the math of bell's inequality, i'm just not sure how hidden variables can ever be completely ruled out. Take super-determinism for example, where anything that ever happens or will happen has been predetermined, how can you ever rule that out? Isn't that fundamentally impossible? – Yogi DMT May 10 '15 at 20:49
  • The concept of a physical observation is an operational machine called "an experiment". Sometimes that machine is just your pair of eyes and a stick, sometimes it's a 17km circumference accelerator. I have yet to meet a philosopher who was good with eyes and a stick or who could actually understand how an accelerator really works. Any which way, there is no other operational definition of "observation" in physics. It is always the interaction of one piece of the physical world with another. Somehow, it seems to me, though, that you haven't outgrown solipsism, quite yet. – CuriousOne May 10 '15 at 20:58
  • I didn't know solipsism had anything to do with this discussion... My question has less to do with observation and more to do with the fundamental concept of hidden variables. I'm not saying that entanglement isn't non-local as much as i'm saying that theoretically, a function can produce any value, such a truth is inescapable. Sure such functions may be of arbitrary complexity but that's besides the point. Wisdom > knowledge my friend. Have you ever thought that it's not that your philosopher friends couldn't understand how an accelerator works, but rather that they did not care to know? – Yogi DMT May 11 '15 at 00:04
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    @YogiDMT: I don't completely understand what you don't understand, but it seems that you posit the problem: "If we assume that there is no 'free will', that is if we limit the measurement settings, then we can do this in such a way that hidden variable theories cannot be ruled out" (see also the "free will theorem"). If that is your problem, then yes, it seems you can never fully rule out hidden variable theories, but you should turn to the philosophy of science. – Martin May 11 '15 at 12:52
  • It's not that i don't understand, it's just that i'm not sure how bell's inequality definitively rules out some sort of preprogramming. I definitely understand why people think it does, i'm just not sure i agree. And free will really has nothing to do with things. I'm not saying that non-locality isn't the case, i'm just saying that hidden variables, by definition, can't be ruled out. Maybe more philosophical i don't know, but such implications definitely do affect the physics side of things too. If you want to talk more we can open up a chat or something @Martin – Yogi DMT May 12 '15 at 02:03
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    @YogiDMT: And I'm trying to get your point - but I don't. What do you mean by "preprogramming"? I never said anything about locality. – Martin May 12 '15 at 07:56
  • My point is that there is no difference between non-locality and locality (in this context at least). By preprogramming i mean that every possible outcome to every possible situation could have been established at that moment of entanglement, allowing for any possible behavior to be the result of that initial, local, "collaboration" if you will. Any behavior of a "greater" non-local system, can be explained just as well with two separate components collaborating as to what behavior they will display at any point in time from then on. That's the best i can give you in 600 characters. @martin – Yogi DMT May 12 '15 at 08:04
  • I guess the main premise of bell's inequality is that the particle doesn't know what axis it will be measured in. I'll have to get back to you on that one. – Yogi DMT May 12 '15 at 08:13
  • Regardless though i feel like local and non-local theories are one in the same here. The behavior of any non local entity can be explained just the same as with corresponding parts. The problem with entanglement is that it doesn't seem to be explained by either. – Yogi DMT May 12 '15 at 08:18
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    @YogiDMT: Do you know about the Kochen-Spekker-theorem and contextuality? That seems to contradict your "preprogramming" approach (it has nothing to do with Bell inequalities though). Maybe we should move this discussion to chat? – Martin May 12 '15 at 08:49
  • Alright after a bit of thought i think i understand now why hidden variables have been ruled unless your willing to give up free will. I think the heart of bell's theorem is that you're able to choose which axis to measure the particles at right? @martin – Yogi DMT May 13 '15 at 05:53
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    @YogiDMT: Yes. If you cannot choose or have limited/"preprogrammed" choice, I believe there are known ways how to get around the implications of Bell's theorem. This idea can also be found here: http://en.wikipedia.org/wiki/Loopholes_in_Bell_test_experiments#Free_choice_of_detector_orientations. This is one paper trying to close this loophole on a scientific basis: http://arxiv.org/abs/1310.3288 – Martin May 13 '15 at 08:44

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As previously said (e.g. in this answer), you’re right, any possible physical theory can be described by hidden variables. The whole point of Bell inequality is to look at some properties of these hidden variables. The bell tests rule out local hidden variables. But non-local hidden variable are still allowed, and quantum physics can be seen as a non-local hidden variable theory, with the state being the non-local hidden variable.

The main interesting point of hidden variables is in their generality. Since any theory can be described in a hidden variable framework, you can define “natural” constraints (like locality) and test experimentally these constraints without further assumption. Taking again the canonical example of the Bell inequalities, it allows to properly define the set of all possible local physical theories (local hidden variables, or LHV), and show that

  • there is no way to rephrase quantum mechanics as a LHV, because the exeprimental prediction of qunatum mechanics are different than a LHV

  • we can (and did) effectively test Nature is described by a LHV or not, without assuming the validity of quantum mechanics.

So one can exclude some broad categories of hidden variable theories, but never all such theories. But that is not the point.

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Frédéric Grosshans
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