Scholarpedia article on Bell's Theorem

DrChinese

If you want to retain more of Bell's words, you would want to add this important phrase to your first sentence: "In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements". I.e. a theory "supplemented by additional variables". A hidden variable theory.

This distinction in phrasing probably wouldn't be so important to ttn, since he believes that perfect correlations imply hidden variables.

lugita15

DrChinese, I still don't understand why you don't agree with this. You said that EPR argument is only that "simultaneous perfect correlations" implies hidden variables, but it seems to me that perfect correlations implies simultaneous perfect correlations, assuming the no-conspiracy condition.

I claim that the following two statements together imply hidden variables:
1. There is perfect correlation at identical polarizer settings.
2. When you don't set the polarizers to identical angles, it is still true (and meaningful) that you WOULD have gotten perfect correlations if you HAD set the polarizers to identical angles.

Do you disagree with this?

harrylin

I had not elaborated on this as my comment there was directed at ttn and martinbn, and I suppose that ttn understands this well.

An important difference in the two papers that I cited is that the second paper clearly does not suggest that his conclusion would only be valid for the addition of variables. And his conclusion as expressed in his first paper evidently also applies to a null-variable. Therefore I hold that citing that other phrase without explaining the history (he was obviously simply referring to EPR) or without also citing his reformulation in a later paper (as I did in my post #294) can put people on a wrong track. My summary in post #305 for martinbn points to what I believe to be the essence of Bell's theorem.

mattt

After a second thought, I changed my mind. I think that the way Bell defines "local causality" for a fundamental theory to respect the causal structure of Relativity Theory, is correct for a deterministic fundamental theory, but I would not use that definition for a stochastic fundamental theory. I'll expand on this in the following days...

DrChinese

It is the word "simultaneous" that is at issue here. So I agree with your 1 and 2. Certainly EPR *assume* that this is reasonable, as they explicitly said this is part of any reasonable definition of reality. Which is my entire point. A reasonable definition of reality (let's call that realism) requires you to assume your 2. Since it can never be proven, it must be assumed to make the EPR and Bell programs work.

For EPR: That assumption (along with locality) led them to their final conclusion that QM is incomplete and a greater specification of the system is possible (i.e. because you have the values of 2 non-commuting observables). Since I don't believe that a greater specification is possible, I call their assumption into question. However, that is just an opinion, and so there were 2 camps after EPR: those that followed EPR and those that followed Bohr on this particular matter.

For Bell: That assumption (also along with locality, explicitly assumed) is necessary to arrive at the contradiction - see after Bell's (14) where we now have the 3 angles a, b and c in one equation simultaneously. (There were only 2 in the EPR program.) As with EPR, if either locality or realism are bad assumptions, then there is no contradiction. Because Bell extended the idea of realism from 2 (in EPR) to 3 simultaneous values, he was able to latch on to a tiebreaker in the debate.

lugita15

OK, we're on the same page. So what ttn needs to understand is that for a given photon pair, Bell's argument involves meaningfully discussing not only the two polarization attributes that are measured but also a third polarization attribute that is unmeasured but that could have been measured had the experimenter chosen to. In other words, the argument assumes counterfactual definiteness.

ttn

http://www.scholarpedia.org/article/...e_EPR_argument

ttn

No, it doesn't. The confusion giving rise to the impression that it does is called positivism -- i.e., the insistence that everything we're ever talking about has to be entirely reducible to directly measureable things.

But in fact the whole argument is about *candidate theories* and what predictions they make in various situations. There is nothing at all like "counter-factual definiteness" assumed in saying, e.g.: consider candidate theory A; in situation 1 it predicts such-and-such; in situation 2 it predicts thus-and-so; and so on. That is the structure of the argument. It's about what a theory predicts when various different things are measured. The question of whether some outcome of some experiment "really exists" even when that experiment isn't actually performed, is a completely and total philosophical red herring. Strictly speaking, this all means that, at the end of the day, the conclusions is that *no local theory can explain the quantum predictions*. So maybe there is some wiggle room if, for example, you think that you can explain the quantum predictions in a local way without using a theory, or some such thing. Good luck with that.

ttn

Sorry, no, I'm not comfortable doing that. This paper of mine quotes *extensively* from "la nouvelle cuisine", though, so maybe you could look at this if for some reason you really can't get a copy of Bell's book (2nd edition).

http://arxiv.org/abs/0707.0401

lugita15

ttn, you make an interesting argument there that I can't seem to immediately refute:

"Here is the formulation of the "several axes" version of the EPR argument that does not involve counterfactuals: in order to explain (without violation of locality) the fact that the outcomes will be perfectly anti-correlated if the experimenters both measure spin along the z-axis, one has to assume that these outcomes are pre-determined. The same goes for measurements of spin along the x-axis. Even though, in each run of the experiment, either the z-axis or the x-axis is chosen along which to perform the measurements, the elements of physical reality that exist before the measurements cannot depend on choices that will be made later by the experimenters! This, indeed, doesn't follow from the assumption of locality itself but it does follow from the so-called "no conspiracy" assumption which states, roughly speaking, that the pair of particles prepared by the source does not "know" in advance what experiments are going to be performed on them later." (italics in original)

DrChinese

I think it is safe to say that ttn is comfortable with his position as is. On the other hand, ttn is unlikely to sway (with his argument) those who follow MWI or one of the other non-realistic (or non-deterministic) interpretations (since the vast majority of physicists are not Bohmian).

So my point to ttn remains: why make an argument that depends on wording ("simultaneous") that is soundly rejected? In other words: I reject his starting point that perfect correlations implies hidden variables*, a position I am quite comfortable with and involves no controversy. With my position, I can peacefully coexist with other interpretations, and await additional evidence to clarify matters. A position shared by most, and for which ttn has no lever to move any of us (since his assertion that he is right and we are wrong doesn't even make sense unless we all start from the same point).

Other than perhaps badgering, but I get than from the other side (local realists) just as well.

*In a time symmetric interpretation, there are no hidden variables but there are perfect correlations. Ditto for MWI. Ditto for the Copenhagen interpretation, because there is no possible greater specification of the system, and we live in a non-deterministic world. All of these interpretations reject realism. And all of these interpretations reject the idea that the current position of ALL distant particles in a system directly determines the outcomes of measurements here and now.

harrylin

I have read that argumentation and it looks sound to me - not that I'm sure that it gets rid of "counterfactuals", but simply that there is no need for the introduction of such additional complex new concepts.

harrylin

OK, you're right of course that Bell's argument assumes realism, and in the Bertlman's socks paper he mentions that point - I guess that without realism (like in the movie Matrix) about anything is possible because nothing really happens.

DrChinese

The fact that the Bohmian view is contextual should be an immediate tipoff that there is something wrong with his argument. Contextual essentially being code for "non-realistic". So of course in the end, there are no simultaneous definite values for a, b and c which is my assertion. If there are no counterfactuals, there is no realism. Of course, the Bohmian view is that there is determinism. So again we are back to the meaning of words. The Bohmian view is non-local deterministic, i.e. there are non-local hidden variables. But it is not any more realistic than other interpretations.

To ttn, of course, this distinction is meaningless: he argues "against realism". But to you, you must decide if you accept the idea that at the time entanglement begins, the outcomes have been predetermined in the context of the inevitable future measurement settings and NO OTHERS (since Bohmian theories don't address the DrChinese challenge either). If that doesn't blatantly violate ttn's premise ("cannot depend on choices that will be made later by the experimenters") to you, then I would say his argument can be accepted. I see a contradiction, but hey, that's why my conclusion is different.

So the answer is: your viewpoint subtly colors your definitions. A slight change will make a difference. I, for example, would be likely to answer ttn's "Against Realism" with an argument we can call "Against Locality". By a suitable shift in definitions, we would be left concluding that locality is irrelevant to the matter; i.e. realism is not tenable by any theory agreeing with the predictions of QM. And you know what: Bohmian types would fall inside, not outside, my definition. For the reasons stated in the first paragraph.

ttn

At least try to pretend that you're not surprised!

ttn

None of this has anything to do with being Bohmian. One of the biggest supporters of Bell's view of all this (which view I of course share) is GianCarlo Ghirardi, the principle proponent of the non-deterministic GRW version of QM. Also, I don't understand why you call MWI "non-realistic (or non-deterministic)". I would call it both realistic and deterministic -- if what you mean by "realistic" is just that it gives some definite account of micro-physical reality. (Of course, if you mean by "realistic" something about non-contextual hidden variables, then, OK, MWI isn't "realistic" in that sense... but maybe the point here is that you and others should stop using the word "realistic" without saying *exactly* what you mean.)


After all these years, I don't hold out any hope of changing your position, that's true. But it is factually wrong to suggest that my attempts to change your mind are based on the mere "assertion that [I am] right". They have instead all along been based on trying to explain the *argument*, which you systematically fail to grasp. Once more for the record, it's not an argument "that perfect correlations implies hidden variables" -- it's rather an argument that perfect correlations *plus locality* implies hidden variables. That is, the only way to explain the perfect correlations locally is for each particle to carry pre-determined answers to all possible questions that can be asked of it.

I honestly have no clue what you have in mind with this word "simultaneous". I think you mean to be referring back to the actual EPR paper, where they talk about simultaneous values for non-commuting operators. But that's just an awkward way of saying that there are more real definite properties than QM can consistently attribute values to, i.e., that QM doesn't provide a complete description of the physical state. But who cares about QM. It plays no role whatever in the argument for the conclusion I wrote in the last sentence of the previous paragraph. Also, you remember that the EPR paper was written by Podolsky, and Einstein thought he botched it, right? So please don't think of its precise wording as somehow perfectly capturing the argument. Einstein didn't think it did, and neither do I.


As I explained back in the beginning of this thread, a time symmetric interpretation isn't local. It involves causal influences coming from outside the past light cone.


It's hardly that simple. Normally the phrase "perfect correlations" denotes the following: the single actual outcome on the right perfectly matches the single actual outcome on the left, for each particle pair. MWI denies that there *is* such a thing as "the single actual outcome on the right", and same on the left. So saying that "there are perfect correlations in MWI" involves, at least, changing the meaning of the terms involved. Probably the right thing to say is that, in an MWI-ish world, the inhabitants will be fooled into thinking that "perfect correlations" occur. That's not quite the same as saying that perfect correlations do actually occur.



Copenhagen is also not a local theory.



What do you mean by "realism"? Hidden variables? If that, then I would put the conclusion differently: there are a bunch of ("regular type") theories, some "realistic" and some not, and they're all nonlocal. (Oh and then there's this one very irregular type theory, MWI, where nothing is as it seems and it's not really clear what the heck to say.) So the upshot is clear: you can have "realism" or not, but what you can't do is explain the correlations in a local way (at least, not without playing MWI games).



Actually, as worded, Bohmian mechanics also rejects this idea. See, you really need to be more careful/precise/clear with what you mean by "realism".

lugita15

Denying realism, in this context, may not necessarily mean you believe the world is an illusion and nothing is real. Realism here just means that measurable attributes have well-defined values no matter what, even if they're not measured.