This may seem like an obscure technical point, but it helps explain differing views about Bell's Theorem:
Cornell solid-state physicist David Mermin has described the appraisals of the importance of Bell's theorem in the physics community as ranging from "indifference" to "wild extravagance".There has been a consensus since about 1930 that hidden variable theory is contrary to the core of quantum mechanics. So another experiment confirming Bell's Theorem is just another affirmation of the legitimacy of those Nobel prizes in 1932 and 1933.
That explains the indifference. So the Bell spooks need a better argument to justify their wild extravagance.
Here is one such attempt, from Wikipedia:
Whereas Bell's paper deals only with deterministic hidden variable theories, Bell's theorem was later generalized to stochastic theories as well, and it was also realised that the theorem is not so much about hidden variables, as about the outcomes of measurements that could have been taken instead of the one actually taken. Existence of these variables is called the assumption of realism, or the assumption of counterfactual definiteness.This is just a sneaky way of defining hidden variables. Quantum mechanics teaches that you cannot precisely measure position and momentum at the same time. If you assume that particles somehow have precise values for those in the absence of a measurement, then you are in the land of anti-QM hidden variables. If there were any merit to this, then much of XX century physics would be wrong.
John Bell himself later tried to fudge his theorem by pretending to be able to deduce hidden variables from other hypotheses:
Already at the time Bell wrote this, there was a tendency for critics to miss the crucial role of the EPR argument here. The conclusion is not just that some special class of local theories (namely, those which explain the measurement outcomes in terms of pre-existing values) are incompatible with the predictions of quantum theory (which is what follows from Bell's inequality theorem alone), but that local theories as such (whether deterministic or not, whether positing hidden variables or not, etc.) are incompatible with the predictions of quantum theory. This confusion has persisted in more recent decades, so perhaps it is worth emphasizing the point by (again) quoting from Bell's pointed footnote from the same 1980 paper quoted just above: "My own first paper on this subject ... starts with a summary of the EPR argument from locality to deterministic hidden variables. But the commentators have almost universally reported that it begins with deterministic hidden variables."The commentators are correct. The argument does begin with hidden variables.
In my view, the core of the problem here that some physicists and philosophers refuse to buy into the positivist philosophy that comes with quantum mechanics. Quantum mechanics is all about making predictions for observables, but some people, from Einstein to today, insist on trying to give values for hypothetical things that can never be observed.
The comment asks:
Could you tell me what you mean by "deterministic and separable", and in particular could you tell me how your concept of "deterministic and separable" can account for the perfect anti-correlation without hidden variables?
By separable, I mean that if two objects are separated by a space-like 4-vector, then one can have no influence over the other. This is local causality, and says that physical causes act within light cones. It has been one of the main 3 or 4 principles of physics since about 1860. It is the core of relativity theory.
Determinism is a dubious concept. It has no scientific meaning, as there is no experiment to confirm or deny it. It has never been taught in textbooks, and few physicists have believed in it, with Einstein being a notable exception.
If determinism were true, then you could prepare two identical Potassium-40 atoms, wait about a billion years, and watch them both decay at the same time. But it is hopelessly impossible to prepare identical atoms, so this experiment cannot be done.
Some interpretations of quantum mechanics claim to be deterministic and some claim the opposite, and they all claim to be consistent with all the experiments. So this notion of determinism does not seem to tell us anything about quantum mechanics.
As I wrote last year:
If determinism means completely defined by observables or hidden variables obeying local differential equations, then quantum mechanics and chaos theory show it to be impossible.So I am not pushing determinism. It is an ill-defined and unscientific concept.
If some EPR-like process emits two equal and opposite electrons, then maybe those electrons are physically determined by the emission process. Or maybe they are intrinsically stochastic and have aspects that are not determined until a measurement. Or maybe it is all determined by events pre-dating the emission. I do not think that these distinctions make any mathematical or scientific sense. You can believe in any of these as you please, and positivists like myself will be indifferent.
When the experimenters get together later to compare their results, they make an astounding discovery: Every time the two experimenters happened to measure a pair of entangled electrons along the same direction, they ALWAYS got opposite results (one UP and one DOWN), and whenever they measured in different directions they got the same result (both UP or both DOWN) 3/4 of the time.What makes this astounding is if you try to model the electron spin by assuming that there is some underlying classical spin to explain all this. That means that there is always a quantitative value for that spin, or some related hidden variable, that defines the reality of the electron. Some people call this "realism", but it is more than that. It is identifying the electron with the outcomes of potential measurements that are never made.
Everything we know about electrons says that this is impossible. You can measure position, and mess up the momentum. You can measure the X-spin, and mess up the Y-spin. And we can only make these measurements by forcing the electron into special traps, thereby making obvious changes to the electron.
Thus, contrary to widespread beliefs, Bell's Theorem and its experimental tests say nothing about locality or determinism or randomness. They only rule out some hidden variable theories that everyone (but Einstein) thought were ruled out in 1930.
I am not saying anything radical or unusual here. This is just textbook quantum mechanics. Those textbooks do not say that Bell proves nonlocality or indeterminism. I don't think so, anyway. That is why so many physicists are indifferent to the subject, and no Nobel prize has been given for this work. It is just 1930s physics with some wrong philosophical conclusions.
Lubos Motl just posted a rant against a BBC documentary:
I have just watched the first of the two episodes of the 2014 BBC Four documentary The Secrets of Quantum Physics. ...I haven't watched it, but it sounds like a lot of other popular accounts of quantum mechanics. They get the early history pretty well, and then they tell how Einstein and Bell did not believe it, and tried to prove QM wrong. Then the experiments proved QM right and Einstein and Bell wrong. But then then end up with some crazy conclusions that do not make any sense.
Needless to say, after having said that Einstein's view has been conclusively disproven, Al-Khalili says that he believes in Einstein's view, anyway. Hilarious. Sorry, Mr Al-Khalili, but you just violate the basic rules of logic in the most obvious way. You should really reduce the consumption of drugs.
Before I watched the full episode, and even in 1/2 of it or so, I wanted to believe that it would be a documentary on quantum mechanics that avoids the complete idiocy and pseudoscience. Sadly, my optimism was misplaced. This is another excellent representative of the anti-quantum flapdoodle that is being spread by almost all conceivable outlets of the mass culture.
Update: There is some discussion in the comments below about whether Bell assumes hidden variables, and when he leaves Bohr's positivistic view of quantum mechanics as a possibility. You can see for yourself in Bell's 1981 socks paper, which is here, here, and here. He uses the letter lambda for the hidden variables.