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.

 

[Morbert]

Honestly, you're paying too much attention to the word "configuration" when it doesn't make a difference wrt the mathematical result.

Honestly, I'm not, as it is what connects a mathematical result to a physical interpretation. It's what lets you regard a quantum system as a generalized stochastic system with dynamical laws and a microphysical ontology. But I have explained that many times by now.

 

[Sambuco]

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

Yes, that's the point! So Barandes' interpretation addresses LF no-go theorem by rejecting AOE.

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.

I think AOE implies something more radical. If a joint probability distribution cannot be constructed from the perspectives of Alice and Bob, then Charlie and Debbie's measurements are only events relative to them, but not to Alice and Bob.

In a way, Barandes's formulation seems to avoid this relationalism by postulating the existence of a configuration that can jump between different branches.

Lucas.

 

[Fra]

My inclination is that emergeables must be as real as beables. In terms of measurement and the Born rule they seem on equal footing. The only difference is that one isn't explicit in the stochastic process; it seems implicit (e.g. in the averaged dynamics) but equally real property of the world, not just of a measuring device. I haven't seen anywhere to my knowledge Barandes' formulation actually picking some preferred beable perspective on the universe; I believe he has even said his formulation is open about ontology. Surely his dictionary would allow you to take any quantum observable and make it a beable. Position beable where momentum is emergeable. Momentum beable where position is emergent.

Spin is an interesting example. Personally, I think that the outcomes of a spin measurement plausibly may very well be entirely a property of spin "measurements" in the moment rather than outside of the measurement. But I don't actually know, obviously. Just seems plausible to me. But surely, even though Barandes talks about spin as an emergeable from dilation, couldn't you describe or directly translate quantum spin as a beable? If that is the case, what would the stochastic process of the unmeasured universe (the spin part) between measurements represent if spin outcomes really were something that only exists after the measurement interaction. In that case, the spin beable between measurements couldn't be real in general but would have an instrumentalist interpretation. It seems to me that even though cases like position and momentum beables / emergeables can be seen as equally real between measurements arguably (albeit measurements will be disturbing), the formulation doesn't seem able to in and of itself specify what the stochastic process representing something in the universe means if it is plausible that outcomes of spin measurements are created in the moment of measurement. How could that stochastic process mean something outside of measurement if the outcomes being described only turn up after the measurement interaction? But maybe they don't, you tell me.

The pace of the discussion here went on faster than i could keep up, so not sure where to start rejoin. But in short I have a feeling that iste is trying to get an intuitive handle on the configuration spaces and what they can mean it exotic cases(where classical mechanical models breaks down) such as fermion spin states.

I think this is good to contemplate, but my way to handling this would required stepping outside of the basic SQC itself. The the line between reflection and speculation becomes fine IMO.

I have a feeling Morbert tries to stick more cleanly to SQC in the discussion, buy you want to get and understnading of it from your perspective. I symphatise with this.

SQC says there is a GSC and thus a configuration space, that correspondes to fermion dynamics in hilbert space. But what does it mean to understand the configuration space? It's just an mahtmaticla correspodence?

To me such understanding come first when we have a (first principle) the configuration space (and thus beables) from a minimal starting point. A starting point simple enough that noone will need further explanation. Ie we need to explain emergence of the "fermion" configuration space. This is something i can imagine when interpreting the GSC from ABM perspective, but then we are not discussing Baranders paper and its direct speculation. I simply can't offer a good answer without som speculation, so this is where it will have to stop to respect the formum guidlines.

The closes reflection that may be rooted in some issues of Barandes picture is that, I would say the "observer indepedence" of the division events is still dependent of how the total system is divided in subsystems. This is the non-trivial part, where I think the physics hides. If you divide a total system into parts, and insist that that is what you have, you need to ADD information. The division is simply ambigous. But Barandes SQC doesnt worry about that. The correspondence is there for any division. But different divisions describes a differnt physical system. And when you push this up to the "total universe" and consider a "closed system", you may thinkg that this is objective, but I disagree with that. I think - again via my projections from ABM and IGUS thinking the interal processes and decompositions correspond to "internal processes" of the system. Ie. internal "computations". An IGUS can be imagined to have different substructures, divide memory to entertain complementary data at hte same time, but in a shared mode (implying a generalized uncertainty relation). This is just general comments, without adding specific specualtiosn.

Then it means, different internal reorganisations of a system, although not immediately visible from outside, does make it a different "observer". This is why in my thining AOE does not hold. It hold if you freeze the ambigous division of the whole system. But for me, it is clear that the division into parts carries physical content.

This I think may also create beables from emeargables, via interal reorganisations. After all the "configuration space" is generically ABSTRACT space. It does not necessarily need to have a simple correspondence to a 3D classical mechanicsm model. I view the configuration space, information theoreitcally as a choice of the IGUS encoding.

Barandes SQC does not explain this, and he is also somewhat agnosic of the meaning of the space, just like the meaning of hilbert space is even more obscure. But the GSC is at least classically looking from each inside perspective. But not from the system perspective. So it is a step forware but more work todo? I would only guess that Barandes would both expect and appreciate discussing potential connections to the correspondence. That is how i see its value. It does not immediately solve all the problems. I think he encouraged others to examine what the GSC would mean for various systems in one of his youtube interviews.

I hope it is clear that I am not putting forward any speculation here, I am just hinting general potential directions for sake of reflecting on SQC from different perspectives.

/Fredrik

 

[Morbert]

Yes, that's the point! So Barandes' interpretation addresses LF no-go theorem by rejecting AOE.

I think AOE implies something more radical. If a joint probability distribution cannot be constructed from the perspectives of Alice and Bob, then Charlie and Debbie's measurements are only events relative to them, but not to Alice and Bob.

This stochastic formalism rejects everywhere-divisible dynamics, something Bong et al don't consider. This is perfectly reasonable, given how new this stochastic approach is. But ultimately we can have a conditional probability fail to obtain while any observed event is still "a real single event, and not relative to anything or anyone."

In a way, Barandes's formulation seems to avoid this relationalism by postulating the existence of a configuration that can jump between different branches.

Note that, as mentioned before, the jumping across quasiclassical branches is only induced by powerful superobservers with the ability to suspend relativity and with apparatuses many times the size of the observable universe. In the absence of such godlike beings, jumping is effectively impossible. David Albert doesn't have to worry: We can be confident in our history books as records of stuff that actually happened.

 

[iste]

In a way, Barandes's formulation seems to avoid this relationalism by postulating the existence of a configuration that can jump between different branches

Why does the configuration need to jump between branches? I haven't really been following this topic.

 

[Morbert]

The pace of the discussion here went on faster than i could keep up, so not sure where to start rejoin. But in short I have a feeling that iste is trying to get an intuitive handle on the configuration spaces and what they can mean it exotic cases(where classical mechanical models breaks down) such as fermion spin states.

I think this is good to contemplate, but my way to handling this would required stepping outside of the basic SQC itself. The the line between reflection and speculation becomes fine IMO.

I have a feeling Morbert tries to stick more cleanly to SQC in the discussion, buy you want to get and understnading of it from your perspective. I symphatise with this.

SQC says there is a GSC and thus a configuration space, that correspondes to fermion dynamics in hilbert space. But what does it mean to understand the configuration space? It's just an mahtmaticla correspodence?

I am not sure what GSC is. Do you mean GSS (generalized stochastic system)?

What Barandes shows is that we can associate any quantum system with a stochastic process unfolding on a classical configuration space of arrangements, and dynamics given by stochastic maps, allowing us to conceptualize a quantum system as such a process. He goes on in other papers to flesh out microphysical ontologies and microphysical causal relations enabled by this association. What iste is pointing out iiuc is that we can instead associated a quantum system with other stochastic processes: Ones for which the sample space does not have a straightforward classical conceptualization beyond measurement outcomes. Iste believes this undermines the former association. I don't. Nor do I take the ontological models enabled by the former as dogmatic metaphysical commitments. It is enough for them to be useful conceptualizations.