Assumptions of the Bell theorem

[Demystifier]

Is a preferred Lorentz frame necessary, or is it more that absolute simultaneity is required?

Absolute simultaneity is what is actually required.

 

[PeterDonis]

I'm saying that the system must be 'somewhere' prior to measurement - a very weak claim.

No, it isn't, it's a strong claim. It includes the claim that "location" (or "position" or whatever you want to call it) is an element of reality for all quantum systems at all times. That is a much stronger claim than just claiming that statistical-type interpretations of QM are incomplete by the EPR criterion. The latter claim says nothing whatever about what, specifically, is missing from statistical-type interpretations; it just says that something is.

 

[Lynch101]

No, it isn't, it's a strong claim. It includes the claim that "location" (or "position" or whatever you want to call it) is an element of reality for all quantum systems at all times. That is a much stronger claim than just claiming that statistical-type interpretations of QM are incomplete by the EPR criterion.

I really don't think the claim is as strong as it appears, particularly when we consider the question that is being asked.

The question is simply, where is the system prior to measurement? Would you agree that, very broadly speaking, there are two possible answers:
1) The system is somewhere.
2) The system is nowhere.

The latter claim says nothing whatever about what, specifically, is missing from statistical-type interpretations; it just says that something is.

The latter claim says that everything is missing. It says that nothing in the mathematics corresponds to the 'elements of reality' of the system. Instead, it says the mathematics tells us what we will observe on measurement devices at the classical level.

 

[PeterDonis]

I really don't think the claim is as strong as it appears, particularly when we consider the question that is being asked.

The question you are asking is itself part of the strong claim--since you must already have established that "location" is an element of reality, for all quantum systems, all the time, in order for the question to make sense.

Would you agree that, very broadly speaking, there are two possible answers:
1) The system is somewhere.
2) The system is nowhere.

Only if your strong claim has already been established. Otherwise the question itself is not well-defined.

The latter claim says that everything is missing.

This rewording does not change any of the points I am making.

 

[Lynch101]

The question you are asking is itself part of the strong claim--since you must already have established that "location" is an element of reality, for all quantum systems, all the time, in order for the question to make sense.

Only if your strong claim has already been established. Otherwise the question itself is not well-defined.

OK, let's take it back a step.

Do you agree that one of the two following propositions must be true:
1) Location is an element of reality of the system, prior to measurement.
2) Location is not an element of reality of the system, prior to measurement.

Do the following make sense:
A) If someone tells you that they have hidden something valuable and if you find it, you can keep it. You ask, where should I look and they tell you, in that field over there. Would that make sense to you?
EDIT: i.e. they tell you that 'it's somewhere in the the field'.

B) If we have two laboratories, one in Paris the other in Rome. Does it make sense to say that, as part of our experiment to test quantum theory, a system was prepared in the lab in Paris?

C) If the system is prepared in the lab in Paris, does it make sense to say that the system is located in the lab in Paris and not in the lab in Rome?

This rewording does not change any of the points I am making.

It does. The claim that every element [of reality of the system] is missing is a stronger claim than a single element of reality is missing. Not only does it say that every element of reality is missing, it says, no matter what element of reality we can think of, it is missing from the theory.

Either way, it establishes the primary claim of EPR, that the QM description of physical reality is incomplete.

 

[PeterDonis]

The claim that every element [of reality of the system] is missing is a stronger claim than a single element of reality is missing.

I didn't say "a single" element of reality. I just said "something" was missing, with the "something" being "elements of reality", which makes no claim whatever about what specifically the missing elements are, or how many elements there are that are missing, or anything else. Saying "every" element of reality is missing is saying the same thing, just in different words.

 

[PeterDonis]

let's take it back a step.

We already have. I've already agreed with the claim that "statistical" interpretations of QM (ones that say the quantum state just gives probabilities for measurement results and doesn't say anything about the actual state of individual systems) are incomplete by the EPR criterion. I don't see the point of belaboring that any further.

Your argument for location being an element of reality for all quantum systems, all the time, seems to boil down to the observation that classical, macroscopic systems (which includes measurement devices) have well-defined locations. This is by no means a new argument in this area, and probably deserves a thread of its own, based on some of the (voluminous) literature on it, if you really want to discuss it further. It is well off of the topic of this thread, since Bell's theorem does not say anything specifically about location as a possible element of reality or hidden variable.

 

[PeterDonis]

Either way, it establishes the primary claim of EPR, that the QM description of physical reality is incomplete.

Only for "statistical" interpretations (as I defined that term in post #742). I've already agreed to that, as I have pointed out.

 

[vanhees71]

And it's not incomplete even for "statistical interpretations" (i.e., the standard or "orthodox" interpretation of QT) if nature "really" is random at the most fundamental level, and I think all the Bell tests quantum theory passed with bravour indicate that this is pretty likely.

It's also pretty clear that, given the atomistic structure of matter, the EPR criterion cannot be right, because you cannot observe something without disturbing it, when it comes to probing the elementary atomistic building blocks. E.g., to the best of our knowledge electric charge of the observable (i.e., asymptotic free) particles come in integer multiples of $e$ (the elementary charge). If you want to measure the electric field of, e.g., an electron (charge $-e$) you have to use another charged particle. To do this "without disturbing" the electron you'd need a particle with a much smaller charge with $|q| \ll e$, but that doesn't exist. So it's the EPR "reality" criterion which is quite "unrealistic" given the fact that matter is atomistic and not QT, which describes all phenomena in accordance with all observations.

 

[Lynch101]

Only for "statistical" interpretations (as I defined that term in post #742). I've already agreed to that, as I have pointed out.

Yes, my apologies, I should have been clearer in my wording.

I didn't say "a single" element of reality. I just said "something" was missing, with the "something" being "elements of reality", which makes no claim whatever about what specifically the missing elements are, or how many elements there are that are missing, or anything else. Saying "every" element of reality is missing is saying the same thing, just in different words.

We already have. I've already agreed with the claim that "statistical" interpretations of QM (ones that say the quantum state just gives probabilities for measurement results and doesn't say anything about the actual state of individual systems) are incomplete by the EPR criterion. I don't see the point of belaboring that any further.

Your argument for location being an element of reality for all quantum systems, all the time, seems to boil down to the observation that classical, macroscopic systems (which includes measurement devices) have well-defined locations. This is by no means a new argument in this area, and probably deserves a thread of its own, based on some of the (voluminous) literature on it, if you really want to discuss it further. It is well off of the topic of this thread, since Bell's theorem does not say anything specifically about location as a possible element of reality or hidden variable.

Good call. I'll start a separate thread, thank you.

Just for the purpose to try and link this back to the topic of this thread, 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. With the violation of Bell's inequality having implications for this assumption?

 

[Lynch101]

And it's not incomplete even for "statistical interpretations" (i.e., the standard or "orthodox" interpretation of QT) if nature "really" is random at the most fundamental level, and I think all the Bell tests quantum theory passed with bravour indicate that this is pretty likely.

It's also pretty clear that, given the atomistic structure of matter, the EPR criterion cannot be right, because you cannot observe something without disturbing it, when it comes to probing the elementary atomistic building blocks. E.g., to the best of our knowledge electric charge of the observable (i.e., asymptotic free) particles come in integer multiples of $e$ (the elementary charge). If you want to measure the electric field of, e.g., an electron (charge $-e$) you have to use another charged particle. To do this "without disturbing" the electron you'd need a particle with a much smaller charge with $|q| \ll e$, but that doesn't exist. So it's the EPR "reality" criterion which is quite "unrealistic" given the fact that matter is atomistic and not QT, which describes all phenomena in accordance with all observations.

The EPR criterion of 'not disturbing the system', in their words, 'far from exhausting all possible ways of recognizing a physical reality'.

The more general claim was that all elements of reality must have a counterpart in the physical theory. Therefore, 'statistical interpretations' would have to say that the wave function or probability distribution corresponds to elements of physical reality.

 

[AndreiB]

...if nature "really" is random at the most fundamental level, and I think all the Bell tests quantum theory passed with bravour indicate that this is pretty likely.

Bell's theorem is designed for local deterministic theories for the simple fact that the local non-deterministic ones were already ruled out by EPR. So, if you accept all Bell's assumptions you need to conclude that physics is non-local. If this is the case, both random and deterministic theories are possible. So, EPR + Bell do not increase the probability that nature is random. On the contrary, determinism is more likely, since it is still possible in its local form if Bell's statistical assumption is denied. Local non-deterministic theories are completely ruled-out since EPR does not use any other assumption besides locality.

It's also pretty clear that, given the atomistic structure of matter, the EPR criterion cannot be right, because you cannot observe something without disturbing it, when it comes to probing the elementary atomistic building blocks. E.g., to the best of our knowledge electric charge of the observable (i.e., asymptotic free) particles come in integer multiples of $e$ (the elementary charge). If you want to measure the electric field of, e.g., an electron (charge $-e$) you have to use another charged particle.

This is not true. In the EPR setup you measure particle A and deduce the state of particle B. B could be arbitrarily far away, hence your measurement of A does not disturb B (at least for the case the measurements are space-like).

 

[vanhees71]

The EPR criterion of 'not disturbing the system', in their words, 'far from exhausting all possible ways of recognizing a physical reality'.

The more general claim was that all elements of reality must have a counterpart in the physical theory. Therefore, 'statistical interpretations' would have to say that the wave function or probability distribution corresponds to elements of physical reality.

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.

 

[vanhees71]

Bell's theorem is designed for local deterministic theories for the simple fact that the local non-deterministic ones were already ruled out by EPR. So, if you accept all Bell's assumptions you need to conclude that physics is non-local. If this is the case, both random and deterministic theories are possible. So, EPR + Bell do not increase the probability that nature is random. On the contrary, determinism is more likely, since it is still possible in its local form if Bell's statistical assumption is denied. Local non-deterministic theories are completely ruled-out since EPR does not use any other assumption besides locality.
This is not true. In the EPR setup you measure particle A and deduce the state of particle B. B could be arbitrarily far away, hence your measurement of A does not disturb B (at least for the case the measurements are space-like).

QFT is local (microcausal) by construction and still predicts correctly the violation of Bell's inequality. So what I have to give up is determinism, not locality, because giving up locality would mean to give up a (if not the) deciding cornerstone of relativistic QFT.

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. 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.

 

[Demystifier]

On the contrary, determinism is more likely, since it is still possible in its local form if Bell's statistical assumption is denied.

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

 

[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.