I A new realistic stochastic interpretation of Quantum Mechanics

[Fra]

Assuming you were tying your comments to my comment about quantum repeaters (that utilize entanglement swapping):

I addressed the basic experiment in my comments. Because i think the swapping add nothing. It just add details, the floods the conceptual discussion. It can (MO) be explained by the "selection" later, and the selection requires the input from the swapping experiment, which yes, is a free choice.

1. This is contradicted by experiment. An experimenter's future free choice can create a swap from previously independent systems.

In the swapping experiments. There is still no causal relation between the remote quantum systems that are (selected via BSM) to be correlated. Note here that I am using Barandes notion of causality, not bell's.

Their correlation behave just as if they have been originated from the same creation. That it is POSSIBLE to engineer entangled systems, without previous physical contact as you say is indeed a remarkable and interesting thing, but that tells me more about the nature of entanglement, than it tells me about nature of causality or locality.

2. This is his hypothesis, I guess. Independently created entangled pairs (indivisible systems) cannot, according to quantum theory, have any "pre-tuning". There is no such thing. All such pairs are in the same superposition (Bell State). So if the hypothesis were true, that should show up in experiment - and it would violate Monogamy relations (i.e. theory). So this hypothesis is a huge leap.

In the case to swapping experiments, the correlation is indeed not pre-tuned from the original creation, the tuning of the selected pair, is artificially created using selection and informaion from the clever BSM experiment. That yes, is a free choice. Again to me - this tells me more about the nature of entanglement, than about anything else! It tells me, that entanglement is perhaps not so mysterious after all?

/Fredrik

 

[PeterDonis]

the "hidden variable" that pre-correlates the two systems guided stochastics does not determined the outcomes; it only introduces a bias in the outcomes. The actual outcome also depends on the detector and it's settings, and these are not part of the original stochastic matrix.

So we need no action at distance.

You're contradicting yourself. If the actual outcomes depend on the detectors and their settings, and those are spacelike separated, there must be "action at a distance' of some kind to produce correlations that violate the Bell inequalities. No amount of "predetermination" can change that. That's what Bell's Theorem tells us.

 

[Fra]

You're contradicting yourself. If the actual outcomes depend on the detectors and their settings, and those are spacelike separated, there must be "action at a distance' of some kind to produce correlations that violate the Bell inequalities. No amount of "predetermination" can change that. That's what Bell's Theorem tells us.

But then you assume that the only kind of "pre-determiniation" possible is of the Bell type.

The argument of Barandes, is that Bell's theorem assumes that there is a HV that, had we known it, determines the individual quantum states if the pair; and that causally determined the outcome in combination to any detector setting. From this the inequality is derived. This assumption is effectively related to the divisibility assumption; and this is what Barandes questions. He then paints a different picture.

I tried to line out the potential conceptual causal chain of this different picture; but while the full new theory that reconstructs all the meat on the QM-end, from new first principles. This doesn't exists, which is why I get that appreciated the new picture is hard.

If someone mades the conclusion that what I tried to line out, contradicts with bells theorem then I failed to convey the idea

/Fredrik

 

[Sambuco]

As far as I understand Barandes' approach, given the stochastic-quantum correspondence he introduced in one of his papers (https://arxiv.org/abs/2302.10778), the stochastic map represented by the conditional probabilities $\Gamma_{i,j}(t) = p(i,t|j,0)$ carries the same "information" as the global wavefunction $\Psi(t)$. Therefore, in an experiment involving the spacelike-measurement of an entangled system, when one measurement outcome is known, the $\Gamma_{i,j}(t)$ must be nonlocally updated. Otherwise, the measurement outcomes could violate QM predictions.

In that sense, the stochastic map plays (almost) the same role as the global wavefunction in Bohmian mechanics à la Dürr-Goldstein-Zanghi (https://arxiv.org/abs/quant-ph/9512031), where $\Psi(t)$ is interpreted as nomological.

Barandes tried to avoid nonlocality by replacing Bell's principle of "local causality" by a new principle of "causal locality", which states (https://arxiv.org/abs/2402.16935):

"A theory with microphysical directed conditional probabilities is causally local if any pair of localized systems Q and R that remain at spacelike separation for the duration of a given physical process do not exert causal influences on each other during that process, in the sense that the directed conditional probabilities for Q are independent of R, and viceversa."

To me, this is well known and there is no novelty. In fact, this principle of "causal locality" is also satisfied by Bohmian mechanics, so we could say that Bohmian mechanics is causally local. Personally, I don't see what is the improvement here.

Lucas.

 

[Sambuco]

An experimenter's future free choice can create a swap from previously independent systems.

Just a brief comment about that. As we discussed a lot in a recent thread, this interpretation is observer-dependent. Following the usual convention (photons 1&2 and 3&4 initially entangled, Alice and Bob measure photons 1 and 4, respectively, whereas Victor makes a swap by the BSM on photons 2&3), after Victor makes the BSM, photons 1&4 are entangled according to Victor. However, according to Alice/Bob, the same fourfold experimental outcomes are reproduced without any entanglement between photons 1&4.

Just in case, @DrChinese, I don't want to criticize what you said (your interpretation is perfectly consistent), but rather to strengthen your argument. Even if someone interprets a delayed-choice entanglement swapping experiment in the way Mjelva's did in his paper, the nonlocality is still there. In other words, I completely agree with you that, if we wish to retain certain notion of "causation", this implies action-at-a-distance.

Lucas.

 

[PeterDonis]

But then you assume that the only kind of "pre-determiniation" possible is of the Bell type.

Bell's assumption about "pre-determination" is extremely general. See below.

The argument of Barandes, is that Bell's theorem assumes that there is a HV that, had we known it, determines the individual quantum states if the pair

If this is Barandes's claim, it's wrong; Bell nowhere claims that the hidden variables determine the quantum states.

I strongly suspect, however, that you are misquoting or misunderstanding Barandes here. I find it very hard to believe that Barandes doesn't know what specific assumptions Bell's theorem is derived from.

that causally determined the outcome in combination to any detector setting.

Bell's hidden variables are assumed to determine measurement outcomes, but not by determining quantum states. Bell's hidden variables have nothing to do with quantum states.

 

[PeterDonis]

This assumption is effectively related to the divisibility assumption; and this is what Barandes questions.

Where specifically in Bell's paper is the divisibility assumption made?

 

[Fra]

If this is Barandes's claim, it's wrong; Bell nowhere claims that the hidden variables determine the quantum states.

I strongly suspect, however, that you are misquoting or misunderstanding Barandes here. I find it very hard to believe that Barandes doesn't know what specific assumptions Bell's theorem is derived from.

Bell's hidden variables are assumed to determine measurement outcomes, but not by determining quantum states. Bell's hidden variables have nothing to do with quantum states.

Perhaps this turn out unclear but Bell theorem has been discussed alot, i wanted to focus on painting the alterantive picture to see if it could make sense to Dr Chinese and and others that keep seeing causality issues efter after this long thread..

Of course the bell pair together is one quantum state in the conventional QM picture. So what I mean is that bell assumes that this is not a superposition but a classical probabilistic mixture (of the HV; which determines the individual states or spins).

This is not the situation in Barandes picture.

Where specifically in Bell's paper is the divisibility assumption made?

Bell does not use that terminology at all, so it's hidden. But what I refer to I see implict in equation (2) on paged 2 in this 1964 paper. One single line in Bells paper contains several assumptions baked together; so you need to break it up. It's the idea that you can divide the probability into hypohtetical partitions and then sum it up. This looks innocent as its like the partition of sample space and law of total probability. But in Barandes picture, this artifical partition is not valid. Until Baranders used the term, I myself referred for myself in the past as the "equipartition assumption", but it is essentially the same issue that barandes put the finger on. I think that was the focus on one of the posts or threads somewhere. I'll see if i can find it, it's been highlighted.(edit: found the previous post, it was 191 in this thread. The threads are so long in the end you forget the beginning)

/Fredrik

 

[pines-demon]

Where specifically in Bell's paper is the divisibility assumption made?

Just to add to the Bell conversation. Barandes partially rejects Bell's theorem here:

• New Prospects for a Causally Local Formulation of Quantum Theory (https://arxiv.org/abs/2402.16935)

He claims that Bell's version is not enough and we need a new microscopic theory of causality and under his causality theory, concerns of the violations of causality are "deflated".

Edit: also let me point out that Barandes has confessed to have linked Bell relation to the Reichenbach principle too loosely in that paper. He has acknowledged that Bell's view is a bit more nuanced and has suggested to read this recent paper:

• J. Luc "What are the bearers of hidden states? On an important ambiguity in the formulation of Bell's theorem" (https://arxiv.org/pdf/2501.17521) (2025)

 

[PeterDonis]

bell assumes that this is not a superposition but a classical probabilistic mixture

No, that's not what Bell assumes either. I think you need to actually read Bell's paper.

Bell's actual assumption is that the joint probability for the two measurement results factorizes. That assumption says nothing whatever about any underlying model. The reason "local hidden variable" models get discussed so often in connection with Bell's Theorem is not because Bell assumed such a model in proving his theorem; it is simply because such models are easily imagined and are known to satisfy the assumptions of Bell's theorem. But Bell never claimed that such models are the only possible ones that satisfy the assumptions of his theorem, or that quantum mechanics is the only possible model that violates those assumptions.

 

[PeterDonis]

what I refer to I see implict in equation (2) on paged 2 in this 1964 paper.

That is the factorizability assumption that I referred to in post #610 just now.

One single line in Bells paper contains several assumptions baked together; so you need to break it up.

No, that one single line contains just one assumption--but if you are stuck on a particular mental model of how that assumption can be satisfied, it might seem to you (or to Barandes, for that matter) that it is several assumptions baked into one. But that's not a property of Bell's Theorem or its assumptions; it's a property of your particular mental model. Which, as I remarked in #610, Bell never claimed to be the only possible model that could satisfy his assumptions. If you, or Barandes, want to make claims like the one I quoted above, the burden is on you to prove, mathematically, that your claimed requirement for breaking up that single line in Bell's paper is necessary in order to satisfy the assumption. I don't see any such proof anywhere.

 

[lodbrok]

If the actual outcomes depend on the detectors and their settings, and those are spacelike separated, there must be "action at a distance' of some kind to produce correlations that violate the Bell inequalities.

Not necessarily; you are conflating mathematical dependence with causal dependence. We have from Bell's theorem is:

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

You could say one way for the above to be true is if there is action at a distance. But that is not a necessary conclusion. For example, with post-selection, it is easy to accomplish the above experimentally by using a different subset of data for one side of the expression compared to the other, as we've seen in entanglement-swapping experiments. In other words, contextuality does not require non-locality.

 

[lodbrok]

That is the factorizability assumption that I referred to in post #610 just now.

There's no factorizability assumption in equation 2 of Bell's paper. Here is the equation, where is the factorizability assumption.
$$ P(a,b) = \int d\lambda \rho (\lambda) A(a,\lambda) B(b, \lambda) $$

The assumption that Barandes identifies has to do with the presence of $\rho(\lambda)$ instead of $\rho(a,b,\lambda)$

 

[PeterDonis]

There's no factorizability assumption in equation 2 of Bell's paper. Here is the equation, where is the factorizability assumption

That is equation 2 in the 1964 paper by Bell that @Fra linked to.

 

[pines-demon]

There's no factorizability assumption in equation 2 of Bell's paper. Here is the equation, where is the factorizability assumption.
$$ P(a,b) = \int d\lambda \rho (\lambda) A(a,\lambda) B(b, \lambda) $$

The assumption that Barandes identifies has to do with the presence of $\rho(\lambda)$ instead of $\rho(a,b,\lambda)$

Please, all of you if we are going to discuss the hypotheses of Bell's theorem be clear in what paper of Bell you are referring to. The assumptions are slightly different in each paper and this is partly the origin of the Barandes' disagreement with it.

 

[PeterDonis]

be clear in what paper of Bell you are referring to.

@Fra linked to one in post #608. That's the one I was referring to.

 

[lodbrok]

That is equation 2 in the 1964 paper by Bell that @Fra linked to.

Yes, it is the same 1964 paper. You said the only assumption was the factorizability of joint probability of outcomes,

Bell's actual assumption is that the joint probability for the two measurement results factorizes. That assumption says nothing whatever about any underlying model.

I don't see such an assumption in equation 2 of Bell's 1964 paper. Perhaps you have a different paper in mind. In equation 2 of the 1964 paper, Bell is calculating the expected value of the paired product of outcomes at Alice and Bob for the experiment under consideration.

The implied starting point for the integral is
$$ P(a,b) = \int d\lambda \rho(a,b,\lambda) A(a, b, \lambda) B(a, b, \lambda) $$
Which Bell reduces to his equation 2 as
$$ P(a,b) = \int d\lambda \rho(\lambda) A(a, \lambda) B(b, \lambda) $$

This transition implies the following assumptions:
- $A(a, b, \lambda) =\pm 1, B(a, b, \lambda) = \pm 1$ (aka determinism assumption)
- $A(a, b, \lambda) = A(a,\lambda), B(a, b, \lambda) = B(b,\lambda)$ (aka locality assumption)
- $\rho(a,b,\lambda) = \rho(\lambda)$ (aka, no enhancement, free-will assumption)

I see nothing concerning the factorizability of the joint probability of measurement outcomes.

 

[Fra]

The discussion is going backwards, i didn't mean to discuss the bells thereom again per see. I tried to paint the picture by failed to convey it apparently.

Anyway: the fatal assumption is none of the above. Yes there is a factorisation assumption in there, but that was not the problem. It is existing already in the starting point, which i highlighted in post 191 already.

They problem of the premise of hte theorem is the assumption that there exists a partition, that you can use to consider divisions of the total process into causal parts, that SUM up to the total process, referring to the law of total probability. This is what is not obvious at all. It does not logically follow, because it is not a mathematical statement, it is a physical assumption about HOW the total process can be constructed. And it's baranders says requires "markov divisibility" - thus any "hidden mechanisms" that does not fulfill this aren't ruled out by bells theorem. That is they key point. The picture I pasted into post 191 are from Barandes youtoube clip.

Edit: I can agree that alot of this is about "mental models", but I presume mental models are what the interpretations is about.

/Fredrik

 

[PeterDonis]

You said the only assumption was the factorizability of joint probability of outcomes,

I said no such thing. I said that equation 2 in that paper expresses the factorizability assumption. I did not say that was the only assumption Bell made in proving his theorem.

 

[PeterDonis]

I see nothing concerning the factorizability of the joint probability of measurement outcomes.

By "factorizability" I mean that in Bell's equation (2), we have the factors $A(a, \lambda)$ and $B(b, \lambda)$, i.e., that the $A$ measurement result depends only on the $a$ measurement settings and $\lambda$, not on the $b$ measurement settings, and vice versa for the $B$ measurement result.

You are calling this the "locality" assumption, but that's just a matter of nomenclature.

 

[PeterDonis]

They problem of the premise of hte theorem is the assumption that there exists a partition, that you can use to consider divisions of the total process into causal parts, that SUM up to the total process,

There is no such thing anywhere in Bell's theorem or its assumptions. The theorem is not about "process". It's about the joint probability of measurement results. The "hidden variables" $\lambda$ are not "causal parts" of anything. Bell describes them as a "more complete specification of the state" than the QM wave function.

referring to the law of total probability.

The equation for the joint probability is not about this; it's not making any use of the fact that the total probability for all alternatives must be $1$.

You seem to me to be attacking a straw man.

 

[Fra]

I must admit that what is driving me is that I an fascinated to observe the argumentation between the different perspectics.

I tried to paint a plausible picture of the alternative view of Bells hidden variable, without rehashing all past discussions of bell, but i see the point didnt get throutgh.

I don't want to nitpick others views, to say my interpretation is better, I seek to understand each others perspectives and it would be nice if we could understand each perspective from the other better.

I will try to go back to page 1 of the 1964 Bell paper.

There is no such thing anywhere in Bell's theorem or its assumptions. The theorem is not about "process". It's about the joint probability of measurement results. The "hidden variables" $\lambda$ are not "causal parts" of anything. Bell describes them as a "more complete specification of the state" than the QM wave function.

First let me say that I have not problem with Bells theorem per see. It is fine as a theorem.

My issues are with Bells initial reasoning, or premise: Bell says:

"Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state. Let this more complete specification be effected by means of parameters lambda."

This assumption is well taken. I have no objection to this!

But then Bell then makes a conclusion, which IMO contained another critical hidden assumption to which I object:

"The result A of is then determined by a and lambda"

I think this implicitly contains in disguise the divisivility assumption. Ie. that you can divided the information in sectors of lambda, and that this forms a complete partition of the sample space. This presumes that the "preparation procedure" and lambda are compatible (or "commuting") pieces of information.

If they are not(which to me they clearly are not), the conclusion would rather be.

"The result A of is determined by a, lambda and the preparation"

This is what I see has the potential to explain the correlation, but not the actual outcomes, because the actual outcomes contains intrinsic elements of irreducible randomness.

And as far I understand, this is was also the main issue Einstein had. The big problem is not to accept indeterminate outcomes, it is the the appparent inseparability that he would for good reasons not accept.

My point was to suggest that this is more easily understood in Barandes picture, where new types or "non-commuting" hidden variables, does explain the "apparent inseparability", but retains the irreducible element of randomness that can be understood as having to do with the nature causation between interacting systems; especially if you view the parts as interacting stochastics.

The equation for the joint probability is not about this; it's not making any use of the fact that the total probability for all alternatives must be $1$.

You call equation (2) in his paper for the equation of "joint probability" but I have a more nuanced view and see that is contains more
- assumption: preparation and lambda are commuting => divisibility assumption and lambda partitions
- independence of the conditional probabilities at A and B ("joint probability")

The first assumption is implicit, or taken for granted, because even before getting to the math, Bell conclueds "The result A of is then determined by a and lambda", so his ansatz is at least appears consistent with his thinking.

This is what I mean by, there is nothing wrong with bells theorem, but I have serious issues with the underlying premises, and it only excludes a certain class if hidden variables. Which is good and great.

And to start thing about what these other TYPES of hidden variable might be? That is where I think Barandes picture add value. If you are into Bohmian mechanics(which I am not), then I think Demystifiers "solipsist HV" interpretation is a way to try to adopt a little bit of this as well.

/Fredrik

 

[PeterDonis]

"The result A of is determined by a, lambda and the preparation"

Bell's lambda includes the preparation. That's the whole point of it--it includes everything that is common to both entangled particles that could possibly affect the measurement outcomes, in whatever model you are using that has the properties Bell assumes.

it only excludes a certain class if hidden variables

I think your view of what lambda contains is too limited. See above.

 

[Fra]

Bell's lambda includes the preparation.

Although that wasnt how I interpreted it - it actually makes no difference however.

Except it blurs things more as it's the "missing HV" that is averqaed. We dont average random preparation procedures.
The preparation in the large is not a hidden variable - it is common knowledge to observers.

What is problematic is to assume all the various partitions are not compatible information. This holds wether we define lambda' as (psi,lambda') -> lambda, or as what is "missing" from the prep.

Without this, the partitioning or divisions make no conceptual sense to me.

/Fredrik

 

[PeterDonis]

it's the "missing HV" that is averqaed. We dont average random preparation procedures.

In Bell's paper, everything that's included in lambda is "averaged". So I don't know where you're getting this from.

I think you are reading things into Bell's paper that aren't there.

 

[PeterDonis]

that wasnt how I interpreted it

Then you aren't reading Bell's paper very carefully. He says lambda includes whatever is necessary for a "more complete specification of the state" than the quantum wave function. That includes anything that is produced by the preparation process and is not included in the wave function. Bell simply does not say any of the other things you keep atributing to him.

 

[Fra]

In Bell's paper, everything that's included in lambda is "averaged".

Yes, but it was you that claimed that information of preperation procedure, thought you wrote "preparation" was included? not me.

He says lambda includes whatever is necessary for a "more complete specification of the state" than the quantum wave function. That includes anything that is produced by the preparation process and is not included in the wave function.

I was maybe unclear, i was not referring to the individual "outputs" of the preparation procedure in repeats, but defining the procedure itself; which would be a prospensity. Perhaps there was confusion between prepration output ~ state; and preparation procedure.

The prospensity is given, the outputs are presumably random. But if parts of the interaction is causally guided by the prospensity and another part by the output containing a HV. Then how can the ansatz make sense?? Then the partitions will involve incompatible info, and that get undefined ambigous.

If we just accept the ansatz the rest is fine.

But if we keep using bells theorem to dismiss all ideas that entertains some sort of HV, i think analyzing the premises is in order.

/Fredrik

 

[Fra]

Bell also writes in the end of the paper...

"In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the set-ting of one measuring device can influence the reading of another instrument, however remote."

But if we are not concerned with the indeterminacy of outcomes in the entanglement experiments, but only with the correlation, if other type of hidden variable that explain the correlation by pre-determination, but without necessarily restoring determinism and each output: it's in this type i put Baranders concepts when he says "These results therefore lead to a general hidden-variables interpretation of quantum theory that is arguably compatible with causal locality."

I supposed it is difficuly to even imagine, how would that work? Right?
How can be have a pre-determined CORRELATION; but NOT a pre-determined output?

I think this is why we have the discussion? I felt that Baranders picutures helps here, and I tried to elaborate but somehow failed to get the picture across.

/Fredrik

 

[iste]

As far as I understand Barandes' approach, given the stochastic-quantum correspondence he introduced in one of his papers (https://arxiv.org/abs/2302.10778), the stochastic map represented by the conditional probabilities $\Gamma_{i,j}(t) = p(i,t|j,0)$ carries the same "information" as the global wavefunction $\Psi(t)$. Therefore, in an experiment involving the spacelike-measurement of an entangled system, when one measurement outcome is known, the $\Gamma_{i,j}(t)$ must be nonlocally updated. Otherwise, the measurement outcomes could violate QM predictions.

In that sense, the stochastic map plays (almost) the same role as the global wavefunction in Bohmian mechanics à la Dürr-Goldstein-Zanghi (https://arxiv.org/abs/quant-ph/9512031), where $\Psi(t)$ is interpreted as nomological.

Barandes tried to avoid nonlocality by replacing Bell's principle of "local causality" by a new principle of "causal locality", which states (https://arxiv.org/abs/2402.16935):

"A theory with microphysical directed conditional probabilities is causally local if any pair of localized systems Q and R that remain at spacelike separation for the duration of a given physical process do not exert causal influences on each other during that process, in the sense that the directed conditional probabilities for Q are independent of R, and viceversa."

To me, this is well known and there is no novelty. In fact, this principle of "causal locality" is also satisfied by Bohmian mechanics, so we could say that Bohmian mechanics is causally local. Personally, I don't see what is the improvement here.

Lucas.

$\Gamma_{i,j}(t)$ doesn't need to be non-locally updated because, according section H on entanglement in the arxiv:2302 paper you linked, the non-Markovian transition matrices store statistical information cumulatively extending back to the initial locally interacting composite state at time 0. At the level of Barandes' formalism, non-local updating isn't needed because the system just somehow remembers the correlation created at the earlier time even though its subsystems may be spatially distant. He notes somewhere else in the paper that his analogue to collapse is just statistical conditioning - just an epistemic tool which doesn't make any actual contribution to the behavior of the systems. And presumably, given the correspondence theorem, collapse in orthodox quantum theory should be functionally the same. But yes, I don't think what he has said has added anything additional other than quite a suggestion that Bell's theorem is inadequate.

 

[PeterDonis]

it was you that claimed that information of preperation procedure, thought you wrote "preparation" was included? not me.

Yes, I am saying that in order to correct your understanding of what lambda includes.

i was not referring to the individual "outputs" of the preparation procedure in repeats, but defining the procedure itself

That's also included in lambda. You still don't seem to get the point: lambda includes everything that is common to both entangled particles and might affect the measurement results.

The prospensity is given, the outputs are presumably random. But if parts of the interaction is causally guided by the prospensity and another part by the output containing a HV. Then how can the ansatz make sense?? Then the partitions will involve incompatible info, and that get undefined ambigous.

I have no idea what you are talking about here. Again, you seem to be reading things into Bell's theorem that are simply not there. None of this is anywhere in Bell's paper. It's much simpler than you appear to be trying to make it.