What do violations of Bell's inequalities tell us about nature?

[audioloop]

I know that it doesn't solve all the problems. But i think splitting the world into "quantum" and "classical" is wrong (but useful for practical purposes).

i agree and just another theory.

 

[stevendaryl]

in response to "we can't trust our senses"
Then it is impossible to base conclusions (like, for example, the conclusion that classical mechanics failed to correctly predict things like the H spectrum and all the other stuff that convinced us to abandon classical mechanics in favor of QM!) on empirical data, period.

The meaning of "we can't trust our senses" isn't that "our senses give us no information about the world", it's just that we can't assume that there is a close relationship between the way things are and the way things appear to our senses.

 

[ttn]

The meaning of "we can't trust our senses" isn't that "our senses give us no information about the world", it's just that we can't assume that there is a close relationship between the way things are and the way things appear to our senses.

Yes, obviously this is a complex issue. Is the white color of the flag intrinsic in the flag, or is it somehow a relational property between the flag and my sensory apparatus, or what? All of these sorts of things are tricky and subtle and probably none of us want to get into them here! My point is just: if you think we can get any useful information at all about the external world from our senses (and I certainly do), then surely this will have to include basic facts like that there is a 3D world full of stuff that moves around and interacts and that includes things like little flag-shaped hunks of material that sometimes pop up and down. My view is that, if you regard that as even-possibly-mistaken, then you are never going to get anything remotely resembling empirical science off the ground; certainly, if such things "might be wrong", then *literally everything we have ever taken as empirical evidence for anything in science ever* "might be wrong", and then, well, we're totally at sea.

 

[rubi]

Hi ttn,

i've read your post completely, but i think it's better to answer in a shorter way instead of considering each of your statements separately. After all, we have both made our points more or less clear. If you want me to address any particular statement more carefully than i will do now, please let me know.

--

First of all, i agree that decoherence hasn't solved the quantum-classical transistion completely and that it's controversial. My main point wasn't to talk about decoherence, but to argue that the individual outcomes aren't more real than the wave function itself if we include them into the quantum picture. That's why aren't part of reality, but an emergent phenomenon, although it isn't yet clear how the mechanism of this emergence works and it's also not clear that quantum mechanics can explain it in the end.

--

Here is how i see the connection between theory and experiment:

Quantum mechanics is a theory that contains the following mathematical entities: A Hilbert space with an inner product, a wave function, which is an element of this Hilbert space and some self-adjoint operators corresponding to observables. That's all. Nothing more and nothing less. In particular, there is no real-valued function $x(t)$. With only these few mathematical entities, you are able to compute probability distributions, mean values, standard deviations, correlations and so on. All these mathematical entities are just strings of symbols on a piece of paper. Let's call this paper "QM axioms". Symbolic manipulation of these strings allows us to compute numbers (which are also strings). For convenience, we will collect all these numbers on a piece of paper called "QM predictions".

Now, an experiment is something more down to the earth. An experimentator has a procedure to prepare his apparatus identically a 1000 times. He can repeat an experiment and write down the strings on his display on another piece of paper called "Experimental outcomes". He can use mathematical methods to compute from these values their statistical properties. We will collect all the statistical properties of the measured values on a 4th piece of paper called "Statistical analysis of the experiment".

The wonder of physics is that the values on the paper "QM predictions" for some reason coincide with the values on the paper "Statistical analysis of the experiment". Notice however that you can't compare the papers "QM axioms" and "Experimental outcomes". We can't use any of the papers "QM axioms" and "QM predictions" to write yet another paper called "More QM predictions" that can be compared to the paper "Experimental outcomes". Notice also that our ability to compare the "QM predictions" paper to the "Statistical analysis of the experiment" paper is independent of the ontological status of the "real world". It's completely independent of realism, non-realism, solipsism or whatever school of philosophy you advocate. It's also independent of whether our senses tell us the truth or not. Everyone has the ability to compare these two papersm, independent of whether the outcomes really exist or whether they are emergent from an arbitrary unknown mechanism.

QM is totally divorced from the experimental side of this whole process. The connection between QM and experiment is solely statistics. The individual outcomes of the experiment can't be associated with any mathematical entity of the theory, because there is no such entity in the axioms list. When you talk about individual outcomes as beables, you really are talking about the experimental side. But Bell said, that beables are elements of the theory. However, the theory claims only to predict some aspects of the numbers you collect in the experiments. In particular, it doesn't claim to predict any of the numbers that are written on the "Experimental outcomes" paper, because there is no mathematical object in the theory that can be associated with these outcomes. They are purely on the experimental side. That's why they aren't beables of the theory.

Yes, QM doesn't have definitely existing tables, cats or flags in the model. But that's not a problem, because a model doesn't need to describe every aspect of the world. If the model chooses to only predict statistics without making any claims about "real objects", then that's fine. You can also have a probability theory that predicts probabilities and mean values about dices or coins without making any statement about the existence of dices or coins and their ontology. The dice-theory could for example be: $p(x) = 1/6$ for $x \in \{1,2,3,4,5,6\}$. It doesn't make any reference to a dice, yet it completely describes the statistics that you will find if you throw the dice a hundred times. It's also agnostic with respect to every aspect of the dice other than it's statistics. It's agnostic with respect to it's color, it's material and even it's existence.

I think i can't explain my point any clearer than this now. I hope you can at least understand my thinking and why i find it appropriate.

 

[ttn]

I think i can't explain my point any clearer than this now. I hope you can at least understand my thinking and why i find it appropriate.

I think I do understand it. For you, QM is *merely* a mathematical algorithm for generating statistical predictions. It is not actually a *physical theory* at all. I'm not sure that's the wrong way to understand "ordinary QM". It wasn't Bohr's way, for sure. But in many respects it is more sensible than Bohr's way -- for example, as I think we agree, Bohr's way (involving the shifty ontological split) is crazy and obviously wrong. However, in another crucial respect, I think Bohr's way is much better. Physics is physics, not math. Surely it must be the end goal always to say what the world is like. So if you have some mathematical statistics-generating algorithm that really truly says *nothing* about the physical world, that is totally inadequate. It may be perfectly useful to have it, but it is not a physical theory and I think any true physicist wants a satisfactory physical theory and won't be satisfied by anything less. Hence the search for theories (like Bohm's theory, GRWm/f, MWI) which actually tell (or, in the case of MWI, at least purport to tell) a coherent story about what the *world* is like physically -- a story which doesn't involve any shifty splits and which, at the end of the day, both produces recognizable macroscopic objects and gets the details right for the statistics of how often they should move this way and that.

 

[ttn]

Tomorrow my regular teaching duties resume, so I won't have time to continue posting on this thread with anything like the frequency of the last week (and perhaps not at all). Thanks to all of you for the stimulating discussion. I learned about a few new things, one of which turned out to be a dud, but I'm still hopeful about this, which I plan to read tomorrow:

http://prl.aps.org/abstract/PRL/v48/i19/p1299_1


Just as one final thought on the original topic of the thread, I hope people who voted for "anti-realism" in the poll will make sure not to miss my post #204 in which I sketch a mathematically rigorous version of the EPR argument *from locality to* what (I think) people who voted "anti-realism" mean by "realism". Clearly, just as a matter of sheer elementary logic, anybody who thinks that we can elude the spectre of nonlocality by denying (this) "realism", has something pretty serious to think about there. I will note also that, despite a couple of half-hearted attempts, nobody rose to the challenge of showing how the perfect correlations (observed in the usual EPR-Bell scenario when a=b) can be explained by a local but non-realist model. From the point of view of the theorem in #204 this is of course not surprising: "realism" (meaning here deterministic non-contextual counterfactually-definite hidden variables) is the *only* way to explain these particular correlations locally. The correlations and the assumption of locality *logically entail* "realism". That is what that little mini-theorem says.

I therefore declare all the votes for "anti-realism" to be void, and hence the correct answer, "non-locality", to be the winner of the poll.

 

[Len M]

Yes, obviously this is a complex issue. Is the white color of the flag intrinsic in the flag, or is it somehow a relational property between the flag and my sensory apparatus, or what? All of these sorts of things are tricky and subtle and probably none of us want to get into them here! My point is just: if you think we can get any useful information at all about the external world from our senses (and I certainly do), then surely this will have to include basic facts like that there is a 3D world full of stuff that moves around and interacts and that includes things like little flag-shaped hunks of material that sometimes pop up and down. My view is that, if you regard that as even-possibly-mistaken, then you are never going to get anything remotely resembling empirical science off the ground; certainly, if such things "might be wrong", then *literally everything we have ever taken as empirical evidence for anything in science ever* "might be wrong", and then, well, we're totally at sea.

I don’t follow this I’m afraid (or perhaps I should tentatively say I don’t agree with it!). Surely, all we have to work with is phenomena, the scientific method involving testability works within this framework and it is that framework that I refer to as empirical reality. This (our) reality of phenomena exists within space and time and involves all the phenomena of mechanisms that cause, as you say, flags to pop up and down and everything else that we experience as phenomena. But, to preempt what I say below, I don't consider that space and time, cause and effect or any other familiar and scientific notions exist in that manner outside of phenomena, i.e within independent reality. As far as I can work out, holding such a view in no way diminishes the power of the scientific method, the models work and often work exceedingly well, it's just that I don't extrapolate those models with their scientific credentials to an area outside of the realm in which they were created and tested, i.e. to the realm of independent reality. There is nothing stopping anyone extrapolating them of course to independent reality, but then they cease to become empirical models (how can an empirical model be valid within an arena that lay outside of empiricism), rather I think they become philosophical conjecture because of the reasons I outline below.

What scientists do is to try and step outside of phenomena and apply their empirically verified models to independent reality and they do so via various flavours of realism. Realist conceptions are composed of two elements. The first consists of the notion of a reality conceived as totally independent of our possible means of knowing it (independent reality) – along with the hypothesis that we do have access to this reality, in the sense that we can say something “true” concerning it. But this hypothesis, is not scientifically provable (which is not to say it is incorrect of course and there are legitimate means in which to assert the theory in terms of the no miracle argument, but there are equally valid counter arguments that can be made). The second of these two elements concerns a representation we build up of independent reality worked out from the phenomena, but since the first element can only be an hypothesis, the second element can obviously not be tested and hence lay outside of the scientific method.

The question as to how close empirical reality is to independent reality is an untestable one, so I tend to stay on the side of caution – a miss is as good as a mile, I can’t see the point of assuming a degree of closeness, as if perhaps we only need to concern ourselves with the mechanistic alteration to the “thing in it’s self” by the characteristics of the eye – that to me seems a bit of a cop out, it restores a comfortable feeling that what lay within independent reality is a rough approximation of phenomena. Such a view can act as a counter to the uncomfortable logic associated with taking on board the notion of our reality as existing only as phenomena, and I would tentatively suggest that this may be the stance you take up, it allows a sense of scientific accessibility to some aspects of independent reality, but as I say, for me a miss is as good as a mile. So I go the whole hog, I don’t presuppose that we can know anything about independent reality using familiar notions and the scientific method, in fact I don’t consider that independent reality is embedded in space and time. But none of this stops me in any manner at all in seeing empirical reality as being entirely valid, it is our reality and it works and I don’t invoke solipsism or idealism here. I consider the notion of an unknowable independent reality to be perfectly adequate in providing the means in which to philosophically envisage empirical reality as an “emergent” (“emergent” in this sense not referring to any familiar notions) entity governed by laws that have their “origin” (“origin” here not referring to any familiar notions) within independent reality rather than being entirely referenced to minds (or a single mind) as per radical idealism or solipsism. Of course the logic of this stance entails giving up the notion of (for example) stars as having an intrinsic historical time line outside of empirical reality, from this perspective there was no birth of the star outside of empirical reality, rather that birth is scientifically explained by us in terms of an hypothetical observer being present all those years ago and along its time line there after, after all, all we have to explain the star is phenomena, so to be consistent I can’t extrapolate that phenomena to an arena within independent reality under the name of science (i.e. to a universe outside of empirical reality) - from this perspective of mine, a scientific model is solely a property of human experience and has to stay that way. So the time line of the star is one that only exists within empirical reality, the star does not have an intrinsic historical time line. So it can be an uncomfortable stance, but it’s one that seems to make a lot of sense to me and separates the proper scientific method (in terms of verified models within empirical reality) from what ever we call the mode of inquiry that attempts to investigate independent reality, given that the relationship between empirical reality (our reality) and independent reality (a reality outside of phenomena) is not a scientific one.

Of course such a standpoint confines science to accounting for empirical reality in terms of human experience rather than being able to explain independent reality. I guess such a standpoint is untenable to you, but for me it seems to be the only way forward in terms of what science seemingly can access. Having said that, I am always keen to see if there are grounds in which the scientific method can be shown to be valid in terms of its remit of testability within an arena of independent reality that by definition cannot include any notion of testability because testability can only be invoked by an observer and phenomena which immediately sets up the testability as occurring within empirical reality. But I guess I have already gone too far from the scope of this thread, I have only done so though to illustrate that there are means in which phenomena by itself can be properly dealt with by the scientific method, albeit in a manner of explaining human experience concerning empirical reality (phenomena) rather than explaining independent reality (outside of phenomena).

These issues are explored very comprehensively within the writings of Bernard d’Espagnat (“Conceptual Foundations of Quantum Mechanics”, “Veiled Reality” and “On Physics and Philosophy”). It is d’Espagnat’s strong and well worked out thesis that invokes a notion of unknowable independent reality in the context of an emergent (“emergent” of course not being associated with familiar terms of cause and effect) empirical reality of phenomena “from” independent reality He refers to this version of realism as Open Realism.
It is largely through his writings that I arrived my particular understanding of issues concerning realism, idealism and empiricism.

Incidentally, d’Espagnat was a close colleague of Bell at Cern, and some of the references you make concerning Bell arise within d’Espagnat’s books when he talks about how he and Bell discussed these issues generally, in fact it was d’Espagnat that instigated the Aspect correlation experiments when he was Professor of Physics at the University of Paris-Orsay. Needless to say they were at opposite ends over the realism debate, but they seemed to be good friends despite that! How I wish that he were following this forum, he perhaps could offer an insight into Bell's thinking that you touch upon so often!

 

[bohm2]

I therefore declare all the votes for "anti-realism" to be void, and hence the correct answer, "non-locality", to be the winner of the poll.

Seems very reasonable to me. By the way, I'm sure everyone appreciates your contribution and detailed posts. Irrespective of the "truth", I always seem to get depressed by reading pro-instrumentalism arguments who seem to consider physics to be the science of meter-readings. Physics in that way would be pretty boring. It kinda of reminds me of behaviourism in the cognitive sciences.

 

[rubi]

I think I do understand it. For you, QM is *merely* a mathematical algorithm for generating statistical predictions. It is not actually a *physical theory* at all. I'm not sure that's the wrong way to understand "ordinary QM".

I think there are several equally valid ways to understand it and my way is just one of them.

Physics is physics, not math. Surely it must be the end goal always to say what the world is like. So if you have some mathematical statistics-generating algorithm that really truly says *nothing* about the physical world, that is totally inadequate.

Physics is always expressed using math and thus every physical law is just a string of symbols, independently of whether it predicts outcomes or just statistics. The theories might differ in how much they say about the physical world, but i think it's wrong to say that statistical predictions say nothing about the physical world. They do say something; they just don't say everything. Newtons law of gravity also holds independently of whether the gravitating object is a point mass or a spherical object with an inhomogeneous radial mass distribution.

It may be perfectly useful to have it, but it is not a physical theory and I think any true physicist wants a satisfactory physical theory and won't be satisfied by anything less. Hence the search for theories (like Bohm's theory, GRWm/f, MWI) which actually tell (or, in the case of MWI, at least purport to tell) a coherent story about what the *world* is like physically -- a story which doesn't involve any shifty splits and which, at the end of the day, both produces recognizable macroscopic objects and gets the details right for the statistics of how often they should move this way and that.

That's a nice goal, but i think a physical theory can never tell us what the world is like. It's always just a model that explains aspects of the world. Some explain more aspects of the world and some explain less. None explain all and if they did, then there would probably be equivalent models with entirely different ontologies, so the models could still not tell us with certainty what the world is like. For example Bohmian mechanics might be more pleasing to you, but it makes exactly the same predictions as ordinary QM (as far as i know), so we can never know which of these is right.

Just as one final thought on the original topic of the thread, I hope people who voted for "anti-realism" in the poll will make sure not to miss my post #204 in which I sketch a mathematically rigorous version of the EPR argument *from locality to* what (I think) people who voted "anti-realism" mean by "realism". Clearly, just as a matter of sheer elementary logic, anybody who thinks that we can elude the spectre of nonlocality by denying (this) "realism", has something pretty serious to think about there. I will note also that, despite a couple of half-hearted attempts, nobody rose to the challenge of showing how the perfect correlations (observed in the usual EPR-Bell scenario when a=b) can be explained by a local but non-realist model. From the point of view of the theorem in #204 this is of course not surprising: "realism" (meaning here deterministic non-contextual counterfactually-definite hidden variables) is the *only* way to explain these particular correlations locally. The correlations and the assumption of locality *logically entail* "realism". That is what that little mini-theorem says.

I therefore declare all the votes for "anti-realism" to be void, and hence the correct answer, "non-locality", to be the winner of the poll.

I think that's not a fair way to end the discussion. After all, you just said that the instrumentalist viewpoint might not be "the wrong way to understand ordinary QM". I think that if you take ordinary (instrumentalist) QM and give beable status to only the statistical properties it predicts (including the correlations), then you can formally check Bell's locality criterion (it's just a formal mathematical criterion that can be formally applied to any theory, independent of whether you classify it as physical or not) and it would turn out that instrumentalist QM obeys it. So instrumentalist QM does classify as a Bell-local, non-realistic model that explains the correlations. So in the end, whether there exists such a theory depends on whether you accept individual outcomes as beables or not. There is no mathematical reason that prevents us from applying the Bell-criterion to a theory, which doesn't have individual outcomes as beables and instead gives this status to statistical properties.




--

In the end, i also want to thank you for the discussion. I've also learned something and i will definitely try on a piece of paper, whether the Bell-locality criterion applied to instrumentalist QM classifies it as local. That would probably be one of the coolest things I've come across in the last months.

 

[ttn]

I think that's not a fair way to end the discussion. After all, you just said that the instrumentalist viewpoint might not be "the wrong way to understand ordinary QM". I think that if you take ordinary (instrumentalist) QM and give beable status to only the statistical properties it predicts (including the correlations), then you can formally check Bell's locality criterion (it's just a formal mathematical criterion that can be formally applied to any theory, independent of whether you classify it as physical or not) and it would turn out that instrumentalist QM obeys it. So instrumentalist QM does classify as a Bell-local, non-realistic model that explains the correlations. So in the end, whether there exists such a theory depends on whether you accept individual outcomes as beables or not. There is no mathematical reason that prevents us from applying the Bell-criterion to a theory, which doesn't have individual outcomes as beables and instead gives this status to statistical properties.




--

In the end, i also want to thank you for the discussion. I've also learned something and i will definitely try on a piece of paper, whether the Bell-locality criterion applied to instrumentalist QM classifies it as local. That would probably be one of the coolest things I've come across in the last months.

Unfortunately, the first thing you'll write down on your paper is "P(A..." and then you'll realize that there's trouble, since "A" here refers to the actual outcome of an experiment -- something you've said isn't part of your instrumentalist version of QM at all. How can the probabilities, attributed by a theory to a certain event, satisfy (or even fail to satisfy) a certain mathematical condition, when according to the theory there is no such event?

Anyway, good luck, and thanks again for the enjoyable discussion.

 

[rubi]

Unfortunately, the first thing you'll write down on your paper is "P(A..." and then you'll realize that there's trouble, since "A" here refers to the actual outcome of an experiment -- something you've said isn't part of your instrumentalist version of QM at all. How can the probabilities, attributed by a theory to a certain event, satisfy (or even fail to satisfy) a certain mathematical condition, when according to the theory there is no such event?

Anyway, good luck, and thanks again for the enjoyable discussion.

The beables are the statistical properties like probability distributions, mean values and so on. I will not start writing down $P(A$, but instead i will write down $P(<A>|...)$ and then check whether the formal criteron is obeyed.

 

[ttn]

The beables are the statistical properties like probability distributions, mean values and so on. I will not start writing down $P(A$, but instead i will write down $P(<A>|...)$ and then check whether the formal criteron is obeyed.

Cool. But please describe this as "Rubi's formulation of locality", not Bell's, when you publish...

 

[rubi]

Cool. But please describe this as "Rubi's formulation of locality", not Bell's, when you publish...

Why? You write in your own paper that for the locality criterion $P(b_1|B_3 b_2) = P(b_1|B_3)$,

$b_i$ refers to the value of some particular beable in space-time region $i$ and $B_i$ refers to a sufficient (for example, a complete) specification of all beables in the relevant region.

So if i choose my beables to be the statistical properties (instead of the outcomes as you do for Copenhagen), then i can formally apply this criterion to the theory, where $b_1 = <A>$ and so on. I'm just using the general definiton and applying it to the special case of instrumentalist QM, where the beables are the statistical properties. This is precisely Bell's formulation of locality applied to the theory of QM with a particular choice of beables. It's not Rubi's formulation.


P.S.: I know that as a convinced Bohmian, you will say: "Nooo, the outcomes must be beables, because the world can't be without outcomes." But for someone who accepts that the world is "nothing but wave function", it is a perfectly valid viewpoint to claim that the beables are the statistical properties.

 

[bohm2]

The question as to how close empirical reality is to independent reality is an untestable one, so I tend to stay on the side of caution – a miss is as good as a mile, I can’t see the point of assuming a degree of closeness, as if perhaps we only need to concern ourselves with the mechanistic alteration to the “thing in it’s self” by the characteristics of the eye – that to me seems a bit of a cop out, it restores a comfortable feeling that what lay within independent reality is a rough approximation of phenomena...

But agreement with everything you wrote is not inconsistent with violation of Bell's implying non-locality. And I personally agree with pretty well everything you wrote.

 

[Len M]

But agreement with everything you wrote is not inconsistent with violation of Bell's implying non-locality. And I personally agree with pretty well everything you wrote.

I only made the post in terms of a very small part of ttn’s overall important contribution to this thread, namely when he said:

My point is just: if you think we can get any useful information at all about the external world from our senses (and I certainly do), then surely this will have to include basic facts like that there is a 3D world full of stuff that moves around and interacts and that includes things like little flag-shaped hunks of material that sometimes pop up and down. My view is that, if you regard that as even-possibly-mistaken, then you are never going to get anything remotely resembling empirical science off the ground; certainly, if such things "might be wrong", then *literally everything we have ever taken as empirical evidence for anything in science ever* "might be wrong", and then, well, we're totally at sea.

As I said in my post, I see nothing at all wrong in simply accepting that science (as an experimental discipline) belongs quite properly within phenomena. ttn seems to me to picking and choosing in an arbitrary manner between science as practiced within empirical reality (in terms of testability) and the extrapolation of those models to an independent reality that cannot (and does not) involve testability, without seemingly keeping track of what he is doing (at least not in a formal transparent manner that identifies the difference between the scientific status of a model in terms of empirical reality and the same model in terms of independent reality). It's easier for me to keep track of the mix between empirical reality and independent reality because I go the whole hog, I confine the scientific method to phenomena and I reserve the realm of independent reality as being unknowable in a scientific sense and having no correspondence to empirical models, but philosophically being free to conjecture about the nature (and importance) of its existence. For a less extreme stance though, it becomes more difficult to keep track, but I think you have to and be quite transparent about it in public because there is no question that a mix is being invoked between the scientific method involving testability and the extrapolation of that model to a realm of independent reality that cannot involve testability.

But ttn then says

if you regard that as even-possibly-mistaken

implying that accepting the possibility that empirical reality (phenomena) is not close to independent (external) reality in some manner spells the end of science in that empirical science may all be “wrong”. I don’t see that at all, empirical science is always going to be “right” within empirical reality (in the sense of mathematical predictive models within their domain of applicability) and for me that fact is one of the most remarkable aspects of the scientific method – Newton’s predictive mathematical model, within its domain of applicability, is going to be valid ten thousand years from now, that for me has got enough solidity to more than compensate for being (as ttn says) “totally at sea” because we can't scientifically prove that empirical models have the same applicability within independent reality.

The extract from ttn seems to be something said from the "heart" with conviction and I wondered whether it had any specific relevance to his science as opposed to his philosophical stance. I guess I’m not going to know for sure now that ttn is back to teaching, but I certainly agree with you when you say

But agreement with everything you wrote is not inconsistent with violation of Bell's implying non-locality

so perhaps that would also be the viewpoint of ttn?

 

[Maui]

Correct me if i am wrong, but the fundamental constituent of reality are not inadequate classical concepts like 'particle' and 'wave', but information. We are not seeing particles, but always seeing information about particles. The brain is not just a simple collection of particles(as Newtonain perspective would dictate), but an(emergent) information processor. At the rock bottom of things, we are not seeing tables and chairs but information about tables and chairs and being such, information has no obligation to be material-like, corpusular-like ot classical-like. While there could be a stunning correspondence between tables and our sensation of tables, we should not overlook the simple fact that we only have access to the information about tables, not the tables themselves. Tthe ultimate nature of tables is not accessible, hence it is not a valid scientific question. I totally agree with Bohr, it's only what we can say about Nature, not what or how Nature is. It's surprizing that we have as good models of reality as we do, even if they fail to makes sense at certain scales.

 

[Len M]

Correct me if i am wrong, but the fundamental constituent of reality are not inadequate classical concepts like 'particle' and 'wave', but information. We are not seeing particles, but always seeing information about particles. The brain is not just a simple collection of particles(as Newtonain perspective would dictate), but an(emergent) information processor. At the rock bottom of things, we are not seeing tables and chairs but information about tables and chairs. While there could be a stunning correspondence between tables and our sensation of tables, we should not overlook the simple fact that we only have access to the information about tables, not the tables themselves. Tthe ultimate nature of tables is not accessible, hence it is not a valid scientific question. I totally agree with Bohr, it's only what we can say about Nature, not what or how Nature is.

Yes I think I would agree very much with what you say in that you seem to be placing phenomena as the only entity in which we have access to and it is within that framework that we use the scientific method with spectacular success - why should we ask any more of such a successful method in wanting it to be applicable in the same manner to a realm outside of phenomena where the very essence of the scientific method, namely testability cannot be carried out?

My only difference perhaps would be that I do see a need for "something" outside of phenomena from which empirical reality "emerges" (in an unknowable manner) otherwise we have to adopt solipism or radical idealism. I think the consistencies we all observe as phenomena (and agree on) depend on something other than ourselves, so in this sense I am a realist, it's just that I don't see that we can access my "something" that "exists" within independent reality (i.e outside of phenomena) in any scientific sense (at least not as I understand the scientific method in terms of the method requiring a notion of testability).

 

[stevendaryl]

As I said in my post, I see nothing at all wrong in simply accepting that science (as an experimental discipline) belongs quite properly within phenomena. ttn seems to me to picking and choosing in an arbitrary manner between science as practiced within empirical reality (in terms of testability) and the extrapolation of those models to an independent reality that cannot (and does not) involve testability, without seemingly keeping track of what he is doing...

I think there is a contrast between applied science, the basic research that underlies technology, and pure science, which I think has some kind of understanding as the goal. When you're trying to build a better bridge, or better electronics, or whatever, there really is a sense that you don't need to understand anything, you just need to know reliable rules of the form "In situation S, if you do X, you'll get result Y with probability Z". By this practical criterion for science, there is nothing wrong with describing the orbits of the planets or the energy levels of hydrogen, or the relationship between velocity and kinetic energy as an infinite series, all of whose coefficients are empirically determined. So the Ptolemy scheme for describing planetary motion, with its spheres within spheres within spheres, is really perfectly fine, and Balmer's formula for computing energy levels is perfectly fine. Explaining the null results of the Michelson-Morley experiment by an ad hoc velocity-dependent length contraction and time dilation is perfectly. There is no practical need for fundamental theories, at all.

But there is another kind of science that considers the job not to be done when you have a formula that empirically works pretty well. Some kinds of people are bugged by arbitrariness, by lots of parameters whose values seem meaningless. They prefer to try to understand how those successful formulas come about, why the parameters are what they are. They would like an understanding of the principles involved. Even though we may never experience gravity billions of times stronger than on the Earth, they want to be able to have an idea of what things would be like in those circumstances.

It's really hard to make a decisive partition of science into what's practical and what's pure, because a lot of science that was once considered a matter of intellectual curiosity ended up having practical applications. However, I think that the divorce between practical physics and pure physics has happened, and many of the new discoveries and ideas since maybe the 60s (quantum chromodynamics, supersymmetry, loop quantum gravity, string theory, Hawking radiation, the holographic principle, quark theory, etc.) will likely have no practical applications for decades, if ever.

So to me, it's pretty weird to talk about fundamental physics in purely instrumental terms: All we care about is a way of calculating probabilities for the outcomes of experiments. WHY? Why do you care about a way of calculating probabilities for the outcomes of experiments? If the experiment takes a multi-billion dollar collider to take place, then who cares? Knowing the answer has no practical purpose, it seems to me. If all you care about is the pragmatics of predicting what happens when we perform specific experiments, then fundamental physics is over, it seems to me.

 

[harrylin]

[..] If all you care about is the pragmatics of predicting what happens when we perform specific experiments, then fundamental physics is over, it seems to me.

I agree; regretfully that was the paradigm for the last century, it seems.

 

[DrChinese]

Why? You write in your own paper that for the locality criterion ...

Travis channels Bell. So he can present anything as being what Bell says, and you cannot.

 

[bohm2]

so perhaps that would also be the viewpoint of ttn?

That's a good question and I'm not sure? But my gut hunch is that ttn would not agree with the Kantian and/or epistemic structural realist position that I think both you (if I'm understanding you) and myself seem to subscibe to but who knows?

 

[bohm2]

While many of these have been mentioned on various threads/posts I thought I'd post a list of the major papers I've come across arguing that violations of Bell's inequality implies non-locality, irrespective of any other issues (e.g. realism, determinism, hidden variables, pre-existent properties, etc.):

Bertlmann’s socks and the nature of reality
http://cds.cern.ch/record/142461/files/198009299.pdf

J.S. Bell’s Concept of Local Causality
http://chaos.swarthmore.edu/courses/Physics113_2012/002.pdf

Local Causality and Completeness: Bell vs. Jarrett
http://lanl.arxiv.org/PS_cache/arxiv/pdf/0808/0808.2178v1.pdf

Non-Local Realistic Theories and the Scope of the Bell Theorem
http://arxiv.org/ftp/arxiv/papers/0811/0811.2862.pdf

The uninvited guest: ‘local realism’ and the Bell theorem
http://philsci-archive.pitt.edu/5258/1/The_uninvited_guest__'local_realism'_and_the_Bell_theorem.pdf

A Criticism of the article "An experimental test of non-local realism"
http://arxiv.org/abs/0809.4000

John Bell and Bell's Theorem
http://www.mathematik.uni-muenchen.de/~bohmmech/rt/bbt.pdf

What Bell proved: A reply to Blaylock
http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/Bell_EPR-2.pdf

Not throwing out the baby with the bathwater: Bell’s condition of local causality mathematically ‘sharp and clean’
http://mpseevinck.ruhosting.nl/seevinck/Bell_LC_final_Seevinck_corrected.pdf

Can quantum theory and special relativity peacefully coexist?
http://mpseevinck.ruhosting.nl/seevinck/Polkinghorne_white_paper_Seevinck_Revised3.pdf

What is the meaning of the wave function?
http://www.fyma.ucl.ac.be/files/meaningWF.pdf

The Message of the Quantum?
http://www.maphy.uni-tuebingen.de/members/rotu/papers/zei.pdf

Was Einstein Wrong? A Quantum Threat to Special Relativity
http://www.stealthskater.com/Documents/Quantum_01.pdf

 

[morrobay]

For a counterweight to above :
www.iisc.ernet.in/currsci/jul252000/UNNIKRISHNAN.pdf

 

[rubi]

While many of these have been mentioned on various threads/posts I thought I'd post a list of the major papers I've come across arguing that violations of Bell's inequality implies non-locality, irrespective of any other issues (e.g. realism, determinism, hidden variables, pre-existent properties, etc.): ...

Unfortunately, all these papers include the hidden assumption that individual experimental outcomes correspond to some element of the theory of quantum mechanics. They either fail to understand the difference between values that come from the theory and values that are determined by experiment or they secretly use a non-standard theory of quantum mechanics (standard QM supplemented by a mechanism that can in principle predict individual outcomes; everyone knows that this is not the case in the standard theory) and claim it would be the standard theory.

Bell's criterion actually does capture our intuitive understanding of locality after all. You can for example apply it straightforwardly to any classical theory and it captures what we would consider locality of a classical theory. However, these papers apply it to a quantum theory without acknowledging that fact that the quantum theory isn't a classical theory anymore doesn't have something like trajectories of observables anymore (unlike for example Bohmian mechanics) and thus you can't check the criterion for them. You have to check it for the variables of of the quantum theory (or better: a subclass of them, called the "beables") instead. The word "beable" is assigned to those elements of the theory that correspond to what the theory claims to be physically real. In a classical theory or in Bohmian mechanics, the beables would be things like position. Standard quantum mechanics is basically a theory that describes the evolution of probability, so you would choose the beables to be the probability distributions. Notice that even if you wanted to, you couldn't choose position as a beable, because it isn't an element of the standard theory at all. Locality is a property of a theory, so you must apply the criterion to the theory alone without any supplements. So in the end, Bell's locality criterion is actually really good, but applied in a wrong way. It's just that all the generality and terminology involved makes it quite hard to understand what's wrong with the argument.

So what these papers actually prove is that if your theory assumes reality, which means that it does account for the individual outcomes of the experiment, then you can prove that it must be non-local. You can read the proof in ttn's post #204. However, you must note that this proof only holds if your theory really accounts for the outcomes. So the reality assumption ("the theory does account for individual outcomes") implies Bell-non-locality. If your theory is non-real ("it doesn't account for the individual outcomes of the experiment"), then it is still open, whether the it is local or non-local.

If you take standard QM serioursly (that means you accept that it doesn't account for individual outcomes), then Bell's locality criterion actually implies locality, whenever the no communication theorem holds.

 

[bohm2]

Standard quantum mechanics is basically a theory that describes the evolution of probability, so you would choose the beables to be the probability distributions.

Probability of "what"?

 

[rubi]

Probability of "what"?

The probability to measure a given value for an observable, just as every standard textbook says. But the value itself isn't included in QM, only it's probability distribution. There is no prediction about concrete values. QM just says that the statistics of the measurement is given by the probability distribution. There is no underlying "real" observable that has a particular value.

To say it as briefly as possible: These above papers prove that if a theory can account for the individual outcomes of the experiment, then it must be non-local. Standard QM doesn't do it, so it can be a local theory.

 

[bohm2]

The probability to measure a given value for an observable, just as every standard textbook says. But the value itself isn't included in QM, only it's probability distribution. There is no prediction about concrete values. QM just says that the statistics of the measurement is given by the probability distribution. There is no underlying "real" observable that has a particular value.

Observable of what? If I'm understanding you (I may not be) this has been considered:

Muller (1999) stresses that no space-time formulation of quantum mechanics is as of yet available—thus it can not be regarded a spacetime theory—, and that it is a hard job to formulate one, be it in Minkovskian or Galilean spacetime. However, despite being true, this is not relevant for the problem here. All that is needed to consider the question of local causality are predictions for measurement outcomes at certain space-time locations as in Fig. 3 (see Appendix), and quantum mechanics does give such predictions when the measurements and the state to be measured are specified. It does not matter that the theory itself cannot be taken to be a spacetime theory on some appropriate differentiable manifold.

Can quantum theory and special relativity peacefully coexist?
http://mpseevinck.ruhosting.nl/seevinck/Polkinghorne_white_paper_Seevinck_Revised3.pdf

 

[rubi]

Observable of what? If I'm understanding you (I may not be) this has been considered: ...

An observable like position or spin. That above paper also uses the individual outcomes as input for Bell's criterion and thus the same argument applies.

(By the way, he is even wrong with the statement that relativistic QFT presupposes locality. In fact, it is a framework that provides some general theorems under the assumption of locality. Whether a concrete theory satisfies it or not always has to be checked.)

 

[bohm2]

To say it as briefly as possible: These above papers prove that if a theory can account for the individual outcomes of the experiment, then it must be non-local. Standard QM doesn't do it, so it can be a local theory.

What is your definition of locality?

 

[rubi]

What is your definition of locality?

The Bell local causality condition $P(b_1 |B_3 b_2) = P(b_1 | B_3)$, where $b_i, B_i$ are beables / sets of beables in some regions of spacetime (if you want to know which regions of spacetime, see for example ttn's paper "J. S. Bell's concept of local causality", there's a picture).

 

[bohm2]

Relational BlockWorld is local. I consider it non-realistic.

How about this model? One of the papers just came out today. The author argues that it is local and makes all the predictions of QM:

But, by combining Richard Feynman’s formulation of quantum mechanics with a model of particle interaction described by David Deutsch, we develop a system (the “space of all paths,”- SP) that (1) is immediately seen to replicate the predictions of quantum mechanics, has a single outcome for each quantum event (unlike MWI on which it is partly based), and (3) contains the set λ of hidden variables consisting of all possible paths from the source to the detectors on each side of the two-particle experiment. However, the set λ is nonmeasurable, and therefore the above equation is meaningless in SP. Moreover, using another simple mathematical expression (based on the exponentiated-action over a path) as an alternative to the above equation, we show in a straightforward argument that SP is a local system.

Failure Of The Bell Locality Condition Over A Space Of Ideal Particles And Their Paths
http://lanl.arxiv.org/ftp/arxiv/papers/1302/1302.5418.pdf

Bell inequalities and hidden variables over all possible paths in a quantum system
http://lanl.arxiv.org/ftp/arxiv/papers/1207/1207.6352.pdf

The Space of all paths for a quantum system: Revisiting EPR and BEll's Theorem
http://lanl.arxiv.org/ftp/arxiv/papers/1109/1109.6049.pdf

What is interesting is the author's argument is similar to rubi's, I think (?), but he arrives at it using a different model:

The interesting thing, though, is that all proofs of Bell’s theorem (his original arguments and those by others in the same vein) for two entangled particles involve a probability distribution. This means that there is indeed a hidden premise, a tacitly assumed “X”—namely, that the underlying space for a quantum system is measurable. In other words, if we choose “X” to be “measurable” then in Maudlin’s formula we have the proposition, “No local, measurable theory can make The Predictions for the results of experiments carried out very far apart.” We consider Bell’s simple proof of this specific proposition (that is, when “measurable” is substituted for X) to be obviously valid.

 

[stevendaryl]

How about this model? One of the papers just came out today. The author argues that it is local and makes all the predictions of QM:

Failure Of The Bell Locality Condition Over A Space Of Ideal Particles And Their Paths
http://lanl.arxiv.org/ftp/arxiv/papers/1302/1302.5418.pdf

Bell inequalities and hidden variables over all possible paths in a quantum system
http://lanl.arxiv.org/ftp/arxiv/papers/1207/1207.6352.pdf

The Space of all paths for a quantum system: Revisiting EPR and BEll's Theorem
http://lanl.arxiv.org/ftp/arxiv/papers/1109/1109.6049.pdf

What is interesting is the author's argument is similar to rubi's, I think (?), but he arrives at it using a different model:

Thanks for these references. They are fascinating, and very exciting. However, in
"Bell Inequalities And Hidden Variables Over All Possible Paths In A Quantum System" (http://lanl.arxiv.org/ftp/arxiv/papers/1207/1207.6352.pdf), the author says something false, which already came up in this thread:

It seems surprising that no one until now has noticed the hidden premise of measurability in Bell’s definition of locality

As I pointed out, Pitowky and others came up with counterexamples to Bell's Theorem that exploited nomeasurability of the space of hidden variables. Pitowsky's model was very ad hoc, and Leffler's model seems much more natural and physically meaningful, but it's false to say that nobody had looked at nonmeasurability before.

 

[rubi]

What is interesting is the author's argument is similar to rubi's, I think (?), but he arrives at it using a different model:

The problems with measurability that i mentioned earlier don't apply to the argumentation of ttn, because Bell locality doesn't require something like a translation-invariant measure on the space of wave-functions. It's only needed if you want to rule out all theories with huge hidden-variable spaces using Bell's theorem. That's why the counterexamples stevendaryl mentioned can work.

My latter argument doesn't require any fancy math. I just argue that standard QM doesn't account for individual outcomes of measurements an thus they can't be beables of the theory. Ttn's proof (post #204) of non-locality however requires individual outcomes to be beables and thus it can't be applied to standard QM in this way. The beables are the probability distributions instead and if you apply Bell's condition to them, it reduces to the statement of the no communication theorem, so the theory is Bell local whenever the no communication theorem holds.

 

[stevendaryl]

The problems with measurability that i mentioned earlier don't apply to the argumentation of ttn, because Bell locality doesn't require something like a translation-invariant measure on the space of wave-functions. It's only needed if you want to rule out all theories with huge hidden-variable spaces using Bell's theorem. That's why the counterexamples stevendaryl mentioned can work.

I have to say, though, that there is something philosophically screwy about nonmeasurable sets when you try to apply them to the real world.

Here's a very weird example: Suppose we have a game in which two people, Alice and Bob, generate random real numbers in the set $\lbrace x\ \vert\ 0 \leq x \leq 1 \rbrace$. (Imagine spinning a dial, and taking the resulting angle, divided by $2 \pi$.) Beforehand, we pick a total ordering on the reals $x \succ y$ (not the usual ordering). If Alice's number is $a$ and Bob's number is $b$, then Alice wins if $a \succ b$. Otherwise, Bob wins.

Suppose that our two players are Alice and Bob. Alice generates her real, $a$, and looks at it, but doesn't tell Bob what it is. Based on the value of her real, she is allowed to place a wager on the game. She notices the following fact:

There are only countably many values $b$ that would beat her number $a$.
​

She reasons that the probability of Bob generating a real number that lies in any countable set is rigorously zero. So almost certainly (with probability 100%), Alice will win the game. So she's justified in betting her life savings on the outcome.

However, Bob takes a look at his real, $b$ and sees that there are only countably many values for $a$ that would beat it. So, similarly, Bob is justified in betting his life savings on the outcome of the game.

Obviously, someone is not only wrong, but in a sense is infinitely wrong. The outcome that seemed almost certain didn't happen for one of them. Well, that's the breaks, sometimes things of measure zero happen. But they certainly shouldn't happen very often.

Well, it is mathematically possible to construct a total ordering $\succ$ on reals so that absolutely every round of the game, either Alice or Bob will experience something of probability zero happening. That is, we can arrange it so that for $every$ real $x$, there are only countably many values of $y$ that would beat it.

Pitowsky's model uses exactly the same type of construction as the one that would produce the total ordering $\succ$. So there is something a little unsettling about it. For probabilities to behave the way we think they should, we need for things of probability zero to never happen (or practically never). But in Pitowsky's construction, there are events of probability zero that happen every single time.

 

[DrChinese]

While many of these have been mentioned on various threads/posts I thought I'd post a list of the major papers I've come across arguing that violations of Bell's inequality implies non-locality, irrespective of any other issues (e.g. realism, determinism, hidden variables, pre-existent properties, etc.):

Bertlmann’s socks and the nature of reality
http://cds.cern.ch/record/142461/files/198009299.pdf

...

As rubi and morrobay point out, there are papers that come out the other way on the subject. I.e. that violations of Bell Inequalities indicate it is local non-realism that should be selected. Here is once example:

http://arxiv.org/abs/0909.0015

Abstract:

"It is briefly demonstrated that Gisin's so-called 'locality' assumption [arXiv:0901.4255] is in fact equivalent to the existence of a local deterministic model. Thus, despite Gisin's suggestions to the contrary, 'local realism' in the sense of Bell is built into his argument from the very beginning. His 'locality' assumption may more appropriately be labelled 'separability'. It is further noted that the increasingly popular term 'quantum nonlocality' is not only misleading, but tends to obscure the important distinction between no-signalling and separability. In particular, 'local non-realism' remains firmly in place as a hard option for interpreting Bell inequality violations. Other options are briefly speculated on. "