A Understanding Barandes' microscopic theory of causality

[iste]

However, in my opinion, Barandes postulates (i) a configuration space-based ontology, and (ii) a certain kind of stochastic process as the law determining time evolution, and then shows that this model is equivalent to Hilbert space QM

Sure, but then you could postulate anything. You can talk about physical systems that don't exist, you can talk about macroeconomics, you can talk about biology, psychology. There are conceivably a huge number of disparate models and systems that may evince behaviors of a quantum system to some degree by virtue of being describable as economic systems. For me, the validity of using the indivisible stochastic process as a physical interpretation is by showing that the indivisible stochastic process a quantum system corresponds to is in fact representing freely-evolving physical process and not some kind of amalgam of a physical system within a measurement context. I think Bohmian mechanics doesn't have to do this because with Bohmian mechanics you can more or less separate the parts of it that corresponds to the information in orthodox quantum mechanic, and the part of it that carries information about the other "hidden variables". There is no ambiguity because these hidden variables are effectively intentionally designed to represent what they represent in a way that is distinct from the orthodox quantum system and so don't risk conflation, imo. Whereas in Barandes' case you are pulling them out of a correspondence to (quantum) systems that people don't really have consensus on in the first place; there is nothing in your ontology which is not isomorphic to the information what you get from measurements, which is risky if there are cases where observables actually directly depend on the measurment interaction. To make your ontology incidentally, or accidentally even, contingent on that is imo a mistake. In the Barandes case it seems to me that if you want to make it explicit that some observables depend explicitly on a measurement interaction, like I believe Bohmian mechanics does, then you might have to kind of ignore aspects of the stochastic-quantum correspondence which are mathematically valid but you don't like because they may not agree with your physical interpretation.

 

[Sambuco]

I think Bohmian mechanics doesn't have to do this because with Bohmian mechanics you can more or less separate the parts of it that corresponds to the information in orthodox quantum mechanic, and the part of it that carries information about the other "hidden variables".

To a certain extent, Bohmian mechanics is a typical realist interpretation. There is a clear distinction between the variables that represent the physical state of a system and the way in which probabilities arise as a result of the impossibility of knowing that complete description. Barandes' interpretation combines both concepts, so that the probabilities of future events depend on the information available about past events. This is a kind of combination of realist and information-based interpretations.

So yes, I think Barandes' interpretation is not without problems (*), but at least it seems to be self-consistent.

(*) I don't like those weird jumps as long as there is coherence between branches.

Lucas.

 

[Morbert]

My criticism is that if you take something like spin and translate it into a generalized stochastic process, you get an evolving physical system sampling configurations with certain probabilities that may not actually make sense ontologically in which case the interpretation would be wrong and the generalized stochastic formalism must be carrying information about something else instead. There is also an obvious answer as to  why it is about something else instead: the stochastic process corresponds exactly to an orthodox quantum description of a system, and orthodox quantum theory doesn't really tell you anything outside of what happens when you measure something.

To clarify, I understand "take something like spin and translate it into a generalized stochastic process" in two ways. i) Translate it to a general stochastic system with a configuration space directly constructed from spin labels and ii) Construct a general stochastic system that reproduces all spin statistics of the corresponding quantum theory.

Re/ i) this could be true. My understanding is a classical configuration space can't consist of intrinsic spin configurations. So I can happily grant that: I can happily grant that not all sample spaces can serve as a classical configuration space, and hence cannot be used to construct a general stochastic system. But this isn't implied by the stochastic-quantum correspondence. Instead, the correspondence tells us there is no quantum theory whose empirical content cannot be reproduced by a general stochastic system. E.g. see the next paragraph.

Re/ ii) It is straightforward to construct a general stochastic system that reproduces spin statistics. Barandes touches on it in arXiv:2507.21192. He introduces spin as a dilation-emergeable in a stochastic system with a configuration space of ordinary spatial arrangements. The correspondence guarantees that for any Hilbert space, we can construct a general stochastic system with a classical configuration space that reproduces the statistics of all observables.

 

[Morbert]

I'm not sure that the epistemic nature of probabilities leads to AOE. For example, relational quantum mechanics assumes that probabilities are epistemic, but denies AOE.

Anyway, let's assume you're right and Barandes' formulation/interpretation does not violate AOE, then how does the interpretation address the LF no-go theorem? To reproduce quantum predictions, one of the three assumptions (AOE, non-superdeterminism, locality) must be violated.

Lucas.

I will have to admit my knowledge of the LF no-go theorem is minimal, so my response will be from the hip. From the paper:

In an EWFS, the assumption of AOE implies that, in each run of the experiment—that is, given that Alice has performed measurement x and Bob has performed measurement y on some pair of systems—there exists a well-defined value for the outcome observed by each observer, that is, for a, b, c and d. Formally, this implies that there exists a theoretical joint probability distribution P(abcd∣xy) from which the empirical probability ℘(ab∣xy) can be obtained

The transition map used by Alice and Bob will not have a division event at Charlie's and Debbie's measurement, and so no such joint probability distribution can be constructed. I.e. Once Alice and Bob start to interact with their respective Labs,the configuration of the Lab really can jump across quasiclassical branches. I.e.I.e. their superobservation will suspend the usual, dissipative, thermodynamic time evolution that makes ordinary macroscopic transition maps divisible and quasiclassical. Albert's nightmare is realized during the superobservations. But the labs are nevertheless in a definite configuration after Charlie's and Debbie's measurements, and there will be a standalone probability across lab configurations. It just can't ever be resolved: Alice and Bob can never learn it, and Debbie and Charlie cannot remember it.

 

[iste]

and hence cannot be used to construct a general stochastic system

But the generalized stochastic process exists! Again, the stochastic-quantum correspondence is fully general and can be applied to fields outside of physics. For me, the question is : "what does the indivisible stochastic process represent in quantum physics?" and that if getting an unambiguous physical interpretation out of it requires ignoring your first point i, then that is like overfitting because it doesn't represent the full generality or domain of applicability of the stochastic-quantum correspondence within quantum physics.

 

[Morbert]

But the generalized stochastic process exists! Again, the stochastic-quantum correspondence is fully general and can be applied to fields outside of physics. For me, the question is : "what does the indivisible stochastic process represent in quantum physics?" and that if getting an unambiguous physical interpretation out of it requires ignoring your first point i, then that is like overfitting because it doesn't represent the full generality or domain of applicability of the stochastic-quantum correspondence within quantum physics.

This paper then states and proves a new theorem that establishes a precise correspondence between any generalized stochastic system and a unitarily evolving quantum system.

Barandes does indeed observe in arXiv:2309.03085 that a stochastic process $(\chi,\mathcal{T},p,\mathcal{A})$ is more general than a generalized stochastic system $(\mathcal{C},\mathcal{T},\Gamma, p, \mathcal{A})$. But the correspondence he investigates is between generalized stochastic systems and quantum systems. I.e. It's not just that a quantum system can be modeled as a stochastic process, but that it can be modeled as a stochastic process "unfolding in an old-fashioned configuration space based on ordinary notions of probability and ‘indivisible’ stochastic laws". I.e. A generalized stochastic system. And note that such a system doesn't just get you one observable like spin. It gets you all observables.

You, on the other hand, are sketching a correspondence between specific eigenbases of a quantum system, and stochastic processes. This is fine, but you should not be surprised that it does not offer up ontological models. Instead what offers ontological models is the correspondence between quantum systems and generalized stochastic systems.

If you can show a quantum system (one that includes, say, spin states) has no corresponding generalized stochastic system, that would indeed be a killer blow.

[edit] - Tidied up language to be consistent with literature.

 

[Morbert]

@iste One reason this discussion has gone on for so long is I wasn't sure I fully understood your concern. But now I'm pretty sure I do, and so I will start to wind down the conversation on my end unless some new aspect not previously articulated is brought up.

 

[iste]

Barandes does indeed observe in arXiv:2309.03085 that a stochastic process $(\chi,\mathcal{T},p,\mathcal{A})$ is more general than a generalized stochastic system $(\mathcal{C},\mathcal{T},\Gamma, p, \mathcal{A})$. But the correspondence he investigates is between generalized stochastic systems and quantum systems. I.e. It's not just that a quantum system can be modeled as a stochastic process, but that it can be modeled as a stochastic process "unfolding in an old-fashioned configuration space based on ordinary notions of probability and ‘indivisible’ stochastic laws". I.e. A generalized stochastic system. And note that such a system doesn't just get you one observable like spin. It gets you all observables.

You, on the other hand, are sketching a correspondence between specific eigenbases of a quantum system, and stochastic processes. This is fine, but your should not be surprised that it does not offer up ontological models. Instead what offers ontological models is the correspondence between quantum systems and generalized stochastic systems.

If you can show a quantum system (one that includes, say, spin states) has no corresponding generalized stochastic system, that would indeed be a killer blow.

[edit] - Tidied up language to be consistent with literature.

Where does he talk about the even more general stochastic process? In that paper says he changes from the squiggly X to C because you can't define velocities fir a stochastic system. Honestly, you're paying too much attention to the word "configuration" when it doesn't make a difference wrt the mathematical result.

"the most general kind of stochastic process requires only a sample space, an initial probability distribution, and one or more time-dependent random variables, meaning time-indexed families of functions from the sample space to the real numbers. However, stochastic processes defined in this narrow way lack an ingredient that plays the role of a dynamical law. This paper will be concerned with a slightly modified construction that allows the probability distribution itself to vary in time, and that also includes the notion of a dynamical law."

"In defining a stochastic process to serve as such a model, one can take the sample space to be the system’s configuration space C"

Linguistically, "can take" seems subjunctive tense to me.
It doesn't seem like whether you talk about configuration, phase, state space, anything else, makes any difference. If this formulation can be applied to something like psychology, then it shouldn't make a difference. And in a sense it has been applied to psychology because people have used unitary and unistochastic systems to model psychological phenomena.

arXiv:2507.21192v1

A generalized stochastic system. And note that such a system doesn't just get you one observable like spin. It gets you all observables.

Sure, but all these observables in their Hilbert-space representation are coordinates of generalized stochastic processes.

You, on the other hand, are sketching a correspondence between specific eigenbases of a quantum theory, and stochastic processes

Thats exactly what Barandes does in his example. It should be valid for all observables equally by just doing what he does in reverse. And you can do that because the correspondence is bidirectional.

This is fine, but your should not be surprised that it does not offer up ontological models.

Yes, which is why I think its not a good way to construct a physical interpretation. Quantum mechanics already has an ambiguous physical ontology. This is just giving it a different representation and pretending it makes quantum mechanics less ambiguous when it in fact directly corresponds to the ambiguous quantum mechanics. Yes, you can probably make an acceptable interpretation. But imo this is ad hoc and does not give an honest reflection of what the generalized stochastic process you extract from a quantum theory is actually about.