I also find Bell’s insight fascinating, and I think the fame he got from it is well-deserved. His motivation for doing so is interesting: he was fascinated by Bohmian mechanics, the hidden-variable theory that was thought to be impossible, and was investigating the contradiction between its brutal nonlocality and EPR’s assertion that on the contrary, hidden variables should solve the nonlocality problem. So he decided to see if hidden variables could actually solve the nonlocality problem, and surprise surprise, they cannot.

About EPR: they were not directly inspired by any experiment, just by theory. Since quantum mechanics was formalised in the mid-twenties it was obvious that superpositions are essential for it, and already in the Solvay conference in 1927 Einstein presented a nonlocality argument based only on simple superpositions. It was much less dramatic than the EPR argument, though, and got much less attention.

]]>I found it fascinating that Bell envisioned that “QD Entanglement” and “Hidden Variables” paradigms would actually manifest themselves differently in experimental results, and indeed quantified that difference analytically. I was just trying to heuristically internalize the meaning of that.

Was EPR inspired in response to the fact that Entanglement was an inherent part of QD theory, or, was it inspired by actual experimental findings?

Dave

]]>Long story short, EPR showed that quantum mechanics is nonlocal, and assumed that completing it with hidden variables would make it local. Bell then showed that nope, hidden variables do not help; any local hidden variable theory is in contradiction with quantum mechanics. In order to be compatible with quantum mechanics one needs to make the hidden variables nonlocal, which defeats the whole purpose of the thing.

About entanglement, I don’t know who was the first one that noticed it in an experiment; it was already implicit in the theory, and is exactly what EPR used in their argument. Right afterwards Schrödinger realised that entanglement is what made EPR’s argument tick, and invented the word. I guess the first experimental explorations of entanglement were precisely those prompted by Bell’s inequality, so the first one would be Freedman and Clauser’s experiment in 1972.

]]>I originally was more or less in the EPR camp, and was trying to understand how the EPR argument was being refuted, all of which ended me up in Bell’s world :-)

I have also been attempting to identify a reasonably straight-forward experiment that FIRST raised flags that Entanglement could be in operation. If you can point me in a direction to identify such, I would appreciate it :-)

I apologize for all the “Neophyte Noise” I have injected in this stream.

Dave

]]>I am trying to identify an simple elemental experiment that “raises a flag” that Entanglement could be going on.

I appreciate your help.

Dave

]]>For example, if you’re modelling quantum mechanics, $\lambda$ can be the state $\ket{\psi^-}$ in the ideal case, or some noisy version of it $\ket{\psi^-}’$ if some trouble happens, and you’re considering the probability that the quantum state is either of those.

]]>If I am I interpreting your symbology correctly when I state (?):

“p(ab|xy)” = the “probability of a and b occurring jointly, given that x and y has occurred”,

Then, how might one similarly “finish the line” starting with:

“p(λ|xy)” = …….?

Dave

]]>The thing is that the system $\lambda$ doesn’t need to be fixed, and in practice it never is. In quantum mechanics $\lambda$ would be the quantum state produced by (e.g) a laser, but lasers fluctuate, fibers fall out of alignment, the atmosphere interferes, etc., so that in each round of the experiment a slightly different quantum state comes.

It is also conceivable that the changes of the quantum state depend on the settings $x,y$, which would give us a nontrivial $p(\lambda|xy)$. But, as I argue in the “no conspiracy” assumption, it is extremely implausible.

]]>“Having their settings and outcomes defined like this, our experimenters measure some conditional probabilities p(ab|xy), where a,b are Alice and Bob’s outcomes, and x,y are their settings. Now they want to explain these correlations. How did they come about? Well, they obtained them by measuring some physical system λ (that can be a quantum state, or something more exotic like a Bohmian corpuscle) that they did not have complete control over, so it is reasonable to write the probabilities as arising from an averaging over different values of λ. So they decompose the probabilities as

p(ab|xy)=∑λp(λ|xy)p(ab|xyλ)”

It wasn’t the conditional probabilities that threw me (ie. p(ab|xy) is meaningful to me), but rather the meaning of “p(λ|xy)”….the Probability of the “System”, given “xy” has occurred? I have no idea what this means? Any help?

Thanks Dave

]]>