A Assumptions of the Bell theorem

[Demystifier]

EPR say ...

Didn't you said in another thread that you don't understand the EPR argument?

 

[vanhees71]

I still can cite the words and underly my own (non-)understanding of their meaning. That's common practice among philosophers to confuse everybody discussing with them.

 

[Demystifier]

I still can cite the words and underly my own (non-)understanding of their meaning. That's common practice among philosophers to confuse everybody discussing with them.

Yes, there is a whole book on such methods.
https://www.amazon.com/dp/1906042012/?tag=pfamazon01-20

 

[PeterDonis]

is it correct to say that one of the assumptions of Bell's theorem is that systems have well defined [single] values for position, prior to measurement.

If you think this is correct, then you should be able to go to Bell's paper and point out where this assumption is made. Can you?

 

[Lynch101]

If you think this is correct, then you should be able to go to Bell's paper and point out where this assumption is made. Can you?

$\lambda$

 

[Lynch101]

No! EPR say all elements of reality must have a counterpart in the physical theory. That doesn't mean that any mathematical element of the theory must have a counterpart in reality. The wave function indeed is not observable and thus has not a counterpart in reality. The probability distribution obviously corresponds to elements of reality, because it can be tested by observations on ensembles of equally prepared systems.

I think this is part of the discussion that is off-topic.

 

[PeterDonis]

$\lambda$

What does that have to do with position? Bell explicitly says in the paper that he makes no assumptions at all about what $\lambda$ represents.

 

[vanhees71]

Positions are for sure not "hidden". It's the first observable we introduce in the first lecture of physics (usually on classical mechanics of course) ;-).

 

[Lynch101]

What does that have to do with position? Bell explicitly says in the paper that he makes no assumptions at all about what $\lambda$ represents.

He also says (emphasise mine),

THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality [2]. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics.

$\lambda$ represents 'hidden variables' of which a'pre-defined value for position' would be an example.

 

[PeterDonis]

$\lambda$ represents 'hidden variables' of which a'pre-defined value for position' would be an example.

An example, yes. But not the only possible example, nor a necessary example; there is nothing in Bell's proof that requires $\lambda$ to contain pre-defined values for position. You appear to be claiming that it does, which is false.

 

[AndreiB]

QFT is local (microcausal) by construction and still predicts correctly the violation of Bell's inequality.

QFT does not postulate its "completness", this is why it can be compatible with relativity. It's just statistics. Once you assume completness you make QFT non-local in the sense that space-like events cause each other.

If I measure particle A and I know that it is entangled with particle B I know what an observer at particle B must get when measuring the corresponding observable which is 100% correlated with the variable that I measured.

If your A measurement does not disturb B it means that the A measurement should let B in the same state (or lack of state if you want) as before. So, if we got UP at A we can conclude that B is DOWN, and it was DOWN even before.

That doesn't imply a spooky action of a distance, but just refers to the correlations described by the entangled state being prepared in the very beginning. My local measurement indeed doesn't do anything to particle B.

As explained above, if:

1. Your local measurement indeed doesn't do anything to particle B, and
2. After your local measurement, B is DOWN

it logically follows that B was DOWN even before your local measurement. And from here we can also conclude that A was UP even before you measured it (since it had to be anticorrelated with B).

 

[Lynch101]

An example, yes. But not the only possible example, nor a necessary example; there is nothing in Bell's proof that requires $\lambda$ to contain pre-defined values for position. You appear to be claiming that it does, which is false.

I think you're drawing an incorrect inference here, as I believe you are in the discussion on position in general.

The assumption of pre-defined values for position is included as an assumption of Bell's Theorem because it is included in $\lambda$. That's why we can draw inferences about pre-defined values for position from violations of Bell's theorem, even though it is not expressly stated as a necessary assumption.

 

[vanhees71]

An example, yes. But not the only possible example, nor a necessary example; there is nothing in Bell's proof that requires $\lambda$ to contain pre-defined values for position. You appear to be claiming that it does, which is false.

Well, as I understand the argument, just taken the math and forgetting about all philosophical quibbles, the idea behind hidden variables is that all the observables of a physical system have definite (determined) values at any time and the probabilistic nature of the quantum predictions are due to our lack of knowledge but not inherent in nature. Thus there must some variable(s), called $\lambda$ by Bell, who also take definite values, and if we'd know their values we'd also know the values of all observables. The probabilities in Bell's proof then have the same meaning as in classical statistical physics, i.e., they are just used to describe the incompleteness of our knowledge. The remarkable result of Bell's analysis then indeed is that this assumption leads to probabilistic predictions about certain correlation functions which are not as predicted by QT, and thus it opened the door to test the assumptions of such a deterministic classical picture against QT.

They key difference is the meaning of the concept of "states": In classical physics a state describes the probabilities for all observables of the system, if we have only incomplete knowledge about the system. Complete knowledge ("pure states") describe a situation where all observables have determined, definite values at any time ("determinism"). Bell's class of models extends this picture by the idea that there might be hidden variables/observables we are not aware of and thus there is an incomplete knowledge due to our inability to know/determine the values of these hidden variables, but otherwise it's just as in classical physics, only that we can't prepare "pure states". Nevertheless this latter concepts leads to a contradiction about the probabilistic outcomes of QT and we can test this "realistic" kind of models against it. It brought the vague EPR quibbles to a clearly defined scienctific question, answerable by objective experiments, and from the first experiments on (historically, I guess that's Aspects experiment, but maybe there were also earlier ones) QT was confirmed.

What's not so clear to me is, where the notion of "locality" is implemented in Bell's HV models. I think it's simply assumed that measurements on far-distant parts of a system are indeed local and if the measurement outcomes are registered in local events (in the sense of the the theory of relativity) are spacelike separated these local measurements cannot causally influence each other. Of course, in our standard local (microcausal) relativistic QFTs this locality assumption is implemented by construction and thus they are compatible with locality also within the theory. Still as any QT also local relativistic QFT allows for the long-ranged correlations between parts of a quantum system that are investigated by far-distant local measurements, and indeed many (if not most) of the Bell tests are done with quantum-optical experiments, which are successfully described by standard QED, which is the paradigmatic example for a local relativistic QFT.

 

[AndreiB]

By determinism + denial of Bell's statistical assumption, do you mean superdeterminism?

Yes.

 

[PeterDonis]

the idea behind hidden variables is that all the observables of a physical system have definite (determined) values at any time

Bell makes no such assumption. The hidden variables do not even have to be observables, and they certainly do not have to contain all possible observables. They just have to contain enough information to determine the results of the measurements being conducted.

 

[vanhees71]

The point is that in Bells local realistic HV models with the hidden variables, which we are not aware of (in this sense they may not be observables), all observables are determined, i.e., they are functions of the hidden variables. This is what's called "realism". The unknown HVs are described as random in the same sense as we describe the observables as random in classical statistical mechanics. This assumption of determinism leads to Bell's inequality and thus a contradiction with the probabilities for the outcome of measurements predicted by QT. See the excerpt from Weinberg's book posted above.

 

[Lynch101]

This assumption of determinism leads to Bell's inequality and thus a contradiction with the probabilities for the outcome of measurements predicted by QT. See the excerpt from Weinberg's book posted above.

Isn't it this contradiction with the predictions of QT that tells us that one of Bell's assumptions must be given up?

 

[vanhees71]

Of course, but as this and other threads in the quantum interpretation forum show, people are unable to agree which one it is and that's why you have as many (or more) interpretations as there are physicists discussing about it. For me it's clear that one has to give up determinism, because locality (i.e., relativistic causality) is realized by local relativistic QFT, which is in accordance with the outcome of the Bell tests.

 

[Lynch101]

Of course, but as this and other threads in the quantum interpretation forum show, people are unable to agree which one it is and that's why you have as many (or more) interpretations as there are physicists discussing about it. For me it's clear that one has to give up determinism, because locality (i.e., relativistic causality) is realized by local relativistic QFT, which is in accordance with the outcome of the Bell tests.

Is QFT a statistical interpretation?

 

[Demystifier]

forgetting about all philosophical quibbles, the idea behind hidden variables is

If one forgets all philosophical quibbles, the idea behind hidden variables is - nothing. Without philosophy, there is no idea at all behind hidden variables. Since you are good in math and natural sciences, you would like if everything that matters could be formulated in terms of math and natural sciences. But unfortunately, many things cannot be formulated so. Since you don't like this fact of life, you try to convince yourself that those things are irrelevant. But they are not. Even you care about some of those things, despite the fact that you would prefer if you didn't care and/or try to convince yourself that you don't care.

 

[vanhees71]

Is QFT a statistical interpretation?

As any QT also QFT is a probabilistic description of Nature.

 

[vanhees71]

If one forgets all philosophical quibbles, the idea behind hidden variables is - nothing. Without philosophy, there is no idea at all behind hidden variables. Since you are good in math and natural sciences, you would like if everything that matters could be formulated in terms of math and natural sciences. But unfortunately, many things cannot be formulated so. Since you don't like this fact of life, you try to convince yourself that those things are irrelevant. But they are not. Even you care about some of those things, despite the fact that you would prefer if you didn't care and/or try to convince yourself that you don't care.

But Bell indeed DID finally formulate the philosophical quibbles in a clear mathematical way (as described in less than half a page in Weinberg's textbook). That's the great merit of his work: To make sense of some philosophical vaguely formulated quibbles by EPR (the vagueness mostly due to P, as Einstein lamented) such that it could be subject to clear quantitative observational tests.

 

[Demystifier]

But Bell indeed DID finally formulate the philosophical quibbles in a clear mathematical way

No, Bell formulated a part of his philosophical quibbles in a clear mathematical way. But the fact that we still argue about what his proof actually proves (for you it's absence of determinism, for me and Bell and Ballentine it's absence of locality, for some it's absence of observer-independent reality, or absence of statistical independence of apparatus settings, or ...) clearly demonstrates that an important part of his philosophical quibbles is not formulated in a clear mathematical way.

 

[vanhees71]

Well yes. The problem is that the disagreement is about philosophy and not about physics. The indication for that is that obviously we still have not a clear agreement on the meaning of the words, particularly locality. For me locality is simply microcausality. For you obviously it has a different meaning. The same holds for "reality", which is even harder to define. For me reality is objective, reproducible observability, i.e., what can be tested by experiments.

 

[Demystifier]

The problem is that the disagreement is about philosophy and not about physics.

Do you know why philosophy never makes progress? Because when it does, it's no longer called philosophy.

Philosophers deal with vague questions not because they are not capable of dealing with clear questions, but because the vague questions are a challenge. The challenge is to translate a vague question into a less vague one. But it's often very hard to make such a translation. It's hard to be a good philosopher, possibly even harder than to be a good scientist.

 

[Lynch101]

Well yes. The problem is that the disagreement is about philosophy and not about physics. The indication for that is that obviously we still have not a clear agreement on the meaning of the words, particularly locality. For me locality is simply microcausality. For you obviously it has a different meaning. The same holds for "reality", which is even harder to define. For me reality is objective, reproducible observability, i.e., what can be tested by experiments.

A word that seems to cause less consternation is the word 'universe' or 'nature'. We can define it as 'that which physics seeks to probe', 'that which physics seeks to describe', 'the subject of investigation of physics', or something along those lines. Even if we strictly define 'physics' as 'reproducible observability' it might be the case that there are limits to how far we can probe nature.

The universe itself is not, or at least does not appear to be, reproducible. To what extent the entirety of the universe is observable is a matter of debate.

 

[gentzen]

we still have not a clear agreement on the meaning of the words, particularly locality. For me locality is simply microcausality. For you obviously it has a different meaning.

Did it ever occur to you that locality might be a normal word present in nearly all human languages, and that this is an indication that its meaning is actually pretty clear? And that microcausality might simply one way in which a theory can be local?

I guess microcausality actually implies that there is no faster than light signaling, but the absence of faster than light signaling all by itself is also a way in which a theory can be local. And since more people are able to grasp that meaning, it might even be used more often than microcausality.

And to go further, there appears to be randomness in Bell type experiments, and that randomness seems to include correlations between spatially separated events. And this is one way in which the predictions of quantum mechanics (that have been confirmed in many experiments) seem to not be local. And therefore many people say that quantum mechanics is nonlocal. Can you accept that this meaning does not contradict microcausality, and that therefore both you are right when you point out that quantum theory satisfies locality, but the many other people who say that quantum mechanics is nonlocal are not wrong either?

But more importantly, did it ever occur to you that this is not the fault of philosophy? Philosophy did not invent the concept of locality, because locality is simply an intuivite concept that has been present in human thinking all along. And it is a totally unproblematic concept, if you ask me!

 

[Lynch101]

the many other people who say that quantum mechanics is nonlocal are not wrong either?

I think there is an important distinction to be made here. From my reading of discussions on here and elsewhere, it seems that those you refer to are not necessarily saying that QM is nonlocal rather that nature is nonlocal (or has some form of nonlocal mechanism).

Again, it seems to be bound up in the issue of 'completeness', since the contention - to my mind - appears to be that statistical interpretations are incomplete descriptions of the system and a more complete description would require either:
- nonlocal causal influence
- superdeterminsm
- anti-realism (in the sense of the system not existing until it is measured)
- [possibly others?]

 

[Lord Jestocost]

And therefore many people say that quantum mechanics is nonlocal.

It's clearly an error in thinking. Murray Gell-Mann puts it in “The Quark and the Jaguar” in the following way:

“The label ‘nonlocal’ applied by some physicists to quantum-mechanical phenomena like the EPRB effect is thus an abuse of language. What they mean is that if interpreted classically in terms of hidden variables, the result would indicate nonlocality, but of course such a classical interpretation is wrong.” [bold by LJ]

One should thus avoid the term “quantum non-locality”. “Quantum non-separability” is the correct term in this context. Quantum non-separabilty is indeed rooted in the way the quantum formalism represents systems and sub-systems. Franck Laloë in “Do We Really Understand Quantum Mechanics?”:

“The idea is that different quantum systems, when they have interacted in the past, no longer have in general their own physical properties; they are both part of a larger system, which is the only one possessing physical properties. One should then not try to separate (conceptually) the whole system into two smaller physical systems and attribute them properties; the whole system is non-separable.”

 

[vanhees71]

Did it ever occur to you that locality might be a normal word present in nearly all human languages, and that this is an indication that its meaning is actually pretty clear? And that microcausality might simply one way in which a theory can be local?

In science we cannot use everyday language but we have to clearly define what we mean. Microcausality for sure is a meaning of locality nobody has in mind when using the word in everyday language.

I guess microcausality actually implies that there is no faster than light signaling, but the absence of faster than light signaling all by itself is also a way in which a theory can be local. And since more people are able to grasp that meaning, it might even be used more often than microcausality.

As I said, you have to define what's meant by locality, because it has not a well-defined meaning. Microcausality is a clear property of relativistic QFTs and thus has a well-defined meaning, and it seems to me the meaning most physicists and textbook writers interpret the meaning in Bell's HV model, though one cannot always be sure, because all too often the meaning is not explicitly defined by the authors.

And to go further, there appears to be randomness in Bell type experiments, and that randomness seems to include correlations between spatially separated events. And this is one way in which the predictions of quantum mechanics (that have been confirmed in many experiments) seem to not be local. And therefore many people say that quantum mechanics is nonlocal. Can you accept that this meaning does not contradict microcausality, and that therefore both you are right when you point out that quantum theory satisfies locality, but the many other people who say that quantum mechanics is nonlocal are not wrong either?

That's cause of a lot of confusion (not only in quantum theory). A statistical correlation does not necessarily imply a causal connection, and that is the case for the correlations of observables on far-distant parts of an entangled quantum system. Einstein introduced the much more precise word "inseparability" for this. Of course, this does not locality (in the sense of microcausality), because it's consistently described by local relativistic QFT. That's why I reserve the word "locality" to mean microcausality and talk about "long-ranged correlations" or "inseparability" rather than (non)locality. Definitions are made to make language as simple and concise as possible and thus one should use different words for different things.

But more importantly, did it ever occur to you that this is not the fault of philosophy? Philosophy did not invent the concept of locality, because locality is simply an intuivite concept that has been present in human thinking all along. And it is a totally unproblematic concept, if you ask me!

Obviously it's totally problematic, because I have to repeatedly make clear what I understand using this word as well as you have to make clear what you understand. It would be better not to use the word anymore within physics, but this is of course impossible, because it's all too well established in the literature, including it's fuzzy meaning.

Again, as particularly quantum theory has taught us, intuitive concepts in human thinking is not a sufficient way to talk about the natural sciences.