Understanding Barandes' microscopic theory of causality

[iste]

Most interpretations require some speculative import. But iiuc you are saying this requires some additional contrivance above and beyond other interpretations and I just don't see it.

For example, while the conditional probabilities are sparse, the standalone probabilities are not, and interpreting these epistemically as about a configuration actually existing at all times seems no more burdensome than the myriad of worlds in the MWI or the exotic guiding wave nomology of Bohmian mechanics.

Sure, but the supposed philosopical contribution of the indivisible approach is compromised because you can't say it implies any novel interpretation without begging the question and presupposing that interpretation. If the formalism doesn't specify a trajectory then I can interpret it in anyway I want. Sure, the interpretation isn't refuted but the indivisible formalism doesn't actually contribute anything to or imply the interpretation by itself.

 

[Morbert]

Sure, but the supposed philosopical contribution of the indivisible approach is compromised because you can't say it implies any novel interpretation without begging the question and presupposing that interpretation. If the formalism doesn't specify a trajectory then I can interpret it in anyway I want. Sure, the interpretation isn't refuted but the indivisible formalism doesn't actually contribute anything to or imply the interpretation by itself.

There's no question begging, as the interpretation, like any other interpretation, is presented as an interpretation, not a self-justifying conclusion.

 

[Sambuco]

One can prove that every finite- rank density matrix can be written as a convex combination of projectors, and that every density matrix can be written as the limit of a family of convex combinations of projectors.

Thanks @A. Neumaier! Is this true if we limit ourselves to a single basis? I understand that the work referred to projectors associated with definite configurations.

Lucas.

 

[Sambuco]

There's no question begging, as the interpretation, like any other interpretation, is presented as an interpretation, not a self-justifying conclusion.

I think what @iste points out is interesting and reveals something particular about Barandes' interpretation. It's common to postulate a primitive ontology in $\psi$-ontic interpretations, such as Bohmian mechanics or many-worlds. In those cases, the actual configuration of the system appears explicitly in the equations that define its dynamics. For example, there's the guiding equation that defines the evolution of Bohmian particles. This isn't quite the case in $\psi$-epistemic interpretations, where the ontology is more open to discussion. Barandes' interpretation sits somewhere in between, since it postulates a clear ontology formed by definite positions in configuration space, while the central variable of the formulation is not these configurations themselves, but the evolution over time of the epistemic probabilities associated with them. This means that, as we've already mentioned, the current configuration of the system doesn't influence the evolution of these probabilities.

Lucas.

 

[Morbert]

I think what @iste points out is interesting and reveals something particular about Barandes' interpretation. It's common to postulate a primitive ontology in $\psi$-ontic interpretations, such as Bohmian mechanics or many-worlds. In those cases, the actual configuration of the system appears explicitly in the equations that define its dynamics. For example, there's the guiding equation that defines the evolution of Bohmian particles. This isn't quite the case in $\psi$-epistemic interpretations, where the ontology is more open to discussion. Barandes' interpretation sits somewhere in between, since it postulates a clear ontology formed by definite positions in configuration space, while the central variable of the formulation is not these configurations themselves, but the evolution over time of the epistemic probabilities associated with them. This means that, as we've already mentioned, the current configuration of the system doesn't influence the evolution of these probabilities.

@iste is not merely remarking that the interpretation is peculiar. He is framing it as question begging when instead the microphysical ontology of this interpretation is, as Barandes says, "a speculative metaphysical hypothesis", which are standard ingredients to an interpretation.

 

[Sambuco]

@iste is not merely remarking that the interpretation is peculiar. He is framing it as question begging when instead the microphysical ontology of this interpretation is, as Barandes says, "a speculative metaphysical hypothesis", which are standard ingredients to an interpretation.

Yes, I understand. My comment, somewhat independent of @iste's opinion, is that Barandes' interpretation has the curious characteristic of combining a well-defined ontology with dynamic laws that don't speak directly about it, but only about what each observer can say about it, in the spirit of the Bohr's quote "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature." I don't think this invalidates the interpretation, of course.

Lucas.

 

[iste]

There's no question begging, as the interpretation, like any other interpretation, is presented as an interpretation, not a self-justifying conclusion.

I disagree. I think its throughout his lectures; interviews; and papers, his interpretation and the formalism are put in one box and a clear distinction between them is never made. I think Barandes thinks the formalism justifies his interpretation, but I don't think it does. If Barandes does not distinguish the formalism from his interpretation of it then I think he is begging the question imo.

 

[Morbert]

I disagree. I think its throughout his lectures; interviews; and papers, his interpretation and the formalism are put in one box and a clear distinction between them is never made. I think Barandes thinks the formalism justifies his interpretation, but I don't think it does. If Barandes does not distinguish the formalism from his interpretation of it then I think he is begging the question imo.

The formalism is what allows us to understand quantum systems as a sufficiently general kind of stochastic process, but the formalism does not depend on the interpretation. The formalism is instead justified by its correspondence with standard quantum theory. If you want to interpret these standalone probabilities and indivisible stochastic maps as about measurement outcomes, go right ahead, but it is distinct from the interpretation Barandes develops.

Can you be more specific in your objections? E.g. By quoting something from the papers you find objectionable? Because so far I don't see any distinction between the interpretational commitments asked of here vs any other interpretation.

 

[iste]

go right ahead, but it is distinct from the interpretation Barandes develops.

Barandes has never made this distinction though. He presents it as one indivisible approach. And if the interpretation is different from the formalism then I would say it is incomplete in the sense that the most successful interpretations that postulate trajectories are accompanied by formulations of those trajectories. The interpretation lacks this.

 

[pines-demon]

The most visible problem in Barandes unistochastic formalism as an interpretation is that there is no example of it outside quantum mechanics.

 

[Morbert]

Barandes has never made this distinction though. He presents it as one indivisible approach.

His argument is that "every quantum system can be understood as a sufficiently general kind of stochastic process unfolding in an old-fashioned configuration space according to ordinary notions of probability". You are insisting he is arguing the correspondence he establishes forecloses alternative interpretations. He's not. You are perfectly free to accept the correspondence between a class of indivisible stochastic processes and quantum theory, while rejecting the metaphysical hypothesis of a microphysical ontology.

And if the interpretation is different from the formalism then I would say it is incomplete in the sense that the most successful interpretations that postulate trajectories are accompanied by formulations of those trajectories. The interpretation lacks this.

The question is whether this is a subjective preference of yours or an objective deficiency of the interpretation.

 

[A. Neumaier]

Thanks @A. Neumaier! Is this true if we limit ourselves to a single basis?

The statement is basis-independent. For example, any $\rho=\pi\psi^*$ with normalized $\psi$ is a rank 1 projector.

I understand that the work referred to projectors associated with definite configurations.

Given a Hilbert space and a Hamiltonian (and hence a physical system), what is a definite configuration?

 

[Morbert]

Given a Hilbert space and a Hamiltonian (and hence a physical system), what is a definite configuration?

From https://arxiv.org/html/2507.21192v1
"Schur-Hadamard products are not widely used in linear algebra, in part because they are basis-dependent. For the purposes of analyzing a given indivisible stochastic process, however, this basis-dependence is unimportant, because the system’s configuration space 𝒞 naturally singles out a specific basis, to be defined momentarily."

On the unistochastic side of the correspondence, the physical system would be given by a configuration space and a dynamical stochastic map, and hence the configuration space would yield a configuration basis for the corresponding Hilbert space.

 

[A. Neumaier]

From https://arxiv.org/html/2507.21192v1
"Schur-Hadamard products are not widely used in linear algebra, in part because they are basis-dependent. For the purposes of analyzing a given indivisible stochastic process, however, this basis-dependence is unimportant, because the system’s configuration space 𝒞 naturally singles out a specific basis, to be defined momentarily."

On the unistochastic side of the correspondence, the physical system would be given by a configuration space and a dynamical stochastic map, and hence the configuration space would yield a configuration basis for the corresponding Hilbert space.

So it is extra structure assumed, beyond the textbook requirenments for a quantum system. Not a good sign for an interpretation of quantum mechanics.

 

[iste]

You are insisting he is arguing the correspondence he establishes forecloses alternative interpretations

But he doesn't transparently distinguish formalism from interpretation and even makes specific arguments against other interpretations like Bohm, Many-worlds, Copenhagenism. The distinction between a "general stochastic process" (which could be a misnomer given what is said in the arxiv paper I think Sambuco linked) and a separate underlying interpretation of the formalism doesn't exist in Barandes papers or talks.

The question is whether this is a subjective preference of yours or an objective deficiency of the interpretation.

Well I don't think its just a subjective concern solely of mine in the sense that if people just uncritically accepted the idea of trajectories, Bohmian mechanics probably wouldn't have been invented as a kind of proof-of-plausibility.

As I said before, I think logically-speaking, postulating objective trajectories entails some underlying description(s) that doesn't exist in the indivisible approach in the sense that there would be objective frequencies in any experiment that the indivisible approach cannot speak about in any way whatsoever. My preference is that there is an even more fundamental theory underneath the indivisible approach which then would relieve this burden. What I see as the alternative is some kind of top-down causation from the indivisible description onto the trajectories so that in some sense the indivisible description is more fundamental than the underlying trajectories.

 

[Morbert]

But he doesn't transparently distinguish formalism from interpretation and even makes specific arguments against other interpretations like Bohm, Many-worlds, Copenhagenism. The distinction between a "general stochastic process" (which could be a misnomer given what is said in the arxiv paper I think Sambuco linked) and a separate underlying interpretation of the formalism doesn't exist in Barandes papers or talks.

You're confusing criticism of other interpretations (which he does) with insisting a formalism necessitates a metaphysical hypothesis (which he doesn't). I.e. Arguing for the merits of an interpretation by pointing out difficulties in others is clearly distinct from arguing an interpretation is true because there is a formalism that offers it.

As I said before, I think logically-speaking, postulating objective trajectories entails some underlying description(s) that doesn't exist in the indivisible approach in the sense that there would be objective frequencies in any experiment that the indivisible approach cannot speak about in any way whatsoever.

Then show this entailment.

 

[gentzen]

The question is whether this is a subjective preference of yours or an objective deficiency of the interpretation.

As I said before, I think logically-speaking, postulating objective trajectories entails some underlying description(s) that doesn't exist in the indivisible approach in the sense that there would be objective frequencies in any experiment that the indivisible approach cannot speak about in any way whatsoever.

I guess, the biggest contribution of Barandes' "interpretation" is that it shows just how difficult it is to convincingly "disprove" an interpretation, or at least to nicely explain why it feels really unsatisfactory (in its current form).

You might think that Copenhagen and Bohmian mechanics demonstrate this just as nicely. But people look for shortcuts and invent strawman's, like the instantaneous collapse of the wavefunction as a physical process, suppossedly postulated by Copenhagen, or the trouble of BM with Lorentz covariance. But that stuff is too easy, the challenge would be to explain the real deep flaws, like Barandes' discontinuous trajectories lacking any causal power.

 

[iste]

You're confusing criticism of other interpretations (which he does) with insisting a formalism necessitates a metaphysical hypothesis (which he doesn't). I.e. Arguing for the merits of an interpretation by pointing out difficulties in others is clearly distinct from arguing an interpretation is true because there is a formalism that offers it

This is a fine criticism if there is evidence that Barandes transparently distinguishes interpretation from formalism. Point it out.

Then show this entailment.

I already discussed it earlier. If there are definite trajectories and a particle has a definite position at all times in an experimental trial then logically someone would be able to count the frequencies of this if they were able to observe the particle at every time. This gives you a description of frequencies of any experiment you care to make. It doesn't matter if those frequencies might be complicated or something, they exist and they won't be accounted for by the indivisible formalism.

 

[lodbrok]

This is a fine criticism if there is evidence that Barandes transparently distinguishes interpretation from formalism. Point it out.

If you go back to the video that was posted (the discussion with Tim Maudlin), starting at exactly 1:58:55 up to about 2:17, and pay close attention, this is the clearest explanation that Barandes has given of his approach, very clearly distinguishing interpretation from formalism.

 

[iste]

If you go back to the video that was posted (the discussion with Tim Maudlin), starting at exactly 1:58:55 up to about 2:17, and pay close attention, this is the clearest explanation that Barandes has given of his approach, very clearly distinguishing interpretation from formalism.

Well you'll have to point out the distinguishing going on because it's not immediately apparent to me when watching that.

 

[lodbrok]

Well you'll have to point out the distinguishing going on because it's not immediately apparent to me when watching that.

He presents a simple dynamical system with 17 states with dynamics that is cyclical (ontology). The system can be represented with a 17-dimensional vector (formalism), the dynamical law for the system can be represented as a matrix (formalism), modelling the dynamical evolution of the system by repeated matrix multiplication of the vector with the matrix(formalism), etc, etc. At every point the separation between what is the formalism vs what is ontology is very clear to me. What part isn't clear to you?

 

[iste]

He presents a simple dynamical system with 17 states with dynamics that is cyclical (ontology). The system can be represented with a 17-dimensional vector (formalism), the dynamical law for the system can be represented as a matrix (formalism), modelling the dynamical evolution of the system by repeated matrix multiplication of the vector with the matrix(formalism), etc, etc. At every point the separation between what is the formalism vs what is ontology is very clear to me. What part isn't clear to you?

Theres no transparent distinction between formalism and interpretation here, putting interpretation in a nice box unambiguously distinct from interpretation-independent formalism. I don't know if this description has any interpretation in it. You could list off orthodox quantum axioms like that without implying any interpretation. At the same time, Barandes could be assuming interpretation in this and I wouldn't know because it would be implicit, though that very well could be the case. I don't see a clear transparent distinction being explicitly laid out in that section.
.

 

[Morbert]

This is a fine criticism if there is evidence that Barandes transparently distinguishes interpretation from formalism. Point it out.

"This paper argues that every quantum system can be understood as a sufficiently general kind of stochastic process." The correspondence is not a necessary condition for the interpretation.

I already discussed it earlier. If there are definite trajectories and a particle has a definite position at all times in an experimental trial then logically someone would be able to count the frequencies of this if they were able to observe the particle at every time.

Yes we have discussed this earlier, and I said the knowing of something by an omnipotent being does not mean that thing has a regular lawlike expression. What are regular are the time-parameterized standalone probabilities, and any distribution built from combinations of these.

This gives you a description of frequencies of any experiment you care to make. It doesn't matter if those frequencies might be complicated or something, they exist and they won't be accounted for by the indivisible formalism.

The formalism is perfectly capable of giving you a description of frequencies of any experiment (or sequence of experiments) you care to make, as you are a mortal who must couple the system to an apparatus to learn anything about it.

 

[lodbrok]

Theres no transparent distinction between formalism and interpretation here, putting interpretation in a nice box unambiguously distinct from interpretation-independent formalism. I don't know if this description has any interpretation in it. You could list off orthodox quantum axioms like that without implying any interpretation. At the same time, Barandes could be assuming interpretation in this and I wouldn't know because it would be implicit, though that very well could be the case. I don't see a clear transparent distinction being explicitly laid out in that section.
.

Then I don't know what you mean by "interpretation".

 

[gentzen]

Then I don't know what you mean by "interpretation".

iste is talking about Barandes' formalism. In your example, Barandes talks about the normal Hilbert space formalism of QM. This doesn't help with the unclear distinction between his (or Morbert's?) interpretation of QM and (Barandes' formulation of) the math of indivisible stochastic processes.

 

[lodbrok]

iste is talking about Barandes' formalism. In your example, Barandes talks about the normal Hilbert space formalism of QM. This doesn't help with the unclear distinction between his (or Morbert's?) interpretation of QM and (Barandes' formulation of) the math of indivisible stochastic processes.

It's not my example, it's Barandes' and he is talking about his formalism. Certainly he draws parallels with the Hilbert space formalism but I'm struggling to see what iste's issue is. To just say "I don't know if this description has any interpretation in it" seems too hand-wavy to me, some specifics would be helpful.

 

[iste]

Then I don't know what you mean by "interpretation".

Interpretation in the sense of any regular quantum interpretation. There is the Hilbert-space formalism, and then how people choose to interpret that. I am talking about how, in the same way, there is the indivisible stochastic formalism and then how you give an interpretation to that formalism. Barandes uses the indivisible formalism to present an interpretation where a single particle takes a trajectories with definite configurations at all times. I am saying that the formalism doesn't specify this interpretation.

Morbert has been saying something like there is no problem because you can interpret the formalism however you want and Barandes' interpretation is just one option, which is true. My point is that no where in papers or talks does Barandes make a clear separation between formalism and interpretation. To me, it looks like Barandes' is presenting his interpretation as directly following from the formalism in the sense that the formalism structure maps directly to what he interprets it to be in terms of a single particle having a definite configuration at every time. But the formalism doesn't actually contain the required structure so this one-to-one correspondence between the formalism and interpretation is not case.

Yes, its straightforward to interpret the probabilities as saying that there are particle configurations at all times, but the formalism does not allow you to talk about a single particle taking a trajectory: i.e. saying there are particle configurations at all times is not the same as a single particle having taken a definite position at all times.

Now sure, one could say that the former statement in the above paragraph actually does in some sense imply the latter; but, the point is that this is not explicitly described in the formalism because the indivisible approach doesn't have enough structure to specify these trajectories. If this is the case, there is no strong argument to say that the formalism entails the kind of interpretation Barandes is talking about in terms of trajectories as opposed one where the probabilities just represent what I would see if I chose to measure a system, in a kind of purely instrumental manner like more orthodox interpretatioms of QM. You can then say that the former statement in the above paragraph implies the latter, but this only matters if you presume an interpretation of the formalism in terms of trajectories; and there is simply no reason you have to do this.

And even if you do presume trajectories, the formalism cannot specify Barandes' interpretation; because my impression is that he interprets his formalism is about stochastic, possibly discontinuous trajectories. But if his formalism cannot specify trajectories at all, there is quite literally no contradiction in saying that these trajectories are actually deterministic Bohmian trajectories, which obviously contradicts Barandes' interpretation. Now, you might say that you can simulate a random, discontinuous, non-Bohmian "trajectory" where there is a realized sample configuration of a particle at t1 given t0 and t2 given t0 and t3 given t0. But there is nothing in the formalism that kind of connects these configurations at each time together in a way that necessarily construes it as the same particle going from t1 to t2 to t3. There is no way to construct a joint probability distribution that allows you to sign a single probability that explicitly says a particle went through a definite set of configurations from t1 to t2 to t3. It might seem intuitive that it must have, but this isn't formally rigorous; stochastic processes have a Kolmogorov extension theorem, Kolmogorov consistency conditions establishing this kind of thing rigorously, which you cannot do in the indivisible approach. This makes the intuition an assumption or interpetation about what a single particle is doing that is outside the formalism.

Again, my critique is simply that I believe Barandes is promoting his formalism as implying his interpretation, which is erroneous. Morbert is saying that he is not promoting this approach in this way. But I don't see any evidence in his papers or talks that he is making an explicit, transparent distinction between his formalism and interpretation.

 

[iste]

"This paper argues that every quantum system can be understood as a sufficiently general kind of stochastic process." The correspondence is not a necessary condition for the interpretation.

Those are your words, not Barandes'. I just don't think the opinions you are saying reflect what it seems to me that Barandes is saying in his talks and papers. I am not criticising the interpretation as such, I am criticizing how Barandes seems to be presenting the connection between the formalism and the interpretation. I don't see Barandes himself making any explicit distinction.

Yes we have discussed this earlier, and I said the knowing of something by an omnipotent being does not mean that thing has a regular lawlike expression. What are regular are the time-parameterized standalone probabilities, and any distribution built from combinations of these.

I don't explicitly know what you mean by law-like here. i have been assuming all along that what you mean by law-like is something like that these probabilities are simple and they don't seem to change arbotrarily in different contexts or experiments or something like that. But this doesn't matter. Those probabilities still have to exist. If the formal condition for trajectories existing is by a joint probability distribution, then if you postulate trajectories then you are implying that those joint probability distributions exist. Again, if you can assume that an omniscient observer can literally count and track the positions of particles at all times in all experiments, then he will be able to construct joint probability distributions using those frequencies. These joint probabilities don't exist in the indivisible formalism but they must exist if there are trajectories. If you don't think these probabilities are "law-like" enough, that doesn't change the fact that they exist; the fact that they aren't useful or interesting or something like that doesn't mean they don't exist.

The position I suggest in the last line of post #435 was actually intentionally aimed at the possibility that the trajectories aren't "law-like", in which case the indivisible formalism can be seen in terms of a kind of top-down causation on the underlying trajectories.

So my point here is basically that you saying they are may not be "law-like" does not contradict the entailment I talked about. "Law-like" or not, the joint probabilities must exist if there are trajectories. These probabilities constitute additional structure, additional description. And I believe, invoking this additional structure is actually exactly what that arxiv paper you linked is doing; they are generalizing the correspondence by allowing additional structure because the authors were not satisfied with Barandes' assertion that Markovianity emerges from indivisibility as opposed to vice-versa.

The formalism is perfectly capable of giving you a description of frequencies of any experiment (or sequence of experiments) you care to make, as you are a mortal who must couple the system to an apparatus to learn anything about it

The indivisible formalism is capable of describing frequencies of any quantum experiment under the usual assumptions about what we can empirically observe in quantum theory. In Barandes' interpretation, as I am led to believe, configurations have trajectories even when they are not observed. These trajectories must have frequencies, and the formalism has nothing to say about them, does not encode any structure from which you can even formulate them.

If the formalism doesn't include the frequencies because they are not "law-like", it doesn't mean they wouldn't exist if you indefinitely repeated an experiment such that you can describe objective, frequentist probabilities. If people cannot pragmatically do this, this is a statement about people's limitations, not the objective world. There is an underlying description not accounted for, which must exist if you have literally postulated hidden trajectories that mere mortals have no access to from the get-go.

So I think the mere mortal argument is not a great one because if you were concerned about what mere mortals can or can't do, you simply wouldn't postulate trajectories they cannot see and that entail a certain kind of formal representation that isn't in the formalism. Yes, you are going to say that the fact that they aren't in the formalism is fine and doesn't stop you using the interpretation. My concern is specifically against what Barandes seems to be implying about how the formalism connectd to interpretation. You think he is not making this mistake. I do not see this at all; I do not see any transparent distinction in his writings or talks - distinction between a formalism that does not give you trajectories, and an interpretation that postulates trajectories in virtue of the fact that particles are asserted to always be in a definite configuration at all times.

I don't think the interpretation is intrinsically faulty, just that it wants an explanation regarding the disconnect between the trajectory-less indivisible formalism and postulated trajectories. Again, my personal view is that if you don't want to just discard the trajectories, then being open to a more fundamental trajectory description; the only alternative I personally see right now is some kind of top-down causation which I don't really like because I don't find top-down causation sensical in general. Obviously, you can just say "we don't know, we can't know" but I think if you believe in an objective world beyond measurement, which presumably you do if you have postulated hidden configurations or trajectories, then something like one of these two options would have to be the case imo as it stands.