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.

 

[PeterDonis]

This transition implies the following assumptions:
- $A(a, b, \lambda) =\pm 1, B(a, b, \lambda) = \pm 1$ (aka determinism assumption)

Yes, Bell assumes that the measurement results are predetermined, so his theorem only applies to models for which that is true.

- $A(a, b, \lambda) = A(a,\lambda), B(a, b, \lambda) = B(b,\lambda)$ (aka locality assumption)

Yes. As I said before, I was calling this assumption "factorizability", but Bell does use "locality" to refer to the underlying rationale for it--basically that A's measurement settings can't affect B's results, and vice versa.

- $\rho(a,b,\lambda) = \rho(\lambda)$ (aka, no enhancement, free-will assumption)

No, this is not an assumption. The joint probability being calculated is for measurement results $A$ and $B$ given measurement settings $a$ and $b$. There is no integration over $a$ and $b$, and $\rho$ is not a function of them; $\rho$, as Bell explicitly states, is the probability distribution for $\lambda$, which is the only thing that is integrated over.

 

[Fra]

It's much simpler than you appear to be trying to make it.

Finally something we agree on.

The question is, if reality is as simple as the ansatz in Bells paper? I think not.

I thought it was obvious that I am reconsidering the premises of Bell's assumptions. In particular what is NOT explicitly there, by either beeing implicit and not elaborated or simply overlooked by Bell or both.

My firm opinion is that the "simpler picture" simplifies things too much, and from my perspective (not Bell's original) seems to have a too simple mental model of the nature of micro-causality in interactions between parts of the system. You are correct that this is not explicitly mentioned in Bell's paper.

Baranders picture here gives another perspective. But it is painfully clear how hard it is to convey, and perhaps we need to await the explicit reconstruction from the other perspective, to convinced everyone. That does not exist yet, which is why I try to convey it conceptually.

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


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.

If you and Bell holds the simpler "mental model" that the outcomes can be partitioned by "common factors", some of which we as physicists are ignorant; then that clearly illustrates the oversimplification, that perhaps satisfieds some, but not me. This is exactly the problem, and also why I think what I say makes no sense to you.

The difference beweteen "ignroance" and variables that are known only to parts, is why certain hidden paramters, isn't compatible with the preparation, and thus don't commute in the information processing chain. This is why the simple form of partitioning is an oversimplification. And this is also at the heart of Baranders indivisibility, but you can put it in different ways, but it's related.

/Fredrik

 

[PeterDonis]

The question is, if reality is as simple as the ansatz in Bells paper? I think not.

So far I have not seen from you a correct description of the ansatz in Bell's paper. I think you need to get that right first before trying to form an opinion about it.

If you and Bell holds the simpler "mental model"

We don't. Once more, this "mental model" is something you're reading into Bell's paper that simply isn't there. Bell does not have any specific "mental model" underlying his assumptions; his theorem applies to any model whatever that satisfies the assumptions.

 

[martinduclocher]

sorry to disturb you, but in the barandes approach, knowing that there is no accessible phase and that only the transition probabilities are accessible due to the squaring of the unit matrix. So it's not possible to reconstruct the wave function experimentally ? and have access to phases and amplitudes, which puts its approach in tension with what can be done experimentally . I'm an amateur, so what I say may be inaccurate.

 

[pines-demon]

sorry to disturb you, but in the barandes approach, knowing that there is no accessible phase and that only the transition probabilities are accessible due to the squaring of the unit matrix. So it's not possible to reconstruct the wave function experimentally ?

There is no wave function in Barandes approach...

 

[martinduclocher]

Yes, but the fact that we can experimentally reconstruct the wave function and see that the way it interacts, for example in this experiment, or the way the wave functions interact with each other, dictates the polarization of the material. How can we understand this in the vision of barrrandes? https://arxiv.org/abs/2102.02266
Similarly, how can we understand phenomena such as the bose-einstein condensate in barrandes' vision if there are no more physical waves? Sorry in advance if my porpos is confusing but I would like to understand

 

[pines-demon]

Yes, but the fact that we can experimentally reconstruct the wave function and see that the way it interacts, for example in this experiment, or the way the wave functions interact with each other, dictates the polarization of the material. How can we understand this in the vision of barrrandes? https://arxiv.org/abs/2102.02266
Similarly, how can we understand phenomena such as the bose-einstein condensate in barrandes' vision if there are no more physical waves? Sorry in advance if my porpos is confusing but I would like to understand

That's what this thread is about. I'm not sure that any of us understand what Barandes interpretation really means (I think he is lacking ontology). However we know what are the rules of the game from his stochastic-quantum correpondence. In his dictionary, the wave function is just an operator that when squared tells you about the conditional probabilities. You can always construct such an operator from any given set of probabilities, it is only that in Barandes' formulation "it is no longer wavy".

What you want to understand is how interference arises, like the interference in a double slit experiment or in interacting Bose-Einstein condensates (which is usually a wave like phenomenon). For the double slit this is what Barandes says:

According to the approach laid out in this paper, the particle really does go through a specific slit in each run of the experiment. The final interference pattern on the detection screen is due to the generic indivisibility of time evolution for quantum systems. One cannot divide up the particle’s evolution into, firstly, its transit from the emitter to the slits, and then secondly, conditioned on which slit the particle enters, the particle’s transit from the slits to the detection screen. The interference that shows up in the double-slit experiment may be surprising ,but that is only because indivisible stochastic dynamics can be highly nonintuitive. In the historical absence of a sufficiently comprehensive framework for describing indivisible stochastic dynamics, it was difficult to recognize just how nonintuitive such dynamics could be, or what sorts of empirically appearances it could produce.

After having read and listened to Barandes, I still do not have a clear toy model in my head on how indivisibility gives rise to quantum stuff.

 

[Sambuco]

$\Gamma_{i,j}(t)$ 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.

Thanks for your answer @iste!

I don't fully understand how this happens in Barandes' formulation. Given the quantum-stochastic correspondence, after an interaction between two subsystems, the composite system's transition matrix cannot be factorized, which seems to be equivalent to the non-separable (entangled) wave function. Therefore, if the transition matrix is supposed to play the role of a "dynamical law" as he repeatedly acknowledges throughout the paper, measuring one of the susbystems should "afect" the entire transition matrix.

Lucas.

 

[martinduclocher]

thank you for your reply, but if I understand correctly, the barrandes approach in the context of Bec would no longer be a wave phenomenon? That's right, but it's becoming complex to explain the topological effects linked to the wave function.

 

[iste]

Thanks for your answer @iste!

I don't fully understand how this happens in Barandes' formulation. Given the quantum-stochastic correspondence, after an interaction between two subsystems, the composite system's transition matrix cannot be factorized, which seems to be equivalent to the non-separable (entangled) wave function. Therefore, if the transition matrix is supposed to play the role of a "dynamical law" as he repeatedly acknowledges throughout the paper, measuring one of the susbystems should "afect" the entire transition matrix.

Lucas.

When a measurement happens, the entangled system is no longer entangled - a division event occurs - which I believe might be linked to why there is no signalling. The non-separability is lost whenever the system is disturbed so the measurement device can only interact with the part of the formerly entangled system in its local vicinity, without affecting the distant part.

 

[PeterDonis]

When a measurement happens, the entangled system is no longer entangled

This depends on which interpretation of QM you use. In no collapse interpretations, like the MWI, measurements do not remove entanglement; they extend it to include the measuring devices.

 

[Sambuco]

When a measurement happens, the entangled system is no longer entangled

Yes (in a single-world interpretation, as @PeterDonis clarifies), but for the measurement results to be Bell-correlated, the state of the remote particle must "collapse" into a specific state, depending on the measurement result obtained on the other particle. Otherwise, the correlation would not hold. "Translating" this into the language of Barandes' formulation, the transition matrix $\Gamma(t)$ changes discontinously. I don't see how to avoid that and at the same time reproduce Bell correlations.

Lucas.

 

[iste]

This depends on which interpretation of QM you use. In no collapse interpretations, like the MWI, measurements do not remove entanglement; they extend it to include the measuring devices.

Yes, I was just describing the Barandes entanglement; but there is some at least partial overlap since he explicitly requires inclusion of measurement devices so the loss of entanglement for the measured system coincides with entanglement between a measurement device and one of the measured subsystems. Neither is there collapse for Barandes.

 

[iste]

Yes (in a single-world interpretation, as @PeterDonis clarifies), but for the measurement results to be Bell-correlated, the state of the remote particle must "collapse" into a specific state, depending on the measurement result obtained on the other particle. Otherwise, the correlation would not hold. "Translating" this into the language of Barandes' formulation, the transition matrix $\Gamma(t)$ changes discontinously. I don't see how to avoid that and at the same time reproduce Bell correlations.

Lucas.

This is only the case if you interpret the wavefunction as the particle. But in the Barandes formulation, there is no physical wavefunction - instead it represents statistics of particles when you repeat an experiment many times. But in any given repetition of the experiment, the particle always is in one definite configuration, in one definite position, moving along a definite path.

Collapse in the Barandes formulation is just statistical conditioning which is physically meaningless; physical collapse is unecessary because the particles that exist always have definite configurations anyway. Everything meaningful to say about the quantum behavior is in the long run statistics, even when something ends up in a state with probability 1. Rather than a measurement causing a delocalized superposition to collapse into two matching configurations, particle's statistical behaviors became correlated at a local interaction, and their correlated behaviors just continue over time as they travel, until measurement. I may do a follow up post a bit later.

 

[Fra]

Rather than a measurement causing a delocalized superposition to collapse into two matching configurations, particle's statistical behaviors became correlated at a local interaction, and their correlated behaviors just continue over time as they travel, until measurement.

I think this a good description, and it is the point: it's not the outcomes that are predetermined (this is only a presumed argument based on the local realist dynamics), it's the correlations. And that is tentatively accomplished by means of pre-correlated transition matrixes of the correlated systems; this is the same to say that the two correlated systems have "correlated behavioral responses", and this IMO is what explaines the correalation, but NOT each individual outcomes as the idea is with the non local system dynamics.

When the two systems have become correlated, the indeed "remember" and this is the kind of "hidden variable" that explains the correlated behaviour, so that their interactions with respective detector is correlated regardless of detector settings. This is how I see it. This "memory effecty" is simply hard to model with system dynamics in a intuitive way - it unavoidably "shows up" as weird non-local stuff, but when it's in fact not necessarily non-locally mediated.

To understand the difference between "behaviour" and pre-correlated output, I find the agent based model conceptually superior to system dynamics, because instead of modelling the whole happening as a deterministic evolution of a state as per a fixed dynamical law; we can interacting parts that in principle are autonomous - but can become correlated in their behaviour - because they share a history.

So it seems to me that non-locality is an artifact from the system dynamics paradigm. A no-go theorem that are related to local system dynamics theories (where by construction the hidden variables are global), hardly apply to theories based on agent based models where hidden variables can be shared between a couple of agent only. It's generally considered that agent based models form a larger theory space than system dynamics.

I can't help but associating Baranders stochastic guided process, byt the stochastic learning process of an "agent"(ie any subsystem), but Barandes description of the agent are still not intrinsic, they are extrinsic, which is I think why he manages to get the actual correspondende to QM. I think a true intrinsic "agent" would only have a correspondence to quantum mechanics in a limiting case. This is the relation to Baranders picture and my own preferred perspective. If someone suggests there is a similar no-go theorem also for any agent based model theories, then I would be deeply confused and i have never seen it.

But what makes this still hard to accept conceptually, is that Baranders only (but it's a good start) provices a correspondence, there is stil no indepdent first principle explanation of WHY we have these indivisible general stochastic sytems, and in particular from where we get this time dependent stochastic matrices; which I see as the key to unification progress. I personally like it, but you have to fill in the gaps on your own. It's just acorrespondence after all, not a full reconstruction. But in such a possible reconstruction Baranders correspondence will likely be an importance "correspondence checkpoint" between paradigm.

/Fredrik

 

[iste]

This "memory effecty" is simply hard to model with system dynamics in a intuitive way - it unavoidably "shows up" as weird non-local stuff, but when it's in fact not necessarily non-locally mediated.

To understand the difference between "behaviour" and pre-correlated output, I find the agent based model conceptually superior to system dynamics, because instead of modelling the whole happening as a deterministic evolution of a state as per a fixed dynamical law; we can interacting parts that in principle are autonomous - but can become correlated in their behaviour - because they share a history.

I am not familiar with your agent-based model to understand how this would work; e.g., how would the autonomy work? But I actually think the "memory effect" can be given a reasonably intuitive description, at least from my interpretational perspective.

I believe the "memory effect" is described by these papers by Wharton et al. and Sutherland examining spin weak values that carry information about the intermediate time before a final spin measurement. These spin weak values (both real and imaginary parts) are constant through intermediate times and only depend on the spin directions at initial and final times, which each fix a spin component of the weak value:

"For each possible result, the smallest vector that conforms to both of these constraints, without changing between measurements, is precisely Re(w±)" (Wharton et al.).

The spin weak value calculations in Berry (2011) [section 2] also gives a picture of constant spin values only constrained by pre- and post-selected spin directions. So this seems to be the memory effect - a constant spin vector between initial preparation and final measurement. But the problem is that it kind of looks like retrocausal influence from measurement settings to intermediate times.

But we can look at what they are saying directly from a stochastic mechanical perspective because stochastic mechanical current and osmotic velocities are identical to the real and imaginary momentum weak values, respectively, including for spin. Current velocities (the real part) are constructed using expectations from ensembles of particle trajectories, as explicitly depicted by de Matos et al. (2020) here:

https://images.app.goo.gl/cC2oj

Osmotic velocities (imaginary part) describe the tendency of particles to climb the probability gradient. The expectations of the quantum mechanical momentum and spin operators directly correspond to expectations of stochastic mechanical current velocities (e.g. de Matos, 2020) [section 4.3] - i.e. weak values in the orthodox formalism: Hiley (2012) (6th equation); Hosoya & Shikano (2010) [equations (3)].

In the orthodox picture, spin is a property of an individual particle which then changes at the point of measurement, which is difficult to reconcile in a locally realistic manner. But in stochastic mechanics, spin clearly cannot be identified with any individual particle; it is only meaningful  statistically on the level of ensembles of particle trajectories. This opens up the possibility that different measurement orientations just partition whole (counterfactual) ensembles of intermediate trajectories, associated with an initially prepared spin, in different ways that have different spin statistics in accordance with the current and osmotic spin velocity fields. If you think about it, what Malus' Law cos^2θ when applied to photons is telling you is just how particles will be distributed across two ensembles in terms of relative frequencies / probabilities. Stochastic mechanics is then just saying that the related spin or polarization directions are to do with the statistics associated with each ensemble as a whole.

In the Wharton et al. qubit example you also see that:

"the weighted average of w+ and w− (using their Born-rule probabilities) is exactly (0, 0, 1), with no imaginary part surviving. This average matches ˆi [the initial spin]".

This description seems to be related to how before I said quantum mechanical spin expectations can be described as expectations of weak values, Wharton et al. earlier mentioning this themselves in the paper:

"Nevertheless, in the usual situation where the result of the final measurement is unknown and a weighted average is taken over the possible outcomes, the weak value Re(W[A])(t) can then be shown to be exactly equal to the usual expectation value ⟨A⟩(t)".

From the stochastic mechanical view, the quotes are then saying that the initially prepared spin statistics are related to the statistics of its post-selected components by just a very conventional expectation. That seems to me exactly what you would expect if the final spin outcomes just came from partitioning an ensemble of intermediate trajectories into different subsets which each have different statistics - like any other kind of post-selection in statistics. Its then difficult for me to understand from this perspective why some extra weirdness like retrocausality would be needed (I don't think retrocausality even makes any sense to be honest).

Because any sub-ensemble's statistics at preparation are "remembered" up to final measurement, then in an entanglement scenario you can get the Bell state correlations by having a perfect correlation locally fixed between any and all sub-ensembles of entangled pairs. Obviously, the correlation can actually only be physically, methodologically imposed on particles one pair at a time that go through the experimental set up; experimental repetition then would build up (sub-)ensembles with the appropriate statistics.

 

[Sambuco]

Rather than a measurement causing a delocalized superposition to collapse into two matching configurations, particle's statistical behaviors became correlated at a local interaction, and their correlated behaviors just continue over time as they travel, until measurement.

You're right, measurement does not collapse the configuration of the system. Instead, "collapse" means that the measurement causes the system's transition matrix to change discontinously. Let me give an example. Suppose two particles interact at time $t_0$ and become entangled. Then, Alice measures particle A at $t_1$, while Bob measures particle B at $t_2$ ($t_2 > t_1$). For $t_0 < t < t_1$, the system's transition matrix does not factorize, i.e. $\Gamma_{A,B}(t) \neq \Gamma_A(t) \otimes \Gamma_B(t)$. When Alice measures particle A, as you said in post #640, a division event ocurrs and the system is no longer entangled. So, for $t_1 < t < t_2$, the transition matrix factorize. But the question is: What is the transition matrix $\Gamma_B(t)$ for time evolution of particle B after Alice measured particle A, but before Bob measures particle B. Given the "dictionary" that Barandes introduced to construct the Hilbert space from his stochastic formulation, $\Gamma_B(t)$ after Alice's measurement should correspond to the wavefunction of particle B, which results from the "collapse" of the global wavefunction, according to the remote measurement outcome obtained by Alice. Otherwise, I don't see how Bell correlations could be satisfied. In addition, if we don't know which outcome Alice obtained, we have to consider a statistical mixture.

Collapse in the Barandes formulation is just statistical conditioning which is physically meaningless; physical collapse is unecessary because the particles that exist always have definite configurations anyway.

I slightly disagree. Collapse is just statistical conditioning in information-based interpretations, such as Copenhagen and relational QM where the system has no definite configuration between measurements. Instead, Barandes interprets the system's transition matrix as a dynamic law that plays a nomological role. So collapse is conditioning, as you said, but it's more than that. That's why, in post #638, I made the analogy with the modern view on Bohmian mechanics à la Dürr-Goldstein-Zanghi (https://arxiv.org/abs/quant-ph/9512031). In that sense, we can also say that the effective collapse in Bohmian mechanics can be interpreted as "conditioning", in the same way Barandes say that, after a measurement (division event), "system's density matrix $\rho^S(t)$ can equivalently be expressed as a probabilistic mixture of the conditional density matrices $\rho^{S|\alpha',t'}(t)$ statistically weighted by the measurement probabilities $p_{d(\alpha')}^D(t')$".

Lucas.

 

[Fra]

Got buried in other stuff for a couple of days.

I am not familiar with your agent-based model

I was not referring here to any specific agent-based model as that would get into explicit speculation, I was speaking more of the different paradigms, just to highlight that herein is room for explanation.

In system dynamics, we have a state space, initial conditions and dynamical laws, in differential form; this i essentially timeless, as the future state follows from the initial state and law in a computationally trivial way.

In agent based models, there is not one state space, but more like a "population of statespaces" (ie population of "agents") and there are, initial conditions for each state space, and some rule for how the agent evolves, and interacts with the environment and other agents. The actual evolution of this system is highly non-trivial, and perhaps even computationally irreducible, so one can conceptualize evolution as an "irreducible computation", which is more like a cosmological kind of time; much different than the "parametertime" that you have in system dynamics; which is trivial in comparasion.

In agent based models relations to other agents can be fully emergent, so instead of an external spacetime embedding, relations can emergent - but in a non-trivial way that can't be captured by dynamical law. So certain "mechanism" might be possible to simulate in agent based paradigm, but not necessirly in system dynamics. After all the advantage of agent based models is the focus on mechanism and emergence, rather than overall system evolution. So the notion of "loca causality" needs to be different, one can in ABM note DEFINE it with respect to the external embedding - instead the conditional probabilities independence as Baranders defines it seems the way to go, but t here is still the detail of wether you consider objective or subjective bayesian probabilities.

So the crude idea is that agent based models are more general than sytem dynamics, and can model more heterogenous and non-continous systems, and has natural emergence. Thus I think - a nogo theorem for theoreis in system dynamics paradigm, is not automatically a nogo theorem for theories in agent based models.

Agent-based computational models and generative social science​

Tutorial on agent-based modelling and simulation​

to understand how this would work; e.g., how would the autonomy work?

Conceptually "agents" would be a priori independent stochastic processes or have independent "time evolutions".

But as the interact, they influence each others future even after they "separate". Ie. they are both affected by a common past in a broad sense. There are two kinds of memory I see; one from the actual interaciton(LOCAL hidden memory) and memory with common environment(global shared memory). Entanglement would be like a common past event which happens between two agents now, and as long as they are not disclosed, interacting with all OTHER agents (and in particular the environment, detectors) would be an inteacting between agents that is informed about the preparation proceduire only - (ie "statistics") and the agent that has a hidden variable.

To explain the exact details satisfactory from more agent first principles one would need an explicit toy model, including a toy model for the emergent space, which is why "locality" itself is challenged.

/Fredrik

 

[iste]

Given the "dictionary" that Barandes introduced to construct the Hilbert space from his stochastic formulation, ΓB(t) after Alice's measurement should correspond to the wavefunction of particle B, which results from the "collapse" of the global wavefunction, according to the remote measurement outcome obtained by Alice. Otherwise, I don't see how Bell correlations could be satisfied. In addition, if we don't know which outcome Alice obtained, we have to consider a statistical mixture.

This doesn't happen. It has to be emphasized that in Barandes' formulation, measurements don't produce results. The coupling of the measurement device to a sub-system of an entangled pair is not a one-shot event that causes an outcome, its a statistical description of two statistically coupled systems. So there is then no obligation to change what is going on at the otherside of the now-factorized transition because invoking the measurement device doesn't single out a result. You can invoke statistical conditioning but thats not physical, it is what a statistician does at his desk.

So yes, I think Barandes' theory doesn't consider anything more than statistical mixtures, and there is no inherent problem with this. People describe systems out in the world statistically like this allthe time. I think in quantum mechanics though there is just this extremely strong, in-grained intuition that the theory should be about the behavior of a single particle that tells you what its doing and exactly where it is at some specific moment. But the kind of stochastic interpretation by Barandes or others explicitly does not view quantum theory like this. And historically, I believe collapse is an extra postulate. Its not even an intrinsic part of the theory, its something that was put there because people found the interpretation of the formalism confusing.

In that sense, we can also say that the effective collapse in Bohmian mechanics can be interpreted as "conditioning",

Well surely effective collapse is somethg more than conditioning because its involving the pilot wave or wavefunction or whatever. But in the Barabdes formulation we are just talking about random variables so it is in fact straightforwardly just statistical conditioning like in any other statistical topic. And because Bohmian mechanics explicitly has non-local instantaneous influence, its very difficult to say that it is local without having a very good way of explaining away the formalism itself. But in the Barandes formulation I don't believe such non-local influence has been seen to arise like it does in Bohmian mechanics as of yet.

 

[PeterDonis]

in Barandes' formulation, measurements don't produce results

Does that mean that Barandes is using the MWI? Note that in standard statistical interpretations, such as Ballentine's, measurements do produce results. The quantum state is not interpreted as describing individual systems in these interpretations, only ensembles, so the collapse process in the math doesn't correspond to an actual physical state change on an individual systems. But Barandes, though he talks about statistics, does not appear to be using such a statistical interpretation: he appears to be interpreting the state as describing individual systems, not ensembles. In that context, "measurements don't produce results" seems to me to imply the MWI.