DrChinese said:
This is factually incorrect. The reason L and R MUST be mentioned together is because Non-local HV theories are not excluded by Bell's Theorem. But that does not mean that Non-locality is the only solution.
If you only consider Bell's Theorem, you might fool yourself into thinking that a local theory which dispensed with hv's (e.g., the simultaneously real spin components you were talking about before) could work. But this would be to ignore something that we know thanks to EPR: if you *don't* have those simultaneously real spin components (i.e., if you don't have exactly the kind of hv's Bell assumes in his derivation) you also cannot get the empirically correct predictions without violating locality. Summary: whether you have those extra elements of reality or not, a local theory will conflict with experiment. So... putting *all* the relevant arguments and evidence on the table... non-locality *is* the only solution.
It's interesting that the logic here is the same as the point you made so eloquently to Sherlock. Yes, a LHV theory can explain certain facts. But it can't explain other facts. So LHV theories are excluded. When you put *all* the evidence on the table, it is clear that LHV theories can't account for it. Likewise, when you put all the evidence on the table, it is clear that Bell Locality fails (regardless of what position you want to take on "realism", i.e., hidden variables).
You assume by your statement ("Reality is still a damn reasonable assumption"), exactly as EPR did, that there is simultaneous existence of non-commuting observables. Maybe, maybe not!
No, you're quoting me out of context. There I was using the word "reality" to refer to scientific realism *generally* -- the belief that there is an external physical world independent of my consciousness. (Not *experiments*, mind you, because experiments are part of that physical world -- when I say consciousness I mean it literally.)
If you meant above that, like me, Einstein believed in scientific realism generally, you are absolutely correct. But if you mean by "realism" specifically belief in some particular elements of reality like spin components, then it is absurd to say that EPR *assumed* their existence. They *proved* that they must exist, subject to the assumption of locality. Of course now we know that that assumption isn't true (and Einstein knew all along that it was at least logically *possible* that nature would turn out to violate locality). But that doesn't mean the argument is wrong! Orthodox QM (with the completeness assumption) violates locality, and EPR pointed out that you could perhaps construct an empirically adequate local theory to replace it if you dropped the completeness assumption -- that is, they showed that a LHV theory was the only hope for locality.
But forget all this. Which is more likely? That the EPR paper really is nothing but an emotional ejaculation ("we'd sure would like a hidden variable theory")? Or that you have failed to grasp the *argument* presented in that paper?
There is an explicit assumption in Bell's argument: that of reality ("It follows that C is another unit vector [in addition to A and B] ..."). This is the specific narrower context you are asking about.
Yes, and to avoid any future misunderstanding, we should both refer to Bell's assumption by its standard name ("hidden variables") and not "reality".
Sure, it is reasonable, but that does not make it true!
Bell jumped off from what EPR had proved. They proved that, under the assumption of locality, certain hidden variables had to exist. Bell assumed that those hidden variables existed, imposed the locality condition again, and (by considering more general correlations than EPR had considered) showed that a certain statistical constraint could be derived, the inequality.
Again, your interpretation makes it sound as if Bell just arbitrarily assumed these hidden variables existed. He just woke up one morning and happened to share the emotion that had been previously ejaculated by EPR, so he messed around and found that this contradicted some experiments. So too bad for reality.
But that reading is inexcusably sloppy (not to mention disrespectful to Bell). If you are at all skeptical of my view here, you simply need to read Bell again. He makes it abundantly clear, e.g., here:
"Let me summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. [*] But this has implications for non-parallel settings which conflict with those of quantum mechanics. So we
cannot dismiss intervention on one side as a causal influence on the other."
Everything before the "[*]" is a summary of the EPR argument. The subsequent sentence refers to Bell's theorem: the thing that EPR showed to be required by locality has further implications which turn out to conflict with the QM predictions. And the final sentence is admirably (and characteristically) precise. Note in particular that no mention of "realism" or "hidden variables" (or any relevant synonyms) appear in this final conclusion.
Please note that Locality is implicitly added into Bell's argument - he mentions it, but basically takes if for granted that if there is some FTL communication between A and B (a la Bohmian Mechanics or similar) then there is no problem reproducing the results of QM.
Locality is one of the crucial premises of Bell's derivation of the inequality. Are you suggesting this assumption isn't important, or that Bell didn't think it was important? I think the quote above should dissuade you of that. Or see practically anyone of Bell's later papers, where the locality assumption is highlighted more, e.g., "la nouvelle cuisine."
