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.