The popularized/simplified version is http://en.wikipedia.org/wiki/Free_will_theorem . It's logically impossible for local hidden variables to produce results consistent with this experiment; either the hidden variable must be nonlocal (able to affect two spatially separated experimenters at exactly the same time), or the experimenters' actions must be determined ahead of time (and it's not a hidden variable so much as a hidden constant).
On the contrary, a series of groundbreaking experiments have demonstrated that Bell's Inequality holds, which is incompatible with any local hidden variable theory (and what you are saying here is a local hidden-variable theory.) Non-local hidden-variable theories are just as counter-intuitive as any of the conventional interpretations of quantum mechanics, which is not surprising, as they also have to satisfy Bell's inequality.
I have no opinion on what this says about free will, though I suspect that whatever it does, it is not much.
> how can you prove that both particles were not having the same state from the start?
But this is exactly what these experiments aim to prove. That kind of predeterminism is precisely a form of local hidden variable theory. Such a theory is disproved if we can prove the violation of a Bell inequality. The standard reference for understanding the connection is this laymans-terms paper by Mermin:
If we accept that this experiment is indeed a standard-loophole-free violation of Bell's inequality, we then conclude that we must give up one of three things: locality, realism, or all free will. This rules out any local hidden-variable theory. The mainstream view is then to keep locality and free will. Some alternative theories (notably Bohmian ones) give up locality and keep realism, but this is strongly at odds with what we know from special relativity, and indeed locality is assumed in all work on quantum field theory (through Lorenz invariance) which has been verified to match experiments to a precision above that of any other physical theory. The third option, which essentially no-one supports, is that free will is impossible in our universe and that everything everywhere is predetermined.
Say we have two people performing similar experiments who are far enough apart from each other that the information from one experiment can't affect the result of the other person's experiment. The experiment they are performing is to measure the 'spin' of a particle that has been 'entangled' with the particle measured by the other experimenter. Since the particles are entangled, if the experimenters measure the spin in the same direction, they will both get the same result.
The theorem then states that if the experimenters are 'free' (as in will) to choose which direction to measure the spin of their particle, then the result of measuring the spin cannot be determined by anything previous to the experiments (and can't be determined by the other experimenter, as established above).
Put into everyday terms, its impossible for the universe to be fully determinate and still have actors capable of free will, and vice versa: if people have free will then the world can't be fully determinate.
In other words, modeling particle pairs as having matching static hidden "meta data" in them doesn't work. They do act as if there is instantaneous communication between the particles, but in a limited way that prevents us from using them for instant communication. Quantum mechanics is a weird tease, having magical properties that always serve up loopholes when we try to leverage the magic for real-world benefits. The quantum universe seems built by insurance lawyers who are masters at screwing consumers with fine-print when they go to make a claim.
No it's not, it's many worlds. It's completely local and says nothing about free will or causality.
Step 1) Entangle pair. Parts of wavefunction with up-down and down-up exist.
Step 2) Lab A interacts with pair, they either get entangled with the up-down pair or the down-up pair, or any other subset of the wavefunction.
Step 3) Lab B interacts with any part of the Lab A+pair wavefunction. When they do, they find that, astonishingly, the part of the wavefunction they find themselves entangled with when they speak to Lab A is the same part of the wave function they find themselves entangled with based on their measurements.
No new entities are posited, no new mechanism is posited, no assertions are made about wavefunctions vanishing upon interaction. It's the simplest possible claim. The only effect it has on whether or not you can do reproducible experiments is the entropy in the subset of the wavefunction you can potentially interact with went up.
It's not tested at all. No local hidden variables is just a priori true though. It's not part of any interpretation. All of them are subject to it. This is irrelevant though because there are alternatives to local hidden variables like pilot wave theory, the so-called many words interpretation, relationalism (i.e. inherent nondeterminism) and there's no way to test between any of them.
In the particular context of this post, it isn't. The local hidden variable theory is conclusively wrong. Not sure if there are recent results about nonlocal hidden variables, but last time I checked we couldn't say anything about that.
There's a great (and pedagogical enough) discussion of this at the back of Griffith's Introduction to Quantum Mechanics
Note the first assumption: "The choice of which measurement is performed can be made randomly and independently of the system under observation". In the Physics Today article, this becomes "if an experimenter is free to make spin measurements anywhere".
Either way, the conclusion that "systems in hidden-variable theories must have an infinite memory" only holds if you assume free will.
I think you forgot one: "The principle of locality always applies" / "no spooky action at a distance" -- while local hidden variable interpretations have been ruled out, nonlocal ones are still very much on the table.
I thought the hidden variable idea was proven not to hold, though? Like, I thought that was the point? That the behavior observed can only be explained using the state of the remote measure as part of the explanation?
I have not looked back at the book I read. I definitely remember it had examples that were not paired off. I'm assumingy memory is simply off.
The balls in a bag experiment is exactly the kind that does use hidden variables that are local. No information has to be transmitted in either direction.
Bell showed that the correlation is even greater than you can get using that sort of thinking. Reality is more like this:
Bob and Alice each get a pair of bags, one black and one white. They open one of the bags in which they get either a red ball or a blue ball.
If they both choose the white bags, their balls are different colors. However if either or both of them choose the black bag, the colors of the balls are the same.
If you think about it, there's no way to put the balls in the bags to satisfy these conditions in all cases. This is a simplification of what's going on with Bell's theorem.
This is far from a new idea, and is called the "hidden-variable theory" [1]. In fact, it has been mathematically proven that locality and hidden variables are fundamentally incompatible in the context of quantum mechanics.
It's explained in the footnote of the article. Bell's experiment rules out local hidden variable theories but it's still possible to formulate non-local hidden variable theories that work.
No, no. This is what makes Bell's Theorem so amazing. It conclusively proves that local hidden variables is impossible (given some simple assumptions).
I know you asked for a better explanation, but it's rather long so I won't give one. But the general idea is that you can show that no system of hidden variables can simultaneously satisfy all the experimental results we see.
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