Classicality in Bell's original reasoning

[A. Neumaier]

This so called "classicality" is inferred (not assumed) from locality and prediction of perfect correlations.

Please give a reference to Bell's original papers (if possible in a free online version) that demonstrates this, so that we can discuss it.

 

[A. Neumaier]

Where does it shows in the arguments of Norsen?

From what you had quoted: ''what you actually mean by “classicality”, when we hold hands and look at the mathematical derivations (of the inequality) that you undoubtedly have in mind, is nothing but the idea of deterministic hidden variables. But then it is immediately obvious that you cannot “save locality” by abandoning these hidden variables: having the hidden variables was the *only way* to account for the perfect correlations (when Alice and Bob both measure along z) without nonlocality!''

First you can see a clear instance of mind reading, and second, he takes his position absolute by talking about the *only way*, closing the eyes to something obvious to Werner: The fact that analysing the situation in terms of hidden variables is already assuming classicality and hence the result is determined by the assumption, not by the argument.

 

[zonde]

Please give a reference to Bell's original papers (if possible in a free online version) that demonstrates this, so that we can discuss it.

Here www.drchinese.com/David/Bell_Compact.pdf right after stating assumption of locality:

Since we can predict in advance the result of measuring any chosen component of $\vec{\sigma}_{2}$, by previously measuring the same component of $\vec{\sigma}_{1}$, it follows that the result of any such measurement must actually be predetermined.

 

[zonde]

second, he takes his position absolute by talking about the *only way*, closing the eyes to something obvious to Werner: The fact that analysing the situation in terms of hidden variables is already assuming classicality and hence the result is determined by the assumption, not by the argument.

Assumption is that there is physical model that can explain results of measurements that show perfect correlations. There is no assumption of hidden variables per se.

 

[A. Neumaier]

''This'' was supposed to be the statement

This so called "classicality" is inferred (not assumed) from locality and prediction of perfect correlations.

upon which I responded in the old thread.

Here www.drchinese.com/David/Bell_Compact.pdf right after stating assumption of locality:

I don't see why classicality (in the sense used by Norsen, i.e., as the existence of hidden variables) follows from the sentence you quoted. In fact, the sentence itself (''it follows that the result of any such measurement must actually be predetermined'') is based on a fallacy.

One cannot predict anything before one knows what has been measured when testing the component of sigma_1. And knowing this ''in advance'' means being at the place where this measurement has been performed. Hence assuming locality one cannot know whether the other spin has been measured (maybe the particle carrying it had an encounter with a stray particle from the environment), so one only knows a hypothetical thing ''if the second spin were measured then the result would be the opposite of what was found measuring spin 1''. This is very different knowledge. Ensuring that nothing can possibly interfere with a pre-scheduled measurement puts so much prior classical correlation into the environment that the argument based on the independence of the measurement devices becomes very unconvincing. Nothing is predetermined until the moment the measurement is actually made. Only then the value is fixed, at the value predicted by quantum theory.

Even when the prediction comes out correctly (namely in the case a measurement was indeed made), nothing allows one to infer that the cause were hidden variables, or in Bell's words, ''this predetermination implies the possibility of a more complete specification of the state''. This is a claim, not something proved.

I see not the slightest evidence for the validity of this claim. Instead of proving the claim, Bell goes on to assume hidden variables, i.e., classicality. The hidden variables did nowhere enter the argument so far - they are pulled out of the magician's hat, producing a rabbit from an empty hat by diverting the audience's attention to elsewhere.

 

[rubi]

Let me explain quickly, where the the classicality assumption is made in the proof of Bell's theorem. For any four random variables $A, B, C, D:\Lambda\rightarrow\{-1,1\}$, we have the inequality
$$\left|A(C+D)+B(C-D)\right|\leq 2 \text{.}$$
We can then easily derive an inequality between the correlations of these random variables.
$$\left|\left<AC\right>+\left<AD\right>+\left<BC\right>-\left<BD\right>\right|\leq 2 \text{.}$$
We see that this inequality holds whenever we have four such random variables. If we now put $A=A_\alpha$, $B=A_{\alpha^\prime}$, $C=B_\beta$ and $D=B_{\beta^\prime}$, we get the CHSH inequality
$$\left|\left<A_\alpha B_\beta\right>+\left<A_\alpha B_{\beta^\prime}\right>+\left<A_{\alpha^\prime}B_\beta\right>-\left<A_{\alpha^\prime}B_{\beta^\prime}\right>\right|\leq 2 \text{.}$$
This is possible, because we have used exactly four random variables to derive it. One way to violate it is by introducing non-locality, such that we have $8$ combinations $A_{\alpha\beta}$, $A_{\alpha^\prime \beta}$, $B_{\alpha\beta}$, $\ldots$ instead of just $4$. Obviously, the derivation of the CHSH inequality is blocked this way and hence non-locality allows for a violation of the CHSH inequality.

Of course, there is also another way to violate the inequality by noting that in QM, you can never measure $A_\alpha$ and $A_{\alpha^\prime}$ simultaneously, because they correspond to incompatible observables (this is often discussed under the name counterfactual definiteness). Thus we need to introduce a dependence on the measurement context, i.e. we have observables $A_\alpha^{\chi_1}$, $A_\alpha^{\chi_2}$, $\ldots$ and so on. Again, we get more than $4$ random variables and hence the derivation of the CHSH inequality is blocked. Furthermore, we know from the Kochen-Specker theorem that such a contextuality is absolutely required if you want to reproduce the predictions of quantum mechanics in a classical description and hence, if you don't make your observables context dependent, you are excluding quantum theory right from the start, before you even state the locality assumptions $A_{\alpha\beta}^{\chi}=A_{\alpha}^{\chi}$. Proofs exist that the way quantum mechanics violates Bell's inequality, is of this sort and that the quantum way of violating the inequality is completely compatible with the EPR criterion, contrary to what zonde wants to make you believe.

You can only derive the CHSH inequality if you require both counterfactual definiteness $A_{\alpha\beta}^\chi = A_{\alpha\beta}$ and locality $A_{\alpha\beta} = A_\alpha$.

 

[zonde]

One cannot predict anything before one knows what has been measured when testing the component of sigma_1. And knowing this ''in advance'' means being at the place where this measurement has been performed. Hence assuming locality one cannot know whether the other spin has been measured (maybe the particle carrying it had an encounter with a stray particle from the environment), so one only knows a hypothetical thing ''if the second spin were measured then the result would be the opposite of what was found measuring spin 1''. This is very different knowledge. Ensuring that nothing can possibly interfere with a pre-scheduled measurement puts so much prior classical correlation into the environment that the argument based on the independence of the measurement devices becomes very unconvincing. Nothing is predetermined until the moment the measurement is actually made.

We can not predict reality to every detail. But this is not the goal of physics theory. Goal of physics theory is much more modest: given conditions of event (excluding some unexpected external conditions that we are not trying to predict) what will happen (what we will measure).
Basically statement ''if the second spin were measured then the result would be the opposite of what was found measuring spin 1'' is exactly the kind of prediction that physics theory can make.

Even when the prediction comes out correctly (namely in the case a measurement was indeed made), nothing allows one to infer that the cause were hidden variables, or in Bell's words, ''this predetermination implies the possibility of a more complete specification of the state''. This is a claim, not something proved.

Hidden variables is not the cause. Variables is description of cause in a quantitative form.

Look, there is very general assumption in physics. If two events correlate then they are either causally connected or they are connected by common cause or this is coincidence.
1. Causal connection in this context would mean FTL influence.
2. Connection by common cause means predetermination. Predetermination in mathematical form is described using variables.
3. We assume that possibility of coincidence can be reduced by making many repetitions of the test.

Do you see any other option?

 

[A. Neumaier]

Do you see any other option?

Our views of what constitutes good foundations are too different to have a productive discussion.

We can not predict reality to every detail. But this is not the goal of physics theory.

But it should be possible in principle, and this is what counts in foundations. In practice, there is no measurement problem, so our discussion is moot from the point of view of what you see as the goals of physics.

 

[RockyMarciano]

Look, there is very general assumption in physics. If two events correlate then they are either causally connected or they are connected by common cause or this is coincidence.
1. Causal connection in this context would mean FTL influence.
2. Connection by common cause means predetermination. Predetermination in mathematical form is described using variables.
3. We assume that possibility of coincidence can be reduced by making many repetitions of the test.

Do you see any other option?

Sure, what experiments show when one rejects observation of effects without causes, non-classicality in the form of quantum field theory predictions. When you say that correlation due to causal connection means FTL influence you are only taking into account classical correlations which are not the ones predicted by quantum theory. Quantum correlations respect microcausality and therefore are incompatible with any acausal result of any observation/measurement.

 

[RockyMarciano]

Of course, there is also another way to violate the inequality by noting that in QM, you can never measure $A_\alpha$ and $A_{\alpha^\prime}$ simultaneously, because they correspond to incompatible observables (this is often discussed under the name counterfactual definiteness). Thus we need to introduce a dependence on the measurement context, i.e. we have observables $A_\alpha^{\chi_1}$ and so on. Again, we get more than $4$ random variables and hence the derivation of the CHSH inequality is blocked. Furthermore, we know from the Kochen-Specker theorem that such a contextuality is absolutely required if you want to reproduce the predictions of quantum mechanics in a classical description and hence, if you don't make your observables context dependent, you are excluding quantum theory right from the start, before you even state the locality assumptions $A_{\alpha\beta}^{\chi}=A_{\alpha}^{\chi}$. Proofs exist that the way quantum mechanics violates Bell's inequality, is of this sort and that the quantum way of violating the inequality is completely compatible with the EPR criterion, contrary to what zonde wants to make you believe.

You can only derive the CHSH inequality if you require both counterfactual definiteness $A_{\alpha\beta}^\chi = A_{\alpha\beta}$ and locality $A_{\alpha\beta} = A_\alpha$.

But then you seem to be holding on to classicality, while not dropping locality. That is not possible according to the BI violations.

 

[rubi]

Sure, what experiments show when one rejects observation of effects without causes, non-classicality in the form of quantum field theory predictions. When you say that correlation due to causal connection means FTL influence you are only taking into account classical correlations which are not the ones predicted by quantum theory. Quantum correlations respect microcausality and therefore are incompatible with any acausal result of any observation/measurement.

QFT has nothing to do with this. Bell's theorem is a mathematical theorem with certain assumptions and this thread is about what those assumptions are. zonde claims that the only assumption is locality, but of course, it is generally accepted and also easy to see that this is false. The microcausality assumption in QFT is completely unrelated.

But then you seem to be holding on to classicality, while not dropping locality. That is not possible according to the BI violations.

No. By classicality I mean the counterfactual definiteness assumption $X_{\alpha\beta}^\chi=X_{\alpha\beta}$ that I have explained. This assumption is provably violated by quantum mechanics. If you don't assume that, the derivation of the inequality is blocked, because you have more than four observables that you need to fill in the $A,B,C,D$ slots in my post. If you think you can prove the inequality in the presence of the $\chi$ index, then please post your proof.

 

[zonde]

Sure, what experiments show when one rejects observation of effects without causes, non-classicality in the form of quantum field theory predictions.

Where do you find non-classicality (whatever that means) in QFT predictions?

When you say that correlation due to causal connection means FTL influence you are only taking into account classical correlations which are not the ones predicted by quantum theory.

No, I mean that (direct) causal connection between spacelike separated events is FTL causality.

Quantum correlations respect microcausality and therefore are incompatible with any acausal result of any observation/measurement.

QFT description of entangled particles is basically the same as in NRQM. So I don't understand your point of bringing into discussion microcausality.

 

[Boing3000]

If two events correlate then they are either causally connected or they are connected by common cause or this is coincidence.

The third option you keep missing: non locality. Those two events are sharing the same "variable", they are not "connected", because a connection requires two end points.

 

[zonde]

The third option you keep missing: non locality. Those two events are sharing the same "variable", they are not "connected", because a connection requires two end points.

This option requires some completely novel philosophy. It would be good to give some arguments why it is consistent with scientific approach.

 

[Boing3000]

This option requires some completely novel philosophy. It would be good to give some arguments why it is consistent with scientific approach.

I am surprised by your post. As a simple programmer with a curiosity for science, the only way I can simulate Bell's results (or more accurately the side of the inequality matching natures behavior) is to simply exactly do that in terms of computer variable: you share the "hidden" polarization value. At least with a simple polarity entangled photon pair. You don't even need complex number.
Everything is classical in the program, even the random generator used to pick up an event result. And the only way to make it work is to share the variable between photon. Nothing else will do.
I thought it was that that Bell proved. Apparently, I was wrong again

 

[zonde]

I am surprised by your post. As a simple programmer with a curiosity for science, the only way I can simulate Bell's results (or more accurately the side of the inequality matching natures behavior) is to simply exactly do that in terms of computer variable: you share the "hidden" polarization value. At least with a simple polarity entangled photon pair. You don't even need complex number.
Everything is classical in the program, even the random generator used to pick up an event result. And the only way to make it work is to share the variable between photon. Nothing else will do.
I thought it was that that Bell proved. Apparently, I was wrong again

Do not think about reality as matrix (from that movie). It's not scientific.

 

[Boing3000]

Do not think about reality as matrix (from that movie). It's not scientific.

But I don't think that at all. I was just responding to zonde that was trying to make some kind of bizarre argument based on logic. On logic alone (for me logic is mathematic enough to be considered scientific), I was just giving him that additional option (not excluding the possibility that there may be more).

I don't say we are in a matrix, I just say that with a turing machine logic, we can simulate photon entangle quite easily. What is even bizarre is that the simplest the code is, the better the matching with reality is (not the better, in fact: the only). Once you accept that the "variable" polarization can be shared between distant photon, the rest follow Occam's path to "understanding how it works (at least on logical ground)".

 

[DrChinese]

As a simple programmer with a curiosity for science, the only way I can simulate Bell's results (or more accurately the side of the inequality matching natures behavior) is to simply exactly do that in terms of computer variable: you share the "hidden" polarization value. At least with a simple polarity entangled photon pair. You don't even need complex number.
Everything is classical in the program, even the random generator used to pick up an event result. And the only way to make it work is to share the variable between photon. Nothing else will do.
I thought it was that that Bell proved. Apparently, I was wrong again

What happens in your program at different angles setting for the 2 sides?

There's no problem sharing a value when the angle is the same on both sides. It's not so easy when the angle settings are selected independently on both sides. So the programming difficulty is that you must achieve the cos^2(theta) function at all angles. To make everything work out in a computer program, you must know BOTH the angle settings. They cannot be separately and independently evaluated vis a vis your variable.

 

[N88]

But I don't think that at all. I was just responding to zonde that was trying to make some kind of bizarre argument based on logic. On logic alone (for me logic is mathematic enough to be considered scientific), I was just giving him that additional option (not excluding the possibility that there may be more).

I don't say we are in a matrix, I just say that with a turing machine logic, we can simulate photon entangle quite easily. What is even bizarre is that the simplest the code is, the better the matching with reality is (not the better, in fact: the only). Once you accept that the "variable" polarization can be shared between distant photon, the rest follow Occam's path to "understanding how it works (at least on logical ground)". Italics added

"I just say that with a turing machine logic, we can simulate photon entanglement quite easily."

With Turing machine logic, you can derive the QM results for Aspect's experiments with entangled photons?

I'd like to see that.

 

[Boing3000]

What happens in your program at different angles setting for the 2 sides?

A & B can choose any settings they want to. In fact, again, the easiest is that they choose randomly their angle.

There's no problem sharing a value when the angle is the same on both sides.

That's true, if you insist of having two "hidden" variable, and they try anything to make it work at different angle (starting by simply cloning the polarization, then trying to embed weirder and weirder "logic" in those two local (to photon) polarization object.

Even coding FLT and such tricks to "fix" correlation between those two object won't do the trick (beside being somewhat also impossible to implement right, that is describing it in code logic)

It's not so easy when the angle settings are selected independently on both sides.

Indeed, unless you simply assign the same reference to one polarization to both photon. Then .. done.

So the programming difficulty is that you must achieve the cos^2(theta) function at all angles. To make everything work out in a computer program, you must know BOTH the angle settings. They cannot be separately and independently evaluated vis a vis your variable.

Maybe it is easier if I post a few line of code, like N88 requested.
My petty "beat a Bell" project is full of graphical code and unneeded complication. I'll boil it down to a few line of javascript code you could paste in your browser console.
Maybe I should do it on a thread in the computer science forum, not to pollute this thread even more ?

 

[DrChinese]

A & B can choose any settings they want to. In fact, again, the easiest is that they choose randomly their angle.That's true, if you insist of having two "hidden" variable, and they try anything to make it work at different angle (starting by simply cloning the polarization, then trying to embed weirder and weirder "logic" in those two local (to photon) polarization object.

Even coding FLT and such tricks to "fix" correlation between those two object won't do the trick (beside being somewhat also impossible to implement right, that is describing it in code logic)Indeed, unless you simply assign the same reference to one polarization to both photon. Then .. done.Maybe it is easier if I post a few line of code, like N88 requested.
My petty "beat a Bell" project is full of graphical code and unneeded complication. I'll boil it down to a few line of javascript code you could paste in your browser console.
Maybe I should do it on a thread in the computer science forum, not to pollute this thread even more ?

No need to post anything for me. I was just pointing out that you need to know the angle settings of Alice AND Bob in order to get the results right.

 

[Boing3000]

No need to post anything for me. I was just pointing out that you need to know the angle settings of Alice AND Bob in order to get the results right.

I don't know if I understand you correctly. You don't need to know both angle when Alice and Bob do their measurement.
But obviously, when they compare result later on, you have to.

With Turing machine logic, you can derive the QM results for Aspect's experiments with entangled photons?
I'd like to see that.

I don't know anything about the details of Aspect's experiments, but just a simulation of two detectors measuring polarization of two entangled photons.

I have published the code here

 

[atyy]

From what you had quoted: ''what you actually mean by “classicality”, when we hold hands and look at the mathematical derivations (of the inequality) that you undoubtedly have in mind, is nothing but the idea of deterministic hidden variables. But then it is immediately obvious that you cannot “save locality” by abandoning these hidden variables: having the hidden variables was the *only way* to account for the perfect correlations (when Alice and Bob both measure along z) without nonlocality!''

First you can see a clear instance of mind reading, and second, he takes his position absolute by talking about the *only way*, closing the eyes to something obvious to Werner: The fact that analysing the situation in terms of hidden variables is already assuming classicality and hence the result is determined by the assumption, not by the argument.

Yes, that is Norsen's argument - you cannot save locality by abandoning reality because in his definition of reality, reality is a prerequisite for locality.

However, I believe Werner is wrong because he is using an operational definition of locality which does not require reality. His argument is wrong, because when applied to operational locality, Bell's theorem does not say that if we want operational locality we have to give up reality - instead Bell's theorem says that if we want operational locality, we have to give up operational randomness.

There may of course other flavours of locality addressed by neither definition above, eg. the definition of locality in Consistent Histories (not sure CH is correct, but it looks pretty close to me).

 

[RockyMarciano]

QFT has nothing to do with this. Bell's theorem is a mathematical theorem with certain assumptions and this thread is about what those assumptions are. zonde claims that the only assumption is locality, but of course, it is generally accepted and also easy to see that this is false. The microcausality assumption in QFT is completely unrelated.

You are confused here. I was not answering that claim of zonde in that post.

No. By classicality I mean the counterfactual definiteness assumption $X_{\alpha\beta}^\chi=X_{\alpha\beta}$ that I have explained.

That is not exactly what is usually meant by classicality. I was referring to what you call "the EPR criterion".

 

[RockyMarciano]

Where do you find non-classicality (whatever that means) in QFT predictions?

They violate BI. Just like NRQM.

No, I mean that (direct) causal connection between spacelike separated events is FTL causality.

FTL with observable consequences is acausal.

QFT description of entangled particles is basically the same as in NRQM. So I don't understand your point of bringing into discussion microcausality.

Then you don't understand the difference between being relativistic and nonrelativistic.

 

[zonde]

They violate BI. Just like NRQM.

QFT predictions can violate BI because just like in NRQM entangled particles are described with single vector (in Fock space) not two independent vectors.

FTL with observable consequences is acausal.

FTL with observable consequences is causal in preferred reference frame.

Then you don't understand the difference between being relativistic and nonrelativistic.

Hmm, we can analyze BI in a setup where measurements of Alice and Bob are timelike separated. So we don't have to worry about relativity. Let's say Alice has made her measurement and sent her result to Bob. Is everything classical now?

 

[RockyMarciano]

QFT predictions can violate BI because just like in NRQM entangled particles are described with single vector (in Fock space) not two independent vectors.

Yes, that is part of te non-classicality you asked about.

FTL with observable consequences is causal in preferred reference frame.

Yes, and preferred frames are avoided in current theories due to their inconsistence.

Hmm, we can analyze BI in a setup where measurements of Alice and Bob are timelike separated. So we don't have to worry about relativity. Let's say Alice has made her measurement and sent her result to Bob. Is everything classical now?

But we have to worry about relativity. In nrqm there is no notion of spacelike separated, but in QFT there is and that is why we have to bring up microcausality.

 

[zonde]

I will reply here as it seems that A. Neumaier wants these discussions out of the other thread.

This is just playing semantically with the distinction between inferences and assumptions. The premise of BI that measurements in the same direction determines perfect anticorrelation measurements pressumes simultaneous existence of the spin measurement angles at certain initial time t, therefore determinism despite of how common sense this premise might appear. The fact is that this premise is implied by "no action at a distance" i.e. classical locality principle when applied to spacelike separated regions. So here the classical notion of locality based on simultaneity is used, i.e. the classical determinism with an initial state at time t=0 with a Cauchy surface of simultaneous measurements outcomes.

Well, that's the point. Determinism is inferred from "no action at a distance" plus perfect anticorrelations.
But I only do not understand what determinism has to do with simultaneity.

In the context of EPR, EPR realism is clearly well defined, so why not use it? The meaning "not solipsism" is the broadest philosophical meaning and this is indeed confusing in the quantum context of EPR.

Using words in the commonly accepted sense reduces interpretation errors of arguments and reduces amount of useless semantic discussions.

 

[zonde]

Yes, and preferred frames are avoided in current theories due to their inconsistence.

That is news to me.

 

[rubi]

There may of course other flavours of locality addressed by neither definition above, eg. the definition of locality in Consistent Histories (not sure CH is correct, but it looks pretty close to me).

The definition of locality in the CH arguments is the EPR notion (there are no FTL causal influences, independent of whether they can be used for signaling or not). The histories analysis shows that the probability for FTL causality is $0$.

You are confused here. I was not answering that claim of zonde in that post.

I think you are confused. QFT is completely off-topic in this thread. Bell's theorem is of the form $A\rightarrow B$ (or equivalently $\neg B\rightarrow\neg A$), where $A$ are some assumptions and $B$ is Bell's inequality. We know that Bell's inequality is violated ($\neg B$), therefore we must conclude that the assumptions $A$ are false ($\neg A$). Now, if $A$ were only the assumption of some form of locality ($L$), then we would know that this form of locality is false ($\neg L$) and no mention of QFT could fix this. However, if $A$ is the conjunction $L\wedge C$ of locality and something else ($C$), then the violation of Bell's inequality only implies $\neg L \vee \neg C$ and hence we can choose to deny $C$ instead of $L$. But in order to do this, we must isolate clearly, where the assumption $C$ is used (explicitely or implicitely) in Bell's proof. This is the point of this thread.

That is not exactly what is usually meant by classicality. I was referring to what you call "the EPR criterion".

This is exactly what is meant by counterfactual definiteness. "Classicality" is only Werner's personal term for it (and I like it a lot). CFD and locality are the only assumptions in Bell's (and anyone's) proof of the inequality. I didn't assume any EPR criterion and it is irrelevant, since the histories analysis proves that it is compatible with QM (which violates the BI).
I don't know what you could have meant in your post #10. Please clarify, what you believe is mathematically wrong about my post #6.