# I Bell's Theorem and Reality

#### facenian

Hello, I would like to hear some comments on this:
Recently a paper has been published(Sánchez-Kuntz, N. & Nahmad-Achar, E. Found Phys (2018) 48: 27. https://doi.org/10.1007/s10701-017-0126-z) claiming tha QM has a local realist interpretaion.
In this paper it is asserted that:
"The wave nature (as in the double-slit experiment) arises when one observes the statistical behaviour of a
large ensemble of particles, just as ripples in water arise from a statistical behaviour of many water particles, or electromagnetic waves, in quantum theory, are the result of a large collection of photons. We see the phenomenon of superposition in waves, but not in the individual particles which are the building blocks (physical entities) in QM".
This assetion seems to be in contradiction with the the double slit experiment that were performed with individual particles that showed explicitly wave like behavior of individual photons.
Am I correct or this kind of experiments were not actually performed and are only thought experiments?

Related Quantum Physics News on Phys.org

Gold Member

#### DrChinese

Gold Member
After my usual objection that this paper does not meet PF requirements for discussion:

The paper imposes a new requirement to the Bell logic, called "factuality". This requirement is the base for the paper, as I read it. It says:

"Under the factuality condition, each of these sets of [counterfactual] outcomes must come from a different set of hidden variables."

I don't see any reason to include this. In fact, I would initially say that it makes no sense as a requirement. Counterfactual outcomes should be pulled from an overlapping set of hidden variables. Any comments?

#### Mentz114

Gold Member
This assetion seems to be in contradiction with the the double slit experiment that were performed with individual particles that showed explicitly wave like behavior of individual photons.
Am I correct or this kind of experiments were not actually performed and are only thought experiments?
Single electron interference has been observed. I have references somewhere.

This paper seems to throw away most of standard QM so it is not discussing Bell etc but something else.

#### facenian

Something very similar available here

https://arxiv.org/abs/1605.08493[/QUOTE

It's the same paper

After my usual objection that this paper does not meet PF requirements for discussion:
would like to know why it does not meet PF requirements since it has been published in a peer reviewed journal.

#### facenian

Single electron interference has been observed. I have references somewhere.
If it is a known established fact then I am disappointed since, at least this statement, should not have passed the peer review process.

Gold Member

#### Mentz114

Gold Member
Interesting, can you give us the precise citation data?
PACS numbers: 03.65.-w, 03.75.-b, 41.75.Fr, 41.85.-p, 42.25.Fx

I just clicked the link and copied this off the abstract page.

#### DrChinese

Gold Member
If it is a known established fact then I am disappointed since, at least this statement, should not have passed the peer review process.
I see a number of obvious issues.

1. They assume deterministic time evolution of the entangled state, for example. There isn't the slightest piece of experimental evidence for that, and every indication that time is NOT a factor.

2. Their overall logic seems to be: if you assume X (in this case a thing they call Factuality), then Bell fails. So OK, I reject Factuality - something I see no reason to assume in the first place - and ergo their paper fails totally.

3. They include the detector settings as part of the hidden variables. That's essentially contradicted by experiments in which locality is strictly preserved.

4. And of course the real killer is this: failure to take the DrChinese challenge!

I really don't get it. Not just the paper, but that it was accepted for publication. I do not consider the reference suitable myself; but I realize that if your standard is simply that it is published in X publication, then it is automatically suitable. For papers such as this, I hardly consider it meaningful that it is published. The top publications don't even consider "Bell-is-wrong" papers because they are such a time waster for everyone involved.

#### Boing3000

Gold Member
This experiment has passed peer review

arXiv:1210.6243v1 [quant-ph] 22 Oct 2012
I see nothing about single electron interference in that experiment (nor what a single electron having "interference" would mean)

article said:
In two separate landmark experiments, individual electron detection was used to build up interference patterns
Which seems to me to be pretty standard ensemble QM observation.

#### Boing3000

Gold Member
I see a number of obvious issues.
I just stop at this one:

Article Rings a Bell said:
In our view, non-local correlations emerge from the deterministic evolution of a shared hidden variable between two components of an ontological pair. Entanglement arises every time two (or more) physical entities share hidden variables
If a hidden variable is shared (and not copied/identical), it is by definition non-local. I kind of agree with that, because that's what Bell's is all about...

#### stevendaryl

Staff Emeritus
I really don't understand what the authors are talking about.

Bell's hidden-variable model assumed the existence of functions $A(a, \lambda)$ and $B(b, \lambda)$ with the interpretation that:
• If Alice measures the spin of her particle along axis $a$, and the hidden variable has value $\lambda$, then the result will be $A(a,\lambda)$
• Similarly, if Bob measures his particle along axis $b$, he will get $B(b,\lambda)$
Bell assumes that $A(a,\lambda)$ and $B(b,\lambda)$ are both well-defined for all possible values of $a, b, \lambda$.

In contrast, in this paper, they seem to be assuming that for every value of $\lambda$, there is only one pair of axes, $(a,b)$ such that $A(\pm a,\lambda)$ and $B(\pm b,\lambda)$ are well-defined.

But what's supposed to happen if a twin pair is produced with some value $\lambda$, and then later Alice and Bob choose values for $a, b$ for which $A(a,\lambda)$ or $B(b,\lambda)$ are not well-defined?

If they are assuming that that never happens, then they are talking about superdeterminism, which has long been acknowledged as a logically possible (though implausible) loophole to Bell's theorem.

Last edited:

#### stevendaryl

Staff Emeritus
If a hidden variable is shared (and not copied/identical), it is by definition non-local. I kind of agree with that, because that's what Bell's is all about...
No, it's not nonlocal if it is only shared by particles with a common past. Bell assumed local shared hidden variables, and showed that they cannot produce the correlations of the EPR experiment. He definitely didn't assume that shared hidden variables must be nonlocal. They must be nonlocal to agree with QM, but they aren't nonlocal just because they are shared hidden variables.

#### Boing3000

Gold Member
No, it's not nonlocal if it is only shared by particles with a common past.
Then you haven't quite understood Bell's reasoning.

Bell assumed local shared hidden variables, and showed that they cannot produce the correlations of the EPR experiment.
Indeed, but you cannot call that "local shared hidden variables", which is a contradiction. They are simply identical hidden variable.

He definitely didn't assume that shared hidden variables must be nonlocal.
Of course he didn't. This would be in total contradiction with classical thinking. Instead he build some kind of "reduction ad absurdum", except that the reduction is made by experiment.

They must be nonlocal to agree with QM, but they aren't nonlocal just because they are shared hidden variables.
I am sorry but the two parts of your sentence are unrelated. I don't know what "sharing" mean for you, but it has an unique ubiquitous sense. If we share a house, we do it from the common past were we got entangled by signing that real-estate contract. If some property of the house change, it change instantly for both of us.

Bell proved nature cannot use "share" state without non-local "mechanism" (which isn't really that surprising)

I don't think Bell use the word share, because he wasn't confuse about what a unique QM state is. The "paper" of the OP is more than confuse about its "ontology" (and the time evolution they purport to use (which time ?))

Gold Member

#### stevendaryl

Staff Emeritus
Then you haven't quite understood Bell's reasoning.
What I am saying is the consensus way that Bell's theorem is understood.

What we know by observation in an EPR type experiment is that Alice's and Bob's results are correlated: If we let $P(A,B|a,b)$ be the probability that Alice will get result $A$ and Bob will get result $B$, if Alice's setting is $a$ and Bob's setting is $b$, then to say that the results are correlated is to say that the probabilities don't factor:

$P(A,B|a,b) \neq P(A|a) P(B|b)$

A local hidden-variable model for this correlation would be given by a set $\Lambda$ of possible values of some hidden-variable $\lambda$, together with probability distributions $P(\lambda), P_A(A|a, \lambda)$, $P_B(A|b, \lambda)$ such that

$P(A, B) | a, b) = \sum_\lambda P(\lambda) P_A(A | a, \lambda) P_B(B | b, \lambda)$

(where the sum would be replaced by an integral if $\lambda$ is a continuous variable).

Bell proved that for the correlations predicted by QM for the EPR experiment, there is no local hidden-variable model that makes the same predictions.
(Bell's argument is not directly in terms of probabilities, but in terms of expectation values: $E(A,B | a, b)$. This is the expectation value of the product of $A$ and $B$. Since the results $A$ and $B$ are always $\pm 1$, This is related to the probabilities through
$E(A,B | a, b) = P(+1, +1|a,b) + P(-1, -1|a,b) - P(+1, -1|a,b) - P(-1, +1|a, b)$.)

Locality comes into play in the assumption that the probability of Alice's result depends only only $\lambda$ and $a$, while Bob's result depends only on $\lambda$ and $b$.

Bell explicitly gives a toy example of such a local hidden variable model that has some features with EPR, but does not agree in detail.

His example is this (paraphrasing)
• Model spin-1/2 particles as spheres, where one hemisphere is colored red and the other is colored black.
• Bob's and Alice's particles always have opposite colorings.
• When the spheres are produced, the axis running from the center of the red region to the center of the black region is
• When Alice or Bob measures the spin along axis $a$, she gets +1 if $a$ is in the red hemisphere of their respective spheres, and $-1$ otherwise.
This model is a hidden-variables theory that agrees with EPR in two respects:
1. Alice and Bob always get opposite results if they measure along the same axis.
2. The results are always $\pm 1$
3. For each measurement taken separately, the results are equally likely to be +1 or -1.
But the details of the correlations when Alice and Bob measure along axes that are not aligned do not agree with EPR.

#### stevendaryl

Staff Emeritus
I am sorry but the two parts of your sentence are unrelated. I don't know what "sharing" mean for you, but it has an unique ubiquitous sense. If we share a house, we do it from the common past were we got entangled by signing that real-estate contract. If some property of the house change, it change instantly for both of us.
I share a hidden variable with you if the hidden variable has the same value for both of us. If we get together and decide that our club's secret pass phrase is "bologna sandwich", then we share that secret. The assumption of locality is that the only way that you and I can be guaranteed to share a secret is if we have a common past: The value of the secret was determined at some point in the intersection of our backwards lightcones.

#### stevendaryl

Staff Emeritus
I share a hidden variable with you if the hidden variable has the same value for both of us. If we get together and decide that our club's secret pass phrase is "bologna sandwich", then we share that secret. The assumption of locality is that the only way that you and I can be guaranteed to share a secret is if we have a common past: The value of the secret was determined at some point in the intersection of our backwards lightcones.
It occurs to me that you might be thinking of two people sharing a variable in the sense that even if the variable changes value, it will change in the same way for both people. For the purposes of Bell's theorem, the relevant hidden variables are the initial state of the twin pair. He's not considering a model where the hidden variable changes with time.

#### Boing3000

Gold Member
What I am saying is the consensus way that Bell's theorem is understood.
OK, but that consensus is not "No, it's not nonlocal if it is only shared by particles with a common past."

Bell proved that for the correlations predicted by QM for the EPR experiment, there is no local hidden-variable model that makes the same predictions.
Which boils down to the shared(entangled) hidden property (here correlation) is non-local. The OP paper (as well as Bell's one) is all about hidden variable.

(Bell's argument is not directly in terms of probabilities, but in terms of expectation values: $E(A,B | a, b)$
Indeed, and that's even more powerful than probability (which in my view is a subset of expectation value)

Locality comes into play in the assumption that the probability of Alice's result depends only only $\lambda$ and $a$, while Bob's result depends only on $\lambda$ and $b$.
More specifically that is is the same $\lambda$. And that's the thing. He specifically specified that no more assumption as to be applied to that "hidden variable" at the bottom of the first page. Locality comes into play because locality imply a copy of $\lambda$. In math term expressison (2) have to $\lambda$ at different "site"...

Bell explicitly gives a toy example of such a local hidden variable model that has some features with EPR, but does not agree in detail.
Indeed, an other toy model are easy to build even to mimic full EPR setups... you just have to implement non-locality.

I share a hidden variable with you if the hidden variable has the same value for both of us.
That's incorrect. "Same value" means two identical copy of that value. In my example, having two identical (cloned) house does not mean we share a house.
Sharing a hidden variable is a precise term that Bell exclude in precise math. There is two $\lambda$ in equation (2) and that's what imply locality.

It occurs to me that you might be thinking of two people sharing a variable in the sense that even if the variable changes value, it will change in the same way for both people.
That's not only my particular thinking. It is what non-locality means. It doe not mean identical copies magically linked by spooky FLT. It means one value all along, it means total commutative. And it isn't concerned by Bell's proof, because...

For the purposes of Bell's theorem, the relevant hidden variables are the initial state of the twin pair.
As you said, the prove does rely on copy(locality) of $\lambda$ being unable to reproduce QM outcome.

He's not considering a model where the hidden variable(s) changes with time
Nor does it exclude it ... nor does it make any differences... (I added an "s" which made all the difference)

Two local hidden variable which in Bell terms "can be anything" won't do the trick, a (obviously) non-local one would...

#### stevendaryl

Staff Emeritus
OK, but that consensus is not "No, it's not nonlocal if it is only shared by particles with a common past."
It's possible that our disagreement is merely over terminology/definitions. In Bell's argument the shared hidden variables were assumed to describe the initial state of the twin pair. If the correlations can be explained in terms of that common value, then we have a local hidden variables theory.

Nor does it exclude it ... nor does it make any differences... (I added an "s" which made all the difference)
As I said, Bell's theorem did not consider time-dependent hidden variables, because for his purposes, there is no reason to.

#### stevendaryl

Staff Emeritus
That's not only my particular thinking. It is what non-locality means.
Bell's proof was about local hidden variables. He was not making any kind of claim about nonlocal hidden variables. He acknowledged from the start that if you allow nonlocal interactions, of course you can reproduce the predictions of EPR. This can be demonstrated either using the Bohm interpretation, or the "measurement collapses the wave function" interpretation. His proof was a proof about local hidden variables, and for you to bring up nonlocal hidden variables seems completely irrelevant.

#### DrChinese

Gold Member
As I said, Bell's theorem did not consider time-dependent hidden variables, because for his purposes, there is no reason to.
From the OP paper:

We affirm that the evolution function F(λ,t) must satisfy a condition we call factuality. Mathematically, this condition is no news: for any given function, different outcomes of the function must come from different inputs. So, once the values of hidden variable and time are given, our function F(λ,t) can only acquire a certain value (oA,oB). Physically, this is the factuality condition: if a system evolved in time (t0→t1) to a particular state, it is because only this state was accessible to it given the initial condition (λ,t0) and, therefore, different states at time t1 must come from different values of hidden variables λi. This is only a consequence of determinism.

In our view, non-local correlations emerge from the deterministic evolution of a shared hidden variable between two components of an ontological pair. Entanglement arises every time two (or more) physical entities share hidden variables. This suffices for the time being, and for the example we work below. In what follows, we will analyse the emergence of Bell’s inequality within our proposed description of reality.

They constructed their description of "deterministic evolution", which specifically requires one and only one possible outcome for a specific set of inputs. And those inputs would "complete" QM in their view. Heard that before? Everything about their model is essentially what Bell contradicts. They also reference PBR, which I think pretty much refutes exactly what is stated above. They manage to hand-wave everything away!

It is also interesting that their model is flatly contradicted by entanglement experiments in which the entangled particles have never been in causal contact, i.e. they never evolved from a common set of local hidden variables. Such as this experiment, in which the entangled particles are 1.3 km apart and the selection of measurement basis is made under strict locality conditions as well:

https://arxiv.org/abs/1508.05949

#### facenian

I really don't understand what the authors are talking about.
If they are assuming that that never happens, then they are talking about superdeterminism, which has long been acknowledged as a logically possible (though implausible) loophole to Bell's theorem.
Yes, the proposed model is superdeterministic. I believe this is the principal point that makes it uninteresting.

I see a number of obvious issues.

1. They assume deterministic time evolution of the entangled state, for example. There isn't the slightest piece of experimental evidence for that, and every indication that time is NOT a factor.
I don't think that this is a problem because QM states do evolve deterministically. Bell also explains, in his famous 1964 paper, that hiddden variables may be considered as initial values that evolve dinamically with time.

#### kurt101

From the OP paper:

It is also interesting that their model is flatly contradicted by entanglement experiments in which the entangled particles have never been in causal contact, i.e. they never evolved from a common set of local hidden variables. Such as this experiment, in which the entangled particles are 1.3 km apart and the selection of measurement basis is made under strict locality conditions as well:

https://arxiv.org/abs/1508.05949
Is your comment that “they never evolved from a common set of local hidden variables” misleading? My understanding of the experiment so far is that the experiment selects the results that A and B had in common after learning at C whether the photons from A and B had some kind of correlation.

Also, in this experiment are the ZPL and PSB photons considered entangled?

"Bell's Theorem and Reality"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving