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ttn Mar31-12 07:52 AM

Scholarpedia article on Bell's Theorem
 
Hi everybody. I dropped in to Physics Forums for the first time in a while just to see what was going on in one of my old hangouts. It was nice to see about 10 threads raging about Bell's theorem! But perhaps not so nice to see many people, with whom I argued at length in the old days here, saying the same exact WRONG things still after all these years! =)

Anyway, I just thought it might be helpful to advertise the existence of a really systematic, careful review article on Bell's Theorem that Goldstein, Tausk, Zanghi, and I finished last year (after working on it for more than a year). It's free online here

http://www.scholarpedia.org/article/Bell%27s_theorem

and addresses very explicitly and clearly a number of the issues being debated on the other several current Bell's Theorem threads. It is, in my hardly unbiased opinion, far and away the best and most complete existing resource for really understanding Bell's Theorem, so anybody with a remotely serious interest in the topic should study the article. I'd be happy to try to answer any questions anybody has, but post them here and base them somehow on the scholarpedia article since I won't have time to follow (let alone get entangled in) all the parallel threads.

Travis

Doc Al Mar31-12 08:31 AM

Re: Scholarpedia article on Bell's Theorem
 
Looks great!

DrChinese Apr2-12 09:40 AM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by ttn (Post 3843118)
Hi everybody. I dropped in to Physics Forums for the first time in a while just to see what was going on in one of my old hangouts. It was nice to see about 10 threads raging about Bell's theorem! But perhaps not so nice to see many people, with whom I argued at length in the old days here, saying the same exact WRONG things still after all these years! =)

Anyway, I just thought it might be helpful to advertise the existence of a really systematic, careful review article on Bell's Theorem that Goldstein, Tausk, Zanghi, and I finished last year (after working on it for more than a year). It's free online here

http://www.scholarpedia.org/article/Bell%27s_theorem

and addresses very explicitly and clearly a number of the issues being debated on the other several current Bell's Theorem threads. It is, in my hardly unbiased opinion, far and away the best and most complete existing resource for really understanding Bell's Theorem, so anybody with a remotely serious interest in the topic should study the article. I'd be happy to try to answer any questions anybody has, but post them here and base them somehow on the scholarpedia article since I won't have time to follow (let alone get entangled in) all the parallel threads.

Travis

Hi Travis, nice to see you again! I will definitely check out... (especially since I am probably tops on your list of "mistaken" posters). :smile:

-David/DrC

billschnieder Apr2-12 10:38 AM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by ttn (Post 3843118)
Anyway, I just thought it might be helpful to advertise the existence of a really systematic, careful review article on Bell's Theorem

...

It is, in my hardly unbiased opinion, far and away the best and most complete existing resource for really understanding Bell's Theorem

Although the above presents some interesting perspectives, it is hardly a review (let alone a complete resource) but a rehashing of the views of the authors (in support of non-locality). I was very dissapointed for many reasons including:

- No mention of the relationship between Bell's inequalities and very similar Booles inequalities developed a century before Bell.
- No mention of a growing series of very significant critiques of non-locality (maybe the authors are not aware of these):

DrChinese Apr2-12 10:45 AM

Re: Scholarpedia article on Bell's Theorem
 
By the way, very nicely done article and I must say, pretty well balanced all things considered. Especially everything prior to the "Bell's theorem proves the impossibility of 'local realism'" section. I think it is better than the Wiki article on the subject, which has been in severe need of attention for a long time.

In some ways even your early conclusion that "our world is non-local" is not too bad. Aspect prefers "non-separable". I personally prefer the term "quantum non-local" because there are time-symmetric models (Relational Blockworld for example) that yield the appearance of non-locality but still respect light cones in your sense that "...goings-on in one region of spacetime should not affect — should not influence — happenings in space-like separated regions."

Any implication that Bell's Theorem leads to any conclusions regarding dBB are not suitable for an article surveying Bell. For the most part, you stay away from that. On the other hand, there is a pretty fair amount of the latter material that is not generally accepted. I would say that controversy regarding the term "realism" is reserved for those with a more philosophical bent (and I might be one of those). I would definitely say that the vast majority of published articles dismiss the idea that particle observables have well-defined values at all times. You may consider that an imprecise definition of realism, but nonetheless I would say it is the most common.

PS ttn: You don't need to comment or refute these comments, you already know where I stand as I you. But it is a nice article, much of it could go straight to the Wiki page and it would be an improvement there as well.

DrChinese Apr2-12 12:28 PM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by billschnieder (Post 3846358)
- No mention of a growing series of very significant critiques of non-locality (maybe the authors are not aware of these):

Hey, I could add to this list but since these papers are not generally accepted, they do not belong in the Scholarpedia article. I would not call the above a growing list anyway, there have been critiques of Bell virtually non-stop since inception. Ditto with relativity, which still draws deniers.

ttn Apr2-12 12:40 PM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by DrChinese (Post 3846363)
I think it is better than the Wiki article on the subject, which has been in severe need of attention for a long time.

Well that's a relief. Some of us actually tried for a while to clean up the wikipedia pages about Bell's theorem, dBB, etc., and it was just too frustrating to deal with established editors who don't understand the issues but who have the power to revert changes, etc. So we jumped instead at the chance to create a better alternative to the wikipedia pages. Hopefully it will become widely known as such.

Quote:

In some ways even your early conclusion that "our world is non-local" is not too bad. Aspect prefers "non-separable". I personally prefer the term "quantum non-local" because there are time-symmetric models (Relational Blockworld for example) that yield the appearance of non-locality but still respect light cones in your sense that "...goings-on in one region of spacetime should not affect ó should not influence ó happenings in space-like separated regions."
Bell simply defines "nonlocality" as: any causal influence on an event that comes from outside the past light cone. An influence coming from the future light cone hence counts as "non-local" and is in no way a counterexample to the theorem. Some people (maybe because they think it is easier to reconcile with fundamental relativity) would prefer to respond to Bell's theorem by having slower-than-light-but-backwards-in-time influences. Some people (maybe because they think the idea of a "backwards-in-time influence" doesn't make any sense) prefer to have direct influences between spacelike separated events. And maybe there are other possibilities too, that combine these or don't fit nicely into either option. But what all these have in common is that they violate "locality" as defined by Bell. That's the theorem.

Incidentally, it's not really true that a time-symmetric model avoids causal influences between spacelike-separated events. You will still have such influences in such a model -- they just won't be "direct". For example, you can zig-zag from A to (spacelike separated) B by going forward in time at the speed of light, then backward in time at the speed of light. (One of the problems faced by advocates of such models is to give some kind of coherent definition of "direct" so that we'd have a basis for worrying less about such zig-zag influences than we would about "direct" influences from A to B.)



Quote:

On the other hand, there is a pretty fair amount of the latter material that is not generally accepted.
I'm not sure what you mean. You mean there is stuff in the article that is "not generally accepted"? That's certainly true, but that's what happens when you write an accurate article about a subject that most people are confused about!


Quote:

I would say that controversy regarding the term "realism" is reserved for those with a more philosophical bent (and I might be one of those). I would definitely say that the vast majority of published articles dismiss the idea that particle observables have well-defined values at all times. You may consider that an imprecise definition of realism, but nonetheless I would say it is the most common.
Yes, that definition of "realism" is somewhat imprecise -- for example, do you mean that *all* observables have a definite value at all times? If so, then, e.g., dBB is not a "realist" theory. (That should strike you as absurd!) Or if it means that *some* observables have a definite value all the time, then dBB is realist (and, e.g., ordinary QM isn't). Or if it means that some observables have a definite value some of the time, then even ordinary QM is realist. So you should be more precise.

But the real point, vis a vis Bell's theorem, is that this doesn't matter at all, because "realism" is not at all an *assumption* of the theorem. To the (very limited) extent to which it plays a role at all, it is *inferred*, from locality and the perfect correlations (predicted by QM). That is, in the usual EPR-Bell setup (measuring spin along 3 possible directions on each side on a pair of spin 1/2 particles in the singlet spin state) it follows from locality that each particle must carry pre-scripted "answers" to the three possible measurements/"questions". So if you want to call that "realism", then the theorem has the following logical structure:

(a) locality + perfect correlations --> "realism"

(b) "realism" --> Bell's inequality

-----

(conclusion) locality + perfect correlations --> Bell's inequality

Since, experimentally, "perfect correlations" is true and "Bell's inequality" is false, it follows that locality is false.

See how "realism" only comes up as an intermediate term in the logic, about which (therefore) nothing at all follows? Note in particular that denying the truth of "realism" in no way allows you to avoid the conclusion that locality is false.

DrChinese Apr2-12 01:04 PM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by ttn (Post 3846518)
You mean there is stuff in the article that is "not generally accepted"? That's certainly true, but that's what happens when you write an accurate article about a subject that most people are confused about!

I hear you on that. But I think that it is best to focus a lay or summary article on content which is generally accepted. I don't think it makes sense to have an article of, let's say, 10,000 words of which 3,000 are devoted to relatively controversial items (especially when not identified as such). Maybe more like 250. The key elements should be reasonably true to the usual rendering of Bell, even if you are right and those are wrong. Because otherwise, there is a noticeable editorial slant.

ttn Apr2-12 02:16 PM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by DrChinese (Post 3846574)
But I think that it is best to focus a lay or summary article on content which is generally accepted. I don't think it makes sense to have an article of, let's say, 10,000 words of which 3,000 are devoted to relatively controversial items (especially when not identified as such). Maybe more like 250. The key elements should be reasonably true to the usual rendering of Bell, even if you are right and those are wrong. Because otherwise, there is a noticeable editorial slant.

I have a very different view here. First off, there is a meta-consensus about the fact that Bell's theorem is controversial. We acknowledge that openly in our article and explain in particular that what we are presenting is Bell's own view of the meaning and significance of the theorem. (If anybody's opinion on this controversial subject has a special, privileged status, it is surely Bell's own.) We also explain in extensive (perhaps even excessive) detail how and where people with different views go wrong. So it seems frankly ridiculous to say that the article is "slanted" or "biased". It wears its bias on its sleeve, so to speak -- and more importantly, what it is biased toward is the truth.

If you disagree with the arguments or conclusions presented, then by all means tell me what you think is wrong and we can discuss it. But it seems preposterous to criticize the article for not just repeating the same old stale misconceptions that most physicists suffer from. What would be the point of such an article? (Indeed, that article already exists -- on wikipedia. See also nearly any QM textbook.)

In any case, what I'm most interested in discussing here (if anybody cares to discuss it) is not what "style" of article is appropriate to write, but the actual content of the article (as written, for better or worse). If you think the article is wrong and the "consensus" (indicated by wikipedia and QM texts) is right, tell me where the article goes wrong.

DrChinese Apr2-12 03:17 PM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by ttn (Post 3846681)
In any case, what I'm most interested in discussing here (if anybody cares to discuss it) is not what "style" of article is appropriate to write, but the actual content of the article (as written, for better or worse). If you think the article is wrong and the "consensus" (indicated by wikipedia and QM texts) is right, tell me where the article goes wrong.

Fair enough, I will look through it in some more detail.

It seems strange to me, though, that Scholarpedia would want material outside the realm of scientific consensus. One line from the wiki page that I think summarizes the meaning of Bell accurately is:

No physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics.

Zeilinger wrote a few years back in a centenary article: "Thus Bell discovered that the assumption of local realism is in conflict with quantum physics itself and it became a matter of experiment to find out which of the two world views is correct. Interestingly, at the time of Bellís discovery no experimental evidence existed which was able to decide between quantum physics and local realism as defined in Bellís derivation." Aspect wrote, in a similar kind of article: "The experimental violation of Bellís inequalities confirms that a pair of entangled photons separated by hundreds of metres must be considered a single non-separable object ó it is impossible to assign local physical reality to each photon." I haven't ever seen any substantive counter-quotes, except by you. My point being that in virtually every discussion of the subject, the author takes pains to give some meaning to the word "realism" (as do I).

As I have said, my definition of realism relates to the idea that any *single* photon has simultaneous well defined values of polarization at the three angles 0, 120 and 240 degrees. I do not believe it has such a thing, and I doubt you could find a roomful of physicists that thinks it does. I also believe that an entangled pair of photons cannot be considered separate, distinct objects; which at any distance would violate ordinary notions of locality. I doubt you could find a roomful of physicists that thinks they are separate objects either!

I realize you think you are correct, and that is good, but you don't need to include all the "extra" stuff in the article for it to be a superior article. I can tell you that as is, I will start using it as a link for those times when I need to pass out a good reference on Bell.

ttn Apr2-12 05:58 PM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by DrChinese (Post 3846786)
Fair enough, I will look through it in some more detail.

Excellent!

Quote:

It seems strange to me, though, that Scholarpedia would want material outside the realm of scientific consensus.
Well, I guess what they want is material that is scholarly and true. Incidentally, the "scientific consensus" you refer to here largely consists of people who have never researched Bell's theorem in a serious way, but instead just repeat what they heard once. Among serious researchers in the foundations/philosophy of physics, Bell's own view is better known and much more widely adopted.



Quote:

One line from the wiki page that I think summarizes the meaning of Bell accurately is:

No physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics.
This commits what Tim Maudlin has eloquently dubbed "the fallacy of the superfluous adjective". Yes, Bell's theorem implies what you say here. But it also implies that no local theory *without* hidden variables can reproduce all of the predictions of QM. That is, Bell's theorem shows that no local theory can reproduce all of the predictions of QM, whether it has hidden variables or not. See our article for more details.



Quote:

Zeilinger wrote a few years back in a centenary article: "Thus Bell discovered that the assumption of local realism is in conflict with quantum physics itself and it became a matter of experiment to find out which of the two world views is correct. Interestingly, at the time of Bellís discovery no experimental evidence existed which was able to decide between quantum physics and local realism as defined in Bellís derivation." Aspect wrote, in a similar kind of article: "The experimental violation of Bellís inequalities confirms that a pair of entangled photons separated by hundreds of metres must be considered a single non-separable object ó it is impossible to assign local physical reality to each photon." I haven't ever seen any substantive counter-quotes, except by you.
Then you need to get out more. Try reading something by Tim Maudlin or David Albert for example. Here is a paper that directly responds to some of Zeilinger's zaniness:

http://arxiv.org/abs/quant-ph/0604173



Quote:

My point being that in virtually every discussion of the subject, the author takes pains to give some meaning to the word "realism" (as do I).
OK, so then we'll have something to talk about after you carefully study the article.


Quote:

As I have said, my definition of realism relates to the idea that any *single* photon has simultaneous well defined values of polarization at the three angles 0, 120 and 240 degrees. I do not believe it has such a thing, and I doubt you could find a roomful of physicists that thinks it does.
I also don't think it does. What I think is that locality requires that it does. That's a problem for people who believe in locality (which I gather includes you?) but not for me.



Quote:

I also believe that an entangled pair of photons cannot be considered separate, distinct objects; which at any distance would violate ordinary notions of locality. I doubt you could find a roomful of physicists that thinks they are separate objects either!
I also don't believe a pair of entangled particles can be considered separate distinct objects. They nonlocally influence each other, and so aren't "separate".

As to roomfulls of physicists, I'm in them all the time, and generally I find that they are not good judges of these kinds of issues, because none of them have ever thought about them carefully. (It's an operational hazard of becoming a physicist -- you are trained not to ask certain questions about the foundations/interpretation of QM.)


Quote:

I realize you think you are correct, and that is good, but you don't need to include all the "extra" stuff in the article for it to be a superior article.
What extra stuff?



Quote:

I can tell you that as is, I will start using it as a link for those times when I need to pass out a good reference on Bell.
Good, that's our hope -- that people will see the article as the best presentation of at least one important interpretation of Bell's theorem (whether they agree with that interpretation or not).

zonde Apr2-12 11:30 PM

Re: Scholarpedia article on Bell's Theorem
 
Review article should be neutral. But your article is not. Right at the start you are pushing your line:
"The relevant predictions of quantum theory were first convincingly confirmed by the experiment of Aspect et al. in 1982; they have been even more convincingly reconfirmed many times since. In light of Bell's theorem, the experiments thus establish that our world is non-local. This conclusion is very surprising, since non-locality is normally taken to be prohibited by the theory of relativity."

And let me ask what are "the relevant predictions of quantum theory"? And can you give some reference where these predictions are tested?

ttn Apr3-12 05:24 AM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by zonde (Post 3847381)
Review article should be neutral. But your article is not. Right at the start you are pushing your line:
"The relevant predictions of quantum theory were first convincingly confirmed by the experiment of Aspect et al. in 1982; they have been even more convincingly reconfirmed many times since. In light of Bell's theorem, the experiments thus establish that our world is non-local. This conclusion is very surprising, since non-locality is normally taken to be prohibited by the theory of relativity."

Can I ask you, seriously, what you mean by "neutral"?


Quote:

And let me ask what are "the relevant predictions of quantum theory"? And can you give some reference where these predictions are tested?
Huh? The predictions "were first convincingly confirmed by the experiment of Aspect et al. in 1982 ...".

Demystifier Apr3-12 07:30 AM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by ttn (Post 3847634)
Can I ask you, seriously, what you mean by "neutral"?

Hi, Travis!
The question was not addressed to me, but I would like to say something about it.

Of course, it is impossible to write an absolutely neutral review paper on anything. But still, some review papers are less neutral, while others are more neutral. Let me explain the difference.

A quite neutral paper typically contains sentences of the form:
The author a argues A, while, by contrast, the author b argues B.

A less neutral paper typically contains sentences of the form:
The author a argues A. By contrast, the author b argues B, but the argument by a seems more convincing than that by b.

An even less neutral paper typically contains sentences of the form:
The author a has shown A.

By that definition, this review certainly does not belong to very neutral reviews. Indeed, from other papers by the authors who I know quite well, I can tell that this is simply not the style of these authors to be neutral. But I will try to be more neutral here, so I will not say that this is bed, nor I will say that this is good. Indeed, not being neutral certainly has both advantages and disadvantages.

In any case, this review is a review of the opinions of the authors who know very well what they are talking about, and as such it is a very good review.

Demystifier Apr3-12 08:40 AM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by ttn (Post 3843118)
I'd be happy to try to answer any questions anybody has, but post them here and base them somehow on the scholarpedia article since I won't have time to follow (let alone get entangled in) all the parallel threads.

Travis

I have a couple of questions. :smile:

1. I haven't noticed that you discuss attempts to "save locality" through signals traveling backwards in time (like, e.g., in transactional interpretation). Can you comment on such attempts?

2. You say that
"Certain "relational" interpretations of quantum theory also deny that a completed experiment has a well-defined physically real outcome. It is possible that this type of strategy could succeed in evading the consequences of Bell's theorem, allowing for the possibility of a universe governed by a local theory such that conscious observers living in that universe attest to the validity of the quantum predictions."
Would you say that my "solipsistic hidden variables"
http://xxx.lanl.gov/abs/1112.2034
belong to that class of interpretations? (Which, of course, would not imply that you find that paper promissing or appealing, as I know you don't.)

3. Do you have any comments on the Joy Christian's attempt to avoid nonlocality?

4. It's not a question, just a comment:
I particularly liked how you demystified the consistent-histories approach. :approve:

ttn Apr3-12 08:53 AM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by Demystifier (Post 3847755)
By that definition, this review certainly does not belong to very neutral reviews.

Hi Demystifier. Thanks for your comments. I of course agree with what you wrote. But neither does the article belong to the "even less neutral" category as you describe it: we acknowledge openly that the subject is controversial and indeed extensively review and critique the alternative views.

The point I was hoping to get at, though, is that I simply don't believe anybody who criticizes the article for not being "neutral". Do they also complain, for example, that Shimony's article at the SEP, or the wikipedia article, are far from "neutral" because they don't even acknowledge that the view taken is contrary to Bell's own view? That is, by the way some people apparently think about it, our article fails to be "fully neutral" -- largely *because* a whole previous generation of authors failed to be fully "neutral". But... now that we're in this generation, we just have to accept that prior non-neutrality as the given, unquestionable standard against which we judge "neutrality" going forward? It's all just absurd.

People who read this article and say "it's not neutral" really just mean "it disagrees with what I, personally, consider to be the truth". But such people should, first, actually read the article (not just skim the abstract to see whether it endorses their half-baked opinions) -- and then focus on the facts and issues and raise questions about anything from the article they think is wrong. Forget the sociological side issues. What matters at the end of the day is whether it is right or not, not whether it regurgitates some flimsy statistical consensus of non-experts.


Quote:

Indeed, from other papers by the authors who I know quite well, I can tell that this is simply not the style of these authors to be neutral.
It's true, we're primarily concerned with truth, not neutrality. So thanks, I'll take your comment as a big compliment! =)


Quote:

In any case, this review is a review of the opinions of the authors who know very well what they are talking about, and as such it is a very good review.
Thank you. It really should also be stressed that, in this case, the authors are in complete agreement with Bell himself. One of the big tragedies of this whole thing is that Bell died so young. If he had been around for the last 20 years, things would have gone much better, sociologically.

DrChinese Apr3-12 10:24 AM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by ttn (Post 3846970)
I also don't think it does. What I think is that locality requires that it does. That's a problem for people who believe in locality (which I gather includes you?) but not for me.

I follow what I call "quantum non-locality", which I consider simply to be in line with standard interpretations.

To put it another way: suppose you ask the (loose) question, "Where are the hidden variables?" If you answer they are in the present and located elsewhere, then you would likely be a Bohmian. If you answer they are in the future, with that zig-zag world line you mentioned that does not respect time's arrow, you might be a follower of a Time Symmetric interpretation. Or maybe you follow MWI and the answer relates to hidden dimensions.

So I definitely think any entangled particle essentially must be interacting with 1 or more others in such a way that conventional ideas of (Einsteinian) locality cannot possibly apply. I think that is probably true of ANY (non-entangled) particle as well, although that is a bit more of a leap and I can't prove it. So we probably aren't as far apart as it might sometimes seem.

I often find it convenient to think in terms of the Time Symmetric formulations because it conveniently explains how certain experimental setups make "sense". An example being delayed choice setups in which time ordering is not important. I realize that other interpretations support this as well, but you would have to admit to the beauty of the explanation using a Time Symmetric approach (since the entire future/past context, and nothing else*, is considered). And those nicely respect c at all times, just not in the proper direction! If you juggle the terminology a certain way, you can call this a local non-realistic interpretation. But to me it is still quantum non-local.

I don't take any interpretation too literally at this point, they are more of a convenience to me. So if a smoking gun were found tomorrow that proved dBB correct and ruled out other interpretations, I wouldn't really flinch. And it would only enhance the importance of Bell's Theorem in my mind. :smile:


(* "nothing else" other than some unknown random something LOL.)

DrChinese Apr3-12 10:36 AM

Re: Scholarpedia article on Bell's Theorem
 
Quote:

Quote by ttn (Post 3847866)
The point I was hoping to get at, though, is that I simply don't believe anybody who criticizes the article for not being "neutral". Do they also complain, for example, that Shimony's article at the SEP, or the wikipedia article, are far from "neutral" because they don't even acknowledge that the view taken is contrary to Bell's own view?

...

People who read this article and say "it's not neutral" really just mean "it disagrees with what I, personally, consider to be the truth".

Working towards a neutral slant is a goal; of course authors have opinions. The purpose of neutrality is to give suitable room for the reader to form their own opinions. Clearly, a reader coming to any encyclopedia type source is expecting reasonable neutrality. So having a substantial slant that is not discernible to the lay reader would have the effect, however unintentional, of being misleading. I am not accusing you of that, just saying. Further, even an identified slant is cause for concern because the implication is that it is not so substantial as to otherwise tilt the content. No one can really be too sure of that, in the final analysis.

Also, I really cannot hold Bell's own views ahead of others past a point. I often quote Einstein, and it is certainly fair to quote Bell (and I do), but that is not per se authoritative. Einstein was wrong (can't believe I am saying that) about some things, doesn't make him any less great. Bell's views changed somewhat over time, but mostly he was careful to distinguish between things that were and were not his opinion. I value that distinction.


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