I Carroll interviews Barandes on Indivisible Stochastic QM

[jbergman]

TL;DR Summary

Sharing a recent interview with Barandes of his new interpretation

Thought this might be of interest for those following Barandes nee interpretation.

Carroll always has pretty good interviews.

https://www.preposterousuniverse.co...-on-indivisible-stochastic-quantum-mechanics/

 

[iste]

I no longer consider this an interpretation of QM, I think. The stochastic process includes the measurement device and only tells you about measurement outcomes. The dictionary is just based on modulus-squaring and apparently corresponds exactly to standard QM with measurenents. There is no reason to think that the stochastic process being described is not purely just describing the measurement outcomes, no other constraints in the theory to suggest this. There is nothing else to the theory, the ontology, how it behaves other than indivisibility. I don't even think Barandes knows what indivisibility really means, since we hear him say that it is very unintuitive frequently. There is no reason to believe this theory has any deeper physical meaning unless you can give it meaning separate from measurement. The theory clearly doesn't do this if the it can't tell you either how a particle got from point A to B, or why this can't be done physically, and the probabilities it does give you must obviously be measurement probabilities if the theory is consistent with QM in the way suggested. It cannot be an interpretation because the notion of definite configurations obviously exists as measurement outcomes in regular QM; you don't need a further underlying ontology to explain that. Its like arguing that definite measurement outcomes indicate literal point particles or something like that; even people advocating interpretations like that don't believe that is a sufficient argument.

 

[jbergman]

Yes. From the interview he still says he doesn't have much intuition for the theory or have a fundamental ontology. At this point it's just an alternative mathematical formulation of QM which is interesting in and of itself. But it's still a long ways from being an interpretation but maybe this alternative view will eventually lead to something in that direction.

 

[Morbert]

@iste What Barandes presents is a correspondence between quantum theories, and theories of unistochastic processes. This seems quite sturdy ground for an interpretation of quantum theories as about unistochastic processes.

-

The 2nd half of the podcast was the more interesting half. Carroll didn't push back on the approach as much as Scott Aaronson, but when he did, it was more substantive. Aaronson seemed content to merely express his personal disinterest given his satisfaction with alternatives. Carroll's concerns about the approach (the stability of matter, the exactness of the dynamics of subsystems etc.) all have answers, but they are nevertheless interesting concerns.

 

[Morbert]

Yes. From the interview he still says he doesn't have much intuition for the theory or have a fundamental ontology. At this point it's just an alternative mathematical formulation of QM which is interesting in and of itself. But it's still a long ways from being an interpretation but maybe this alternative view will eventually lead to something in that direction.

The unistochastic formalism won't yield a fundamental ontology in the sense that we do not have a fundamental quantum theory of the universe. But given a quantum theory, the formalism tells us what ontology that quantum theory implies if we interpret that theory as about unistochastic processes.

 

[iste]

This seems quite sturdy ground for an interpretation of quantum theories as about unistochastic processes.

But a unistochastic process could feasibly be an effective description for any kind of underlying system you want. The unistochastic process is exactly the random variables that describe what you will see when you measure something. It doesn't tell you anything else. That is an absolute open book. Measurement in Bohmian mechanics would be a unistochastic process when you stick the measurement device in and look at the results, so how can this formulation be saying anything about the physical without additional constraints which are not necessarily baked into indivisibility itself? And it seems strongly apparent to me that indivisibility just corresponds to the existence of measurement disturbance where joint probabilities break down so there is nothing here that really adds anything novel or informative in terms of interpretation because people still believe many different things about why or how measurement "disturbance" happens, what that means, whether the universe is a panpsychic mindscape where physicality is an illusion, etc.

 

[Morbert]

But a unistochastic process could feasibly be an effective description for any kind of underlying system you want. The unistochastic process is exactly the random variables that describe what you will see when you measure something. It doesn't tell you anything else.

Like all established interpretations, it is consistent with quantum theory and hence with experiment. What you get is a simple microphysical ontology.

 

[syed]

I no longer consider this an interpretation of QM, I think. The stochastic process includes the measurement device and only tells you about measurement outcomes. The dictionary is just based on modulus-squaring and apparently corresponds exactly to standard QM with measurenents. There is no reason to think that the stochastic process being described is not purely just describing the measurement outcomes, no other constraints in the theory to suggest this. There is nothing else to the theory, the ontology, how it behaves other than indivisibility. I don't even think Barandes knows what indivisibility really means, since we hear him say that it is very unintuitive frequently. There is no reason to believe this theory has any deeper physical meaning unless you can give it meaning separate from measurement. The theory clearly doesn't do this if the it can't tell you either how a particle got from point A to B, or why this can't be done physically, and the probabilities it does give you must obviously be measurement probabilities if the theory is consistent with QM in the way suggested. It cannot be an interpretation because the notion of definite configurations obviously exists as measurement outcomes in regular QM; you don't need a further underlying ontology to explain that. Its like arguing that definite measurement outcomes indicate literal point particles or something like that; even people advocating interpretations like that don't believe that is a sufficient argument.

sounds a lot like the Copenhagen interpretation :) What's common to both of these is that they fail to concretely define what is actually going on. And when they fail, they say that it's because of a failure of classical intuitions. The problem is that any unclear theory can make this excuse.

 

[iste]

Like all established interpretations, it is consistent with quantum theory and hence with experiment. What you get is a simple microphysical ontology.

Its not an interpretation though. An interpretation adds something. This doesn't add anything at all to quantum theory. It just makes apparent that random variables used to describe measurement can be seen as an indivisible stochastic process, and the answer is already basicslly there in quantum theory as to what that indivisibility means.

Arguably the measured system is just there to give the measurement device something to read, but that doesn't tell you how they got there or why. You could have some irrealist perspective who believes that the ontology disappears outside the measurement interaction. You could have a perspective where the measurement device has interacted with a deterministic Bohmian particle. The unistochastic process requires the measurement device to be inside, and without it you can't say anything about the other system. Its a black box. Stochastic processes can describe anything as they are just mathematical representations; in order to represent something physical you need to flesh that out beyond just measurement results in quantum theory. When Everettians figure out probability, maybe it will turn out the stochastic system is just describing self-locating uncertainty.

Barandes can obviously say he chooses to interpret his theory in terms of microphysical ontology that exists outside of measurement but I don't there is anything in the theory that entails one should believe this or substantiates it. And since the theory doesn't say anything more than orthodox quantum mechanics does, he doesn't know anything about his own interpretation. There is nothing here saying that it is more than a model of the measurement process and nothing more, not of any underlying physical system. What then becomes even more severe I think is that if indivisibility is a property of the measurement process, then there is not even a reason to think that the physical ontology is described by an indivisible process.

Bohmian mechanics is actually a really good example of this because it always implies divisible joint probability distributions for particle positions at different times. This obviously conflicts with orthodox quantum mechanics sometimes; and quantum multi-time correlations where joint probability distributions fail are a good characterization of indivisibility. How does Bohmian mechanics get around this? Just measurr the system and you recover the correct predictions and therefore the indivisibility. The non-classicality of something like the Kirkwood-Dirac distribution for a sequence of measurements is probablyeasurements. fundamentally what indivisibility is about too; and that occurs because projectove measurements disturb the statistics for subsequent measurements. Indivisibility is literally just a surface level description of what your measurement results look like. To me, this is the most parsimonious reason why his trajectories aren't even continuous; its just measurement results. The system evolving in time and watching the realizations of the stochastic system is like someone getting a measuring device and measuring at every single point in time. That makes absolutely no sense for like an actual substantive physical interpretation. Nothing is being said.

 

[Morbert]

Its not an interpretation though. An interpretation adds something. This doesn't add anything at all to quantum theory. It just makes apparent that random variables used to describe measurement can be seen as an indivisible stochastic process, and the answer is already basicslly there in quantum theory as to what that indivisibility means.

I'm not sure an interpretation has to add anything over and above the interpretation itself, but anyway: This formalism adds a microphysical ontololgy not present in ordinary QM, as well as the associated formalism (configurations, a configuration space, distributions over this space, sparse conditional probabilities etc.)

Arguably the measured system is just there to give the measurement device something to read, but that doesn't tell you how they got there or why. You could have some irrealist perspective who believes that the ontology disappears outside the measurement interaction. You could have a perspective where the measurement device has interacted with a deterministic Bohmian particle. The unistochastic process requires the measurement device to be inside, and without it you can't say anything about the other system. Its a black box. Stochastic processes can describe anything as they are just mathematical representations; in order to represent something physical you need to flesh that out beyond just measurement results in quantum theory. When Everettians figure out probability, maybe it will turn out the stochastic system is just describing self-locating uncertainty.

Unistochastic systems have a time-evolution described by a stochastic map. This is very much a realist position.

Barandes can obviously say he chooses to interpret his theory in terms of microphysical ontology that exists outside of measurement but I don't there is anything in the theory that entails one should believe this or substantiates it. And since the theory doesn't say anything more than orthodox quantum mechanics does, he doesn't know anything about his own interpretation. There is nothing here saying that it is more than a model of the measurement process and nothing more, not of any underlying physical system. What then becomes even more severe I think is that if indivisibility is a property of the measurement process, then there is not even a reason to think that the physical ontology is described by an indivisible process.

Established interpretations aren't resolvable by experiment, since they all agree with experiment. Your charge could just as readily be levied at any interpretation.

 

[iste]

I'm not sure an interpretation has to add anything over and above the interpretation itself, but anyway: This formalism adds a microphysical ontololgy not present in ordinary QM, as well as the associated formalism (configurations, a configuration space, distributions over this space, sparse conditional probabilities etc.)

Barandes' interpretation doesn't sit in a vacuum where he just decided to postulate a microphysical ontology. The only reason he has done so is because he has made an interpretation of this formalism. If his interpretation of his own formalism is faulty then his interpretation is pointless; and yes, I think his interpretation is faulty. His microphysical ontology is not informative, it does not stand on its own, it isn't distinguishable from other interpretations that offer microphysical ontology, it isn't distinguishable from other interpretations that have collapse - the system in indivisuble stochastic mechanics could easily be interpreted as a stochastic process describing the collapse of a physical system when it is measured, each realization being an instantiation of collapse. All of those things you mention exist implicitly in orthodox quantum mechanics insofar as they appear in the readout of a measurement device. Sure its a different formulation. Sure it can be an interpretation, but its a tepid one since its based on a formalism that is too sparse give any fleshed out physical description, it can be re-interpreted under other metaphysical views, and the resulting Barandes interpretation says almost nothing anyway.

Unistochastic systems have a time-evolution described by a stochastic map. This is very much a realist position.

A stochastic process can model anything you want. Its a mathematical representation; you can model tings that don't exist. There is no reason to give a specific physical interpretation unless it is fleshed out in the formalism, which it is not here. The stochastic process of a measurement device interacting with another system can be subsumed into any interpretation. Like I said before, the stochastic process can describe self-locating uncertainty, collapse, Bohmian deterministic particles. Sure, you could say Barandes view is still an interpretation but then its compeltely trivial and uninformative. There is absolutely nothing here telling me that the formalism is describing anything more than the statistical description of what happens when you perform measurements. Describing the stochasic evolution of measurement does nto have to be realist in any profound way.

Established interpretations aren't resolvable by experiment, since they all agree with experiment. Your charge could just as readily be levied at any interpretation.

Well then you have missed my point because my point is that every single other interpretation tells you what the world is like beyond measurement. Barandes' doesnt do that except the very bare minimum which isn't even implied by the formalism. All other interpretations are largely empirically indistinguishable but they are not so metaphysically. So my charge cannot be levied against other interpretations because they all have actual distinctive ontological content. Barandes' ontological content is bare minimal and is based on a formalism that he has arguably over-interpreted.

Fine, one can say it is an interpretation. But if he can't tell you whats going on outside of measurement, then what is the point in the realism? Interpretations are meant to explain things; if people were satisfied with the idea that particles are indefinite positions but we don't know what they are doing outside of measurement, this could have easily been settled 100 years ago. Its no different from the statistical ensemble interpretation at all except for the idea that the particle has a definite trajectory between measurements that we have no way of describing - a completely uninformative postulate about reality. But again, I don't see that the formalism actually implies anything beyond a surface description of the measurement process.

 

[Morbert]

and yes, I think his interpretation is faulty. His microphysical ontology is not informative, it does not stand on its own, it isn't distinguishable from other interpretations that offer microphysical ontology, it isn't distinguishable from other interpretations that have collapse - the system in indivisuble stochastic mechanics could easily be interpreted as a stochastic process describing the collapse of a physical system when it is measured, each realization being an instantiation of collapse. All of those things you mention exist implicitly in orthodox quantum mechanics insofar as they appear in the readout of a measurement device. Sure its a different formulation. Sure it can be an interpretation, but its a tepid one since its based on a formalism that is too sparse give any fleshed out physical description, it can be re-interpreted under other metaphysical views, and the resulting Barandes interpretation says almost nothing anyway.

"It isn't informative" seems to be a value judgement here. I'm not sure what you mean by "stand on its own". It is quite distinct from Bohmian mechanics. Bohmian mechanics posits (either ontologically or nomologically) a guiding wave, and markovian dynamics.

There is no reason to give a specific physical interpretation unless it is fleshed out in the formalism, which it is not here.

I don't agree with this at all. E.g. Orthodox quantum theory can assign probabilities to products of time-parameterized projectors. These can be interpreted as a representation of the Everettian multiverse (MWI), or a set of possible histories, one of which occurs (decoherent histories), or an operational procedure for tracking expected sequences of measurement outcomes (instrumentalism). These are all different interpretations of the same formalism.

The stochastic process of a measurement device interacting with another system can be subsumed into any interpretation. Like I said before, the stochastic process can describe self-locating uncertainty, collapse, Bohmian deterministic particles. Sure, you could say Barandes view is still an interpretation but then its compeltely trivial and uninformative. There is absolutely nothing here telling me that the formalism is describing anything more than the statistical description of what happens when you perform measurements. Describing the stochasic evolution of measurement does nto have to be realist in any profound way.

The unistochastic formalism has a very natural interpretation: At every time there is a definite configuration, and dynamics are given by sparse directed conditional probabilities. You can of course contrive other interpretations of the formalism. And the correspondence means this formalism doesn't preclude previously established interpretations.

Well then you have missed my point because my point is that every single other interpretation tells you what the world is like beyond measurement. Barandes' doesnt do that except the very bare minimum which isn't even implied by the formalism. All other interpretations are largely empirically indistinguishable but they are not so metaphysically. So my charge cannot be levied against other interpretations because they all have actual distinctive ontological content. Barandes' ontological content is bare minimal and is based on a formalism that he has arguably over-interpreted.

Not all interpretations are realist. Not all realist interpretations posit a microphysical ontology. Not all realist interpretations with microphysical ontologies posit definite configurations. Not all realist interpretations with microphysical ontologies with definite configurations posit local causal structures.

 

[iste]

"stand on its own"

There is no intelligible description of their behavior without the measurement device being plugged in.

It is quite distinct from Bohmian mechanics. Bohmian mechanics posits (either ontologically or nomologically) a guiding wave, and markovian dynamics.

Its not the same as Bohmian mechanics but its not incompatible with it either.

Look at it this way. Under Bohmian mechanics, we could imagine a God's eye perspective of what is happening at any given time in physical space. Obviously, one time means one outcome so this isn't interesting without repeating the experiment. What would we see? We would see events with Born probability frequencies, right? But we wouldn't be able to predict them due to ignorance of the initial conditions. We have a random variable here, and so we can have a stochastic description of the Bohmian situation. If I didn't know the physical Bohmian laws or whatever of what is going on, there is nothing stopping me from just characterizing thay scenario in terms of a stochastic process due to my ignorance. Otherwise the Born probabilities wouldn't really make sense.

Its true, Bohmian mechanics has Markovian dynamics. But this changes if you put the measurement device in the Bohmian description, because the measurement device disturbs the trajectory statistics, allowing one to get non-Markovian (i.e. indivisible) multi-time correlations of QM.

https://scholar.google.co.uk/scholar?cluster=11957102981612580756&hl=en&as_sdt=0,5&as_vis=1

https://scholar.google.co.uk/scholar?cluster=18082693999119350419&hl=en&as_sdt=0,5&as_vis=1 (Neumaier)

https://scholar.google.co.uk/schola...5#d=gs_qabs&t=1754586959336&u=#p=uhh3Tzb4pBMJ

Similarly, Barandes description requires the measurement device to be part of the unistochastic process.

If we take the stochastic process of the Bohmian situation but make sure that we are only talking about this situation when the measurement device is included in the description at every time, it will be identical to the Barandes stochastic process in the sense of when we try to construct the markovian transition probabilities for multiple times we won't be able to do it. And in the Bohmain scenario this will be because the measurement device perturbs the Bohmian trajectories and prevents us doing this, explaining exactly what indivisibility really signifies - measurement disturbance and the preclusion of joint probability distributions over different times.

The question is: what exactly in Barandes' model prevents me from interpreting his stochastic process for the measured system in the way I have just characterized the Bohmian stochastic process?

Absolutely nothing.

What prevents us intepreting the stochastic process in some other eay?

Absolutely nothing.

I don't agree with this at all

You do agree because what you said in this comment is exactly what I said. QM doesn't entail a specific physical interpretation which is exactly why many can be applied to it.

The unistochastic formalism has a very natural interpretation:

The unistochastic formalism is just an alternate mathematical description of orthodox quantum theory without much else. It is just a direct description of the statistics of measurement. If orthodox mechanics has many different possible interpretations, so does this as I just elucidated.

if the formalism doesn't exclude other interpretations then what are we talking about? Its a formulation which Barandes has chosen to give a specific interpretation. But because he thinks his interpretation is implied by the formalism, because he is using the formalism to build an interpretation, his interpretation is as thin as the formalism and not hugely different from a minimalist statistical interpretation. The only difference is he says that there are definite configurations when not measured. I am not exagerrating when I say that is the only difference because the formalism that Barandes is using to guide his interpretation does not let him say anything else.

So there is Barandes the formalism which is not incompatible with Bohmian mechanics or anything else.

And there is Barandes the interpretation which doesn't really push the river. It might solve the measurement problem, but there is no detail about the underlying physical ontology that gives reason to take up this interpretation. There is nothing really here beyond postulating definite configurations; but no one is convinced by just postulation without deeper arguments, deeper explanation, and I am sure people have made similar postulations many times over the last 100 years. What convinces people is a substantive model of the underlying physical ontology and what it does even when it is not being measured, how the weird quantumness is achieved exactly.

My concerns here are not the semantics of whether Barandes has a proper interpretation here.

My concern is whether Barandes the interpretation is any good. Thats the only thing I am arguing about here with any real substance. I may say its not really an interpretation because imo its so thin that it might as well not be. It is directly taken from a formalism which is consistent with various interpretations because that formalism is just an alternative formulation of quantum theory which only really says as much as orthodox quantum theory does, so any interpretation based on that will be thin. Barandes the interpretation isn't a huge improvement on the statistical ensemble interpretation imo. The single major difference of definite configurations when unmeasured in this interpretation is not a huge improvement for me because nothing else is said about them.

 

[lodbrok]

Well then you have missed my point because my point is that every single other interpretation tells you what the world is like beyond measurement. Barandes' doesnt do that except the very bare minimum which isn't even implied by the formalism.

On the contrary, I think Barandes adds very important things that relate to ontology even without explicitly providing an intuition about the ontology:

It adds:
- Particles exist when we aren't looking
- Particles exist in a single configuration, not multiple configurations at once (The cat is not dead and alive)
- Hilbert space and the wavefunction are not "real"; they are just calculational devices
- It starts from more straightforward, less arbitrary (arguably more reasonable) axioms. It is easier to justify his starting axioms than it is to justify the traditional QM ones.

Allegorically, Barandes has given us a new map that makes the distinction between map and territory clearer. He doesn't know what the territory looks like, but it will be easier not to conflate the two with his approach. The traditional approach makes it very hard to distinguish the map from the territory, and many have stumbled on that stone.

 

[Fra]

Without knowing in depth what Barandes has up his sleeves, as I see it, his correspodence at least provides a valuable handle on in what limits more general stochastic theories should have correspondence to quantum mechanics; not phrased in terms of hilber spaces. This is important, at least if you like me, think that some QM framework may or many not survive to the general case, it is still critical, just like correspodence between qm and classical physics was, to make sure any wilder theory reduce to QFT in the appropriate limit of small subsystems observed from a distance without limiting information processing of data.

Unistochastic process are not the most general ones, so when more general process in some limit somehow, for some reason, converge to unistochastic description, then and we also get "quantum mechanics". This is not bad even if it is all it says.

/Fredrik

 

[Morbert]

@iste I'm finding it difficult to decipher your objections so I'm tapping out for now.

 

[iste]

- Particles exist when we aren't looking
- Particles exist in a single configuration, not multiple configurations at once (The cat is not dead and alive)

Sure, but imo these are not implied by the formulation since the stochastic process requires measurement to get the predicted outcomes. They are an additional interpretation of the formulation imo. I disagree that the description of the measured system as a stochastic system implies any deeper ontology because you can use that stochastic system to describe anything you want. He is choosing to interpret it in one way, whereas a Bohmian might interpret the same stochastic process in terms of what you can expect to see at a given point of time in terms of Bohmian trajectories; someone else might interpret that stochastic process in terms of what you might expect to see in terms of collapse; once many worlders have figured out probability, they will be able to interpret it in terms of something else. Until we can have a description that doesn't involve measurement, I think it is hard to commit to a view imo. I am not entirely sure the stochastic system implies something has to happen between measurements, I feel like it just tells you what  would happen were you to make a measurement.

Hilbert space and the wavefunction are not "real"; they are just calculational devices

Sure, this is a good point. When put like this, the formulation then demonstrates directly an explicit deflation of the wavefunction. This is a good aspect of the formulation and interpretation which is step forward from a mere statistical ensemble interpretation. I guess what has turned me off is that it becomes apparent that the stochastic process doesn't imply any specific physical interpretation. It just says the world is producing outcomes randomly when you measure it and that they then register on your device.

Thinking about wavefunction deflation, one would think a collapse interpretation of the stochastic process seems less justified if the wavefunction is deflated; but then again, I'm pretty sure a bunch of people currently believe that the wavefunction is an epistemic tool and also that definitie configurations we observe in the world also still disappear when they are not being observed or something like that. They could then still interpret the stochastic process in a similar way.

But, yes now I think the indivisible approach does make arguments stronger against the notion that the wavefunction is ontology. I guess maybe that can be used as an argument against many worlds as well given that my impression is that they reify the wavefunction. Thinking about it, I guess the idea of many worlders using the indivisible formulation at all probably would actually undermine their entire raison d'etre. If qm had been formulated as indivisible processes a century ago the complete absence of overt superposition would probably stop anyone from coming up with the idea of many worlds at all. But then I have the funny image in my head of if someone discovered the wavefunction formulation, maybe someone would then think up of the many worlds approach and think it have more explanatory power than the predominant indivisible approach in this imagined world where indivisibility came first.

 

[iste]

This is an interesting approach by Khrennikov with many parallels to Barandes approach including the deflationary aspects, albeit obviously nowhere near as elegant or as comprehensive a characterization of qm in the same way. But still interesting.

https://scholar.google.co.uk/schola...v+total+probability&oq=khrennikov+total+proba

e.g.

​

"We compare the classical Kolmogorov and quantum probability models. We show that the gap between these models is not so huge as was commonly believed. The main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the Kolmogorov model. In particular, we obtain “interference of probabilities” without appealing to the Hilbert space formalism. We interpret “interference of probabilities” as a perturbation (by a cos-term) of the conventional formula of total probability. Our classical derivation of quantum probabilistic formalism can stimulate applications of quantum methods outside of the microworld, for instance, in psychology, biology, economy, and other domains of science."

Khrennikov also notes the connection between Born rule and doubly-stochastic transition probabilities and his interference formula are virtually exactly the same form as those in Barandes, further arguing for the interpretation of indivisibility in terms of contextual probabilities, contexts being related to measurement. Indivisibility isn't actually in Khrennikov's work but im just saying that indivisibility is defined in terms of the same kind of interference terms that Khrennikov constructs. Difference between divisible and indivisible process in Barandes work maps directly to violation of total probability which in Khrennikov's work is just due to context-dependent behavior. Khrennikov's work isn't meant to be an interpretation of QM I think, just an argument for deflating the mystique of quantum probabilities. I think he favors a statistical ensemble interpretation though not entirely sure.

 

[lodbrok]

Sure, but imo these are not implied by the formulation since the stochastic process requires measurement to get the predicted outcomes. They are an additional interpretation of the formulation imo. I disagree that the description of the measured system as a stochastic system implies any deeper ontology because you can use that stochastic system to describe anything you want.

Sure, anyone can come up with their number for how many demons can dance simultaneously on the tip of a pin. It's never a question about the upper bound of SMHs (speculative metaphysical hypotheses) but rather the lower bound required to make sense of the formalism. And there is a good reason for this -- Occam's razor. The fewer assumptions you need to make to explain what's happening, the better. To say it's every model that fits is allowed is severely mistaken.

I am not entirely sure the stochastic system implies something has to happen between measurements, I feel like it just tells you what  would happen were you to make a measurement.

Barandes doesn't provide an intuition of what is happening between measurements. But you don't need to introduce SMHs like instantaneous collapse, particles going through both slits at once, particles taking all paths simultaneously, the universe splits, etc.

 

[jbergman]

On the contrary, I think Barandes adds very important things that relate to ontology even without explicitly providing an intuition about the ontology:

It adds:
- Particles exist when we aren't looking
- Particles exist in a single configuration, not multiple configurations at once (The cat is not dead and alive)
- Hilbert space and the wavefunction are not "real"; they are just calculational devices
- It starts from more straightforward, less arbitrary (arguably more reasonable) axioms. It is easier to justify his starting axioms than it is to justify the traditional QM ones.

Allegorically, Barandes has given us a new map that makes the distinction between map and territory clearer. He doesn't know what the territory looks like, but it will be easier not to conflate the two with his approach. The traditional approach makes it very hard to distinguish the map from the territory, and many have stumbled on that stone.

Some of your points are valid, but, he introduces an entirely new set of problems.

- Violation of locality. Particle paths are not necessarily continuous.

- As Carroll points out, particle behaviors violate expectations of theories like E&M.

At this point, there are so many contradictions with existing theory, if you interpret this as modeling real particles one can really only take this as a calculation device. I encourage you to actually listen to the dialogue with Carroll as eve Jacob admits this.

 

[iste]

To say it's every model that fits is allowed is severely mistaken.

I would say every model that reproduces the predictions of QM can feasibly used as an underlying explanation for why the measured stochastic process spits out the outcomes it does. The formulation is too sparse to refute such.

The fewer assumptions you need to make to explain what's happening, the better.

But you are going to have to make some assumptions to explain something or else you won't get anywhere. Barandes' theory is sparse on assumptions at the cost of intelligible explanation. I am more interested in theories that put their neck out.

Barandes doesn't provide an intuition of what is happening between measurements. But you don't need to introduce SMHs like instantaneous collapse, particles going through both slits at once, particles taking all paths simultaneously, the universe splits, etc

No, but if you already hold those interpretations, they are compatible. And if you don't just want a pragmatic formalism but an actual underlying physical, metaphysical explanation then you are going to start invoking things that go beyond what is in Barandes' formulation - and Barandes' formulation simply doesn't constrain that. I don't see any specific reason a Copenhagenist or a Bohemian should give up their view based on this formulation.

 

[Morbert]

Some of your points are valid, but, he introduces an entirely new set of problems.

- Violation of locality. Particle paths are not necessarily continuous.

Why is discontinuity a problem? Classical and quasiclassical behaviour is recovered as the size of systems increase. And Barandes gives a clear account of local causality suitable for unistochastic systems in section VI. https://arxiv.org/pdf/2402.16935

- As Carroll points out, particle behaviors violate expectations of theories like E&M.

This is only a problem if you suppose the system is classical. A semiclassical or fully quantum treatment is consistent with observed physics. As Barandes says to Carroll, you specify a Hamiltonian as you do in standard QM, and that Hamiltonian will yield the stochastic laws of your system consistent will all observation.

At this point, there are so many contradictions with existing theory, if you interpret this as modeling real particles one can really only take this as a calculation device. I encourage you to actually listen to the dialogue with Carroll as eve Jacob admits this.

What's nice about the correspondence is you effectively guarantee agreement with existing theory.

 

[gentzen]

It adds:
- Particles exist when we aren't looking
- Particles exist in a single configuration, not multiple configurations at once (The cat is not dead and alive)
- Hilbert space and the wavefunction are not "real"; they are just calculational devices
- It starts from more straightforward, less arbitrary (arguably more reasonable) axioms. It is easier to justify his starting axioms than it is to justify the traditional QM ones.

Nice contribution. I agree with two of your points:

- Particles exist in a single configuration, not multiple configurations at once
- It is easier to justify his starting axioms than it is to justify the traditional QM ones.

I would have liked him to do more work on that „quantum reconstruction“ side, especially those „propagation of rate of change“ from the stochastic side to the quantum side questions.

For

- Particles exist when we aren't looking

I am with iste: Because no consequences at all follow from their existence in Barandes‘ formalism, not even any limit on their discontinuous jumping around, they might as well not exist, and nothing would change.

- Hilbert space and the wavefunction are not "real"; they are just calculational devices

This point seems to be important for Barandes. But he doesn‘t succeed in proving this. Maybe he should try harder, because this point seems close to his heart.

 

[iste]

This point seems to be important for Barandes. But he doesn‘t succeed in proving this

Could you elaborate on this? I thought that it at least deflates it. The wavefunction no longer seems essential as an ontology for physical events if it corresponds to this stochastic process. The measured system and measuring device both would represent physical things; albeit, as I have said before, I don't think the measured system does speaks to deeper underlying ontologies, systems, explanations that generate those outcomes ans tells you what is happening. And without those things it doesn't really say anything substantive about the deeper physical universe.

 

[gentzen]

Could you elaborate on this? I thought that it at least deflates it. The wavefunction no longer seems essential as an ontology for physical events if it corresponds to this stochastic process.

Did he succeed to convince Sean Carroll? Did he even try? In the comments below the transcript, I found a pingpack to the following:

This reminds me of a new approach that Jacob Barandes has been promoting on various podcasts (see this recent Sean Carroll episode as an example). Barandes calls it Indivisible Stochastic Quantum Mechanics. I won’t pretend to understand exactly what he’s trying to accomplish with it, but it involves rejecting the wave function completely, and replacing it with something more stochastic from the beginning. Which strikes me as less structurally complete than the wave function, and so a move in the wrong direction. But maybe I’ll turn out to be wrong.

You might also ask, why did he not succeed, and what would it take to deflate the wavefunction. But that is his task to figure out, not mine. For me, not even trying to analyse the „propagation of rate of change“ doesn‘t help either: How important is the current state of the wavefunction? Can the wavefunction just follow along continuously if the stochastic matrix changes continuously, or not? Those are totally doable mathematical questions.

 

[Fra]

The problem here is we are iteration interpretations as we are interpreting Baranders possible interpretations, that said I take a constructive view and try to see the good things, as it's obvious that there are many questions...

There is absolutely nothing here telling me that the formalism is describing anything more than the statistical description of what happens when you perform measurements.
T

If we take the stochastic process of the Bohmian situation but make sure that we are only talking about this situation when the measurement device is included in the description at every time, it will be identical to the Barandes stochastic process in the sense of when we try to construct the markovian transition probabilities for multiple times we won't be able to do it. And in the Bohmain scenario this will be because the measurement device perturbs the Bohmian trajectories and prevents us doing this, explaining exactly what indivisibility really signifies - measurement disturbance and the preclusion of joint probability distributions over different times.

The question is: what exactly in Barandes' model prevents me from interpreting his stochastic process for the measured system in the way I have just characterized the Bohmian stochastic process?

Its no different from the statistical ensemble interpretation at all except for the idea that the particle has a definite trajectory between measurements that we have no way of describing - a completely uninformative postulate about reality. But again, I don't see that the formalism actually implies anything beyond a surface description of the measurement process.

Allegorically, Barandes has given us a new map that makes the distinction between map and territory clearer. He doesn't know what the territory looks like, but it will be easier not to conflate the two with his approach. The traditional approach makes it very hard to distinguish the map from the territory, and many have stumbled on that stone.

What's common to both of these is that they fail to concretely define what is actually going on. And when they fail, they say that it's because of a failure of classical intuitions.

I think it's because of our flawed intuition of causal mechanisms, which Baranders makes sharper than Copenhagen in this sense...
integrations.)

"At the level of dynamics, the microphysical laws consist of conditional or transition probabilities of the form
$\Gamma_{ij}(t) \equiv p(i, t \mid j, 0)$"
-- p7, 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 vice versa"
-- p11, https://arxiv.org/abs/2402.16935

Now if you take Q's map of the territory to be $\Gamma_Q(t)$ requiring causality suggests that the microphysical causal influences from Q's perspective is independent of the territory. Similarly the stochastics from P's perspective is independent of the territory. This is a deep blow to old style realism, while it at the same same suggests that the territory can be real, but it does define the nature of interactions. It suggests that the local systems stochastic actions are guided but it's own map only. Wether the map is "wrong" is irrelevant.

This phenomena is common in ang games where each players chooses his actions not upon what the other players are in fact doing or thinking, but based on what he EXPECTS then to think. This rules the actions, irrespective of wether expectations are statistically right or wrong in the simplistic sense.

This is admittedly my biased interpretation,

What is MISSING in Baranders picture, is to explain exactly how the maps evolve and interact. This is pulled from the Hamiltonian, just like in QM. Doing this IMO likely requires us to step OUTSIDE unistochastic processes - this is way beyond what Barandes does. But if we do, Barandes correspondence serves as a checkpoint for when QM is recovered at some informal "equilibrium". I think this process, where the stochastic laws or the map are formed (not given as constraint, like it is now), changes the intuition of realism in some deep ways. In particular does it give a final blow to the idea that laws of nature are fixed an immutable. This is the source of the twisted intuition on realism IMO. We confuse effective law with fundamental law, but we cant' stop there, we need to understand the process where effective dynamical law emerges.

In such a "research program" I think Barandes view first of all brings an importan correspodnece, we can be useful later (when seeking limits of non-unistochastic stuff) and he clarifies some things with "microphysical law".

I choose to see this, which is good. I already pointed out what i thing is missing, but who expects Baranders to solve all worlds problems in a few papers?

/Fredrik

 

[Morbert]

I am with iste: Because no consequences at all follow from their existence in Barandes‘ formalism, not even any limit on their discontinuous jumping around, they might as well not exist, and nothing would change.

This charge can be levied at any interpretations that don't take measurement as foundational.

This point seems to be important for Barandes. But he doesn‘t succeed in proving this. Maybe he should try harder, because this point seems close to his heart.

i) Plenty of interpretations do not frame the wavefuncton as real (e.g. consistent histories).
ii) He shows that, in the same way we have a stochastic map $p(t) = \Gamma(t)p(0)$, we can write $\Psi(t) = \Theta(t)e_j$ where $e_j$ is a configuration basis element and $\Theta(t)$ is obtained from a Schur-Hadamard factorization of the stochastic map. We can see that, under this account, the wavefunction is encoding the non-Markovianity of the time-evolution.

Did he succeed to convince Sean Carroll? Did he even try?

This is simply the nature of interpretational matters. Plenty of interpretations are established and mature. I'll repeat here what I posted on Carroll's blog:

"I suspect the landscape of established interpretation is “Everettian” in the sense that as progress is made, we will not see a pruning of interpretations and convergence towards some unique correct interpretation, but rather a branching of equally viable, robust, mature interpretations. Asher Peres has done much to perfect Copenhagen/instrumentalism. Wallace, Carroll, and Deutsch have done much to perfect Many Worlds. Omnes, Griffiths, Gell-Mann, and Hartle have done much to perfect consistent histories etc etc."

Carroll is happy to stay on a different interpretational branch, but that is not a mark against other branches.

 

[A.T.]

Did he succeed to convince Sean Carroll?

Just in some branches.

 

[iste]

Similarly the stochastics from P's perspective is independent of the territory. This is a deep blow to old style realism

Not sure I follow. His local causality just seems to correspond to non-signalling.

Barandes correspondence serves as a checkpoint for when QM

Not sure I agree because it cannot telling us anything more about observable quantum behavior than is already known, so its not even reqly required as a checkpoint, if I understamd you properly. At the same time, the correspondence is so general it can clearly describe "quantum" systems that are not quantum physics, e.g. quantun cognition.

Did he succeed to convince Sean Carroll? Did he even try? In the comments below the transcript, I found a pingpack to the following:


You might also ask, why did he not succeed, and what would it take to deflate the wavefunction. But that is his task to figure out, not mine. For me, not even trying to analyse the „propagation of rate of change“ doesn‘t help either: How important is the current state of the wavefunction? Can the wavefunction just follow along continuously if the stochastic matrix changes continuously, or not? Those are totally doable mathematical questions.

Yes, I guess one could argue that there is not much point to try to deflate the wavefunction if you don't have an alternative description of what is going on that has greater explanatory power. At the very least, people of other interpretations wouldn't be compelled to convert if they weren't given a superior explanation in return.

 

[iste]

This charge can be levied at any interpretations that don't take measurement as foundational.

Only if they don't tell you whats going on between measurements. Something like Bohmian mechanics tells you. Maybe empirically it would be the same, but people want explanation of how an underlying realistoc description produces those measurement outcomes, which Barandes does not provide.

 

[jbergman]

One other interesting point was that Barandes disputes the idea of a universal wave function for the entire universe. He also views his formalism as describing smaller systems so it seems like he is far from endorsing this as a fundamental ontology as many want to understand QM.

 

[Morbert]

Maybe empirically it would be the same, but people want explanation of how an underlying realistoc description produces those measurement outcomes, which Barandes does not provide.

Both Barandes's formalism and Bohmian mechanics give underlying explanation. A Bohmian system evolves deterministically, a unistochastic system evolves unistochastically, both in accordance with their respective nomological laws.

One other interesting point was that Barandes disputes the idea of a universal wave function for the entire universe. He also views his formalism as describing smaller systems so it seems like he is far from endorsing this as a fundamental ontology as many want to understand QM.

Barandes remarks that the systems we are typically interested in are subsystems of the universe, but given a quantum theory of the universe, there would be a corresponding unistochastic formulation.

One advantage of this formalism is it removes the need for understanding systems in terms of external measurement. We don't need to suppose a measurement apparatus external to the universe, making repeated measurements on the universe. So universe-scale cosmological models aren't an issue.

 

[Fra]

Not sure I follow. His local causality just seems to correspond to non-signalling.

Yes, but in the vision i tried to paint, signalling between "map encoders" is exactly what is required to revise the "map". Causation requires influence other maps, which requires signalling. For me this is not a "just" - it is a key feature, a constructing principle even.

Yes, I guess one could argue that there is not much point to try to deflate the wavefunction if you don't have an alternative description of what is going on that has greater explanatory power. At the very least, people of other interpretations wouldn't be compelled to convert if they weren't given a superior explanation in return.

Fully agreed. I don't expect any opponent to convert, at least until not a full reconstructed theory is in place - that will be hard to understand without changing interpretation.

/Fredrik

 

[Sambuco]

Last week, two new papers by Barandes appeared about his unistochastic formulation: arxiv.2507.21192 and philpapers.BARADA-16.

The following excerpt is taken from one of them:

"From the perspective of this formulation, one sees that wave functions and the Schrödinger equation are secondary pieces of derived mathematics, and not the primary ontological furniture of quantum systems."

It seems to me that Barandes considers that his new formulation brings with it an ontology based on the systems' configuration between measurements.

Lucas.

 

[iste]

One advantage of this formalism is it removes the need for understanding systems in terms of external measurement. We don't need to suppose a measurement apparatus external to the universe, making repeated measurements on the universe. So universe-scale cosmological models aren't an issue.

But Barandes' formalism doesn't work without measurement devices. He has even said in one lecture that the reason you no longer need the phase in the unistochastic description is because it has been substituted by introducing the measurement device into the description. It cannot tell you what a system is doing unless it is coupled to a measurement device.

A Bohmian system evolves deterministically, a unistochastic system evolves unistochastically, both in accordance with their respective nomological laws.

But if you have the measurement device in the Bohmian deription, the readings of the measurement device results / statistics are going to evince the same unistochastic, indivisible behavior when you make attempts to condition on intermediate measurements. A Bohmian can then say that the indivisibile approach is just an effective description of what is really going on in Bohmian mechanics. This generally does not happen with competing interpretations because they usually have enough ontological content that makes them contradict each other. It then makes it difficult to say Barandes is actually giving an underlying explanation here.

 

[iste]

Last week, two new papers by Barandes appeared about his unistochastic formulation: arxiv.2507.21192 and philpapers.BARADA-16.

The following excerpt is taken from one of them:

"From the perspective of this formulation, one sees that wave functions and the Schrödinger equation are secondary pieces of derived mathematics, and not the primary ontological furniture of quantum systems."

It seems to me that Barandes considers that his new formulation brings with it an ontology based on the systems' configuration between measurements.

Lucas.

But it doesn't tell you what the system is doing between measurements. Everything thing the unistochastic system is describing is the system when it is being measured.

Look at around 45:00 - 47:00



Thats why I think the unistochastic system tells you what would happen  if you were to measure it. There's literally no fact of the matter about what is going on otherwise. Is the indivisible stochastic process actually then describing a physical process or just an effective tool that you can add your own underlying ontology that generates the outcomes? Like for instance, using Bohmian mechanics to generate the configuration outcomes. Or maybe the outcomes are generated by something  like the kind of measurement "collapse" that subjectivists would like. I am skeptical that the indivisible process actually makes sense in terms of particle trajectories in the way people interpret realizations of a Wiener process. It seems to me its more like that the marginal probabilities at any given time should be looked at in isolation as the statistics of a one-time measurement given the initial time. And this is how you would view it ordinarily in QM, right? The indivisibility comes from the fact that if you add additional intermediate measurements, the evolution is disturbed. You can't marginalizing over all intermediate measurements at a given time to get the final measurement result probabilities, this is what is being described by the Barandesian interference terms - the statistical discrepancy between the correct marginal probability and the misbehaving joint probabilities. Most clearly seen equation (73) of arxiv.2302 paper.

 

[gentzen]

A Bohmian system evolves deterministically, a unistochastic system evolves unistochastically, both in accordance with their respective nomological laws.

The unistochastic transition matrix evolves continuously. Nothing is said about how the state evolves between division events, and whether it evolves at all in any suitable sense.
And whether the reconstructed unitary matrix can be made to evolve continuously has not yet been investigated, even so I guess this should be a doable mathematical task.

 

[Morbert]

The unistochastic transition matrix evolves continuously. Nothing is said about how the state evolves between division events, and whether it evolves at all in any suitable sense.
And whether the reconstructed unitary matrix can be made to evolve continuously has not yet been investigated, even so I guess this should be a doable mathematical task.

The state (i.e. the configuration) evolves stochastically, with a distribution given by the transition matrix. The distribution is not only given for measurements, but also at all times between measurements. The time-evolution operator $\Theta(t\leftarrow 0)$, when it is not already unitary, can be made unitary with a dilation of the configuration space.

But Barandes' formalism doesn't work without measurement devices. He has even said in one lecture that the reason you no longer need the phase in the unistochastic description is because it has been substituted by introducing the measurement device into the description. It cannot tell you what a system is doing unless it is coupled to a measurement device.

An unmeasured, isolated system evolves unistochastically, yielding a distribution $p(t) = \Gamma(t)p(0)$. I.e. At all times, a system is in a definite configuration, and we can compute a distribution over configurations for the likelihood of the configuration of a system. No measurement devices are needed for these metaphysics to obtain. All a measurement device does in this formalism is allow a physicist to resolve properties of the system, or mutual dynamics of the system+measurement device.

But if you have the measurement device in the Bohmian deription, the readings of the measurement device results / statistics are going to evince the same unistochastic, indivisible behavior when you make attempts to condition on intermediate measurements. A Bohmian can then say that the indivisibile approach is just an effective description of what is really going on in Bohmian mechanics. This generally does not happen with competing interpretations because they usually have enough ontological content that makes them contradict each other. It then makes it difficult to say Barandes is actually giving an underlying explanation here.

A Bohmian would say the indivisible approach is effective, while a unistochastic proponent would say the Bohmian approach is effective. They might also remark that Bohmian mechanics is difficult to extend to relativistic systems.

 

[gentzen]

The state (i.e. the configuration) evolves stochastically, with a distribution given by the transition matrix. The distribution is not only given for measurements, but also at all times between measurements.

Because the connection to the continuity of the time parameter is missing, it currently fails to describe an evolution. The easiest and most-non-commital way to get an evolution is probably to say that there are only finitely many discontinuous jumps in the state between two division events.

If you want to get more commital from there, you can prescribe a probability distribution for the number of discontinuous jumps. Of course, this later more commital way is specific to each concrete physical situation.

 

[Morbert]

Because the connection to the continuity of the time parameter is missing, it currently fails to describe an evolution. The easiest and most-non-commital way to get an evolution is probably to say that there are only finitely many discontinuous jumps in the state between two division events.

If you want to get more commital from there, you can prescribe a probability distribution for the number of discontinuous jumps. Of course, this later more commital way is specific to each concrete physical situation.

The system evolves such that the distribution $p(t)$ tells us the probabilities for the system to be in different possible configurations at time $t$. That's the connection. It sounds like you think it fails because you think we need a distribution over possible trajectories (so that we can evaluate statements like "There were n jumps."). But that's an arbitrary standard.

 

[Morbert]

As an aside, given the elements of the transition matrix look very similar to the decoherence functional for a set of two-time histories, I do think the consistent histories formalism might be able recover division events that are not necessarily measurement events, and hence yield a distribution over coarse-grained trajectories in configuration space, but I am reluctant to explore that since it verges on novel research, which is not allowed.

 

[Sambuco]

But it doesn't tell you what the system is doing between measurements. Everything thing the unistochastic system is describing is the system when it is being measured.

As I mentioned in another thread, I have a similar suspicion to yours, in that I think the configuration of the system between measurements is too hidden, so to speak. In Bohmian mechanics, positions are hidden variables for those who measure, but not for the theory itself, since the position at a future time directly depends on the current position. I have the feeling that, in Barandes's formalism, the current configuration of the system has no bearing on the calculation of the future configuration. In other words, the only configurations that matter are those that occur when a dividing event, i.e., a measurement, occurs.

On the one hand, I agree with what @Morbert says about Barandes' formulation having an ontology based on the systems' configuration, but, on the other hand, I share your opinion that these configurations between measurements don't seem to play a relevant role.

Lucas.

 

[iste]

The state (i.e. the configuration) evolves stochastically, with a distribution given by the transition matrix. The distribution is not only given for measurements, but also at all times between measurements.

An unmeasured, isolated system evolves unistochastically, yielding a distribution p(t)=Γ(t)p(0). I.e. At all times, a system is in a definite configuration, and we can compute a distribution over configurations for the likelihood of the configuration of a system. No measurement devices are needed for these metaphysics to obtain. All a measurement device does in this formalism is allow a physicist to resolve properties of the system, or mutual dynamics of the system+measurement device.

Yes, there is a unistochastic transition matrix at all times, but effectively it is just telling you what would happen  if you were to make a measurement in a counterfactual sense. The time evolution is an evolution about counterfactual measurements. When you actually perform a measurement, that is when a division event occurs that effectively resets the initial time. The distribution you have given for what you have labelled as the unmeasured system is just the Born probability. The fact that the dictionary for the unistochastic transition matrix is expressed in terms of "configuration projectors" would suggest to me the unistochastic matrix is being translated in terms of what is being measured, at least in quantum physics. The correspondence between the unitary evolution and unistochastic process is the correspondence between a stochastic process and a description that only tells you what happens when you measure something. That would imply that the unistochastic process is only telling you about measurements.

In this sense, no the unistochastic process doesn't tell you what happens between measurements. It tells you what the measured configurations of a system is going to spit out when you make a measurement. That is why measurement is needed to be plugged in in Barandes approach.

So this doesn't contradict the idea of definite configurations. But it only talks about them in the presence of measurement. It doesn't tell you what measurement configurations are doing outside of measurement. But rather nicely it tells you what would happen were you to make those measurements at any given time.

A Bohmian would say the indivisible approach is effective, while a unistochastic proponent would say the Bohmian approach is effective. They might also remark that Bohmian mechanics is difficult to extend to relativistic systems.

But there is an asymetry in the sense that it is possible for a Bohemian to use indivisible stochastic approach as an effective one without contradicting their metaphysics. If you truly believe that the universe is as sparse as the Barandesian approach, then Bohmian mechanics contradicts it. You can't incorporate Bohemian deterministic trajectories into indivisibility. You can extract a stochastic process out of Bohemian deterministic trajectories using ignorance.

 

[Morbert]

Yes, there is a unistochastic transition matrix at all times, but effectively it is just telling you what would happen  if you were to make a measurement in a counterfactual sense. The time evolution is an evolution about counterfactual measurements. When you actually perform a measurement, that is when a division event occurs that effectively resets the initial time. The distribution you have given for what you have labelled as the unmeasured system is just the Born probability. The fact that the dictionary for the unistochastic transition matrix is expressed in terms of "configuration projectors" would suggest to me the unistochastic matrix is being translated in terms of what is being measured, at least in quantum physics. The correspondence between the unitary evolution and unistochastic process is the correspondence between a stochastic process and a description that only tells you what happens when you measure something. That would imply that the unistochastic process is only telling you about measurements.

In this sense, no the unistochastic process doesn't tell you what happens between measurements. It tells you what the measured configurations of a system is going to spit out when you make a measurement. That is why measurement is needed to be plugged in in Barandes approach.

So this doesn't contradict the idea of definite configurations. But it only talks about them in the presence of measurement. It doesn't tell you what measurement configurations are doing outside of measurement. But rather nicely it tells you what would happen were you to make those measurements at any given time.

You're imposing an instrumentalist constraint here where there is none. The distributions are evaluated with experiment, yes, but they have an epistemic interpretation: The system is in a definite but unknown configuration, imperfectly resolved by experiment. There are some caveats re/ emergeables vs beables Barandes discusses, but ultimately measurements are ways to know about properties of the system.

But there is an asymetry in the sense that it is possible for a Bohemian to use indivisible stochastic approach as an effective one without contradicting their metaphysics. If you truly believe that the universe is as sparse as the Barandesian approach, then Bohmian mechanics contradicts it. You can't incorporate Bohemian deterministic trajectories into indivisibility. You can extract a stochastic process out of Bohemian deterministic trajectories using ignorance.

The existence of the correspondence means we can interpret the ordinary formalism of quantum theory as effectively encoding the nonmarkovian character of the actually occurring unistochastic processes. Hence, a unistochastic proponent would interpret the nomological equations of Bohmian mechanics (guiding equation etc) as similarly encoding this nonmarkovian character.

-

@iste A broader point: I think I could be convinced that Bohmian mechanics is a more ambitious project. All else being equal, if there were a simple set stochastic laws describing the evolution of a system, and an equally simple set of deterministic laws, the latter would be a more impressive feat. But at the moment all else is not equal. Bohmian mechanics is difficult to generalize, and has more elaborate speculative metaphysical hypotheses.

 

[gentzen]

The system evolves such that the distribution $p(t)$ tells us the probabilities for the system to be in different possible configurations at time $t$. That's the connection.

That is a connection to the time parameter, but not a connection to its continuity.

It sounds like you think it fails because you think we need a distribution over possible trajectories (so that we can evaluate statements like "There were n jumps."). But that's an arbitrary standard.

Without a connection to the continuity of time, it makes no sense to talk of evolution. That is not an arbitrary standard. In fact, I proposed this „finitely many discontinuities“, because it is the weakest and most non-commital connection I could think off.

If you want, you can just forget about the second part. I certainly didn‘t require a distribution over possible trajectories. I just tried to think of a slightly less non-commital connection.

 

[iste]

You're imposing an instrumentalist constraint here where there is none.

I think you and Barandes are overinterpreting what the formalism can possibly say. There is no stochastic process here where the system is not being measured. The stochastic process spits out definite configurations, but this is only random variables describing the physical system when in the presence of a measurement device. Sure, you could give further interpretation but where is that in the formalism? It literally can't tell you anything about what is going on otherwise and this seems pretty straightforwardly what comes out of Barandes' own mouth in the video link I gave between around 45:00 and 47:00.There is no additional stochastic process describing the unmeasured system.

My point isn't that the measured physical system doesn't have definite, physical properties. The issue is that these are only being described in the presence of a measuring device. It doesn't do what Bohmian or Nelsonian mechanics does which is talk about particle behavior evolving freely and independently of the measurement device.

Hence, a unistochastic proponent would interpret the nomological equations of Bohmian mechanics (guiding equation etc) as similarly encoding this nonmarkovian character.

Yes, but my point is that it can't do this without overtly contradicting the the indivisible approach.

I think one way to put it is that indivisible approach can be used to describe a kind of coarse-grained description of the behavior of actual physical ontology in Bohmian mechanics. You cannot do the same the other way round; as in, if you view indivisible approach as describing the literal ontology of the universe, you cannot see Bohmian mechanics as a kind of coarse-grained description of the same ontology. That would be ridiculous. It wouldn't make sense because its far more elaborate and has some kind of additional content.

And I think the indivisible approach can be used in this way to describe any underlying metaphysics like this.

Edited: this post was originally prematurely posted by accident. So this is the intended final form.

 

[iste]

A broader point: I think I could be convinced that Bohmian mechanics is a more ambitious project.

I don't think Bohmian mechanics is the correct interpretation or approach either, I just like this example. Maybe Barandes' might arguably be superior as just a general formulation. But interpretationally I think its arguably worse than Bohmian mechanics because I equally don't see the point in an interpretation that has so little content, and obviously because I disagree that interpretation by Barandes is actually entailed by the formalism.

 

[Morbert]

That is a connection to the time parameter, but not a connection to its continuity.

Without a connection to the continuity of time, it makes no sense to talk of evolution. That is not an arbitrary standard. In fact, I proposed this „finitely many discontinuities“, because it is the weakest and most non-commital connection I could think off.

The transition matrix is continuous. In the limit of $t\rightarrow t_0$, we have $\Gamma(t\leftarrow t_0) \rightarrow \Gamma(t_0 \leftarrow t_0) = \mathbb{1}$. I.e. The continuity of the transition matrix is connected to the definiteness of the configuration at each time. I don't see any problem with this.

I think you and Barandes are overinterpreting what the formalism can possibly say. There is no stochastic process here where the system is not being measured. The stochastic process spits out definite configurations, but this is only random variables describing the physical system when in the presence of a measurement device. Sure, you could give further interpretation but where is that in the formalism? It literally can't tell you anything about what is going on otherwise and this seems pretty straightforwardly what comes out of Barandes' own mouth in the video link I gave between around 45:00 and 47:00.There is no additional stochastic process describing the unmeasured system.

My point isn't that the measured physical system doesn't have definite, physical properties. The issue is that these are only being described in the presence of a measuring device. It doesn't do what Bohmian or Nelsonian mechanics does which is talk about particle behavior evolving freely and independently of the measurement device.

This conversation is starting to loop. The stochastic process spits out a distribution at all times. I.e. The directed conditional probabilities are sparse, but the unconditioned probabilities are not. This metaphysical hypothesis of a system in a definite configuration and evolving stochastically even in the absence of a measuring device is speculative, but no more speculative (and I would argue much less) than realist interpretations like MWI or Bohmian mechanics. A realist interpretation will always involve a commitment to some metaphysics not resolvable by measurement.

I think one way to put it is that indivisible approach can be used to describe a kind of coarse-grained description of the behavior of actual physical ontology in Bohmian mechanics. You cannot do the same the other way round; as in, if you view indivisible approach as describing the literal ontology of the universe, you cannot see Bohmian mechanics as a kind of coarse-grained description of the same ontology. That would be ridiculous. It wouldn't make sense because its far more elaborate and has some kind of additional content.

And I think the indivisible approach can be used in this way to describe any underlying metaphysics like this.

I don't think Bohmian mechanics is the correct interpretation or approach either, I just like this example. Maybe Barandes' might arguably be superior as just a general formulation. But interpretationally I think its arguably worse than Bohmian mechanics because I equally don't see the point in an interpretation that has so little content, and obviously because I disagree that interpretation by Barandes is actually entailed by the formalism.

What I find interesting about this approach is it avoids the pitfalls of Bohmian Mechanics with its alternative speculative metaphysical hypotheses. While both approaches posit a definite configuration even when no measurement is made, the unistochastic approach does not posit a pilot wave or guiding equation. Scott Aaronson disparagingly called it "Bohm minus minus", missing the point that its parsimony is its strength.

 

[Sambuco]

Bohmian mechanics is difficult to generalize, and has more elaborate speculative metaphysical hypotheses.

I'm intrigued by what these "speculative metaphysical hypotheses" you're talking about are.

While both approaches posit a definite configuration even when no measurement is made, the unistochastic approach does not posit a pilot wave or guiding equation.

Without judging whether it's better or worse, I think this is because, in Bohmian mechanics, although the positions are hidden, something about them can be inferred from the measurements. For example, in the double-slit experiment, if the detector that clicks is in the upper half of the screen, the theory indicates that the particle crossed the upper slit. It seems to me that this isn't the case in Barandes's formulation (I need to reread the text you shared a while ago with Barandes' notes where he analyzes the double-slit experiment). In fact, I think it would be very enlightening if Barandes would publish about common experiments analyzed with his formulation.

Lucas.

 

[iste]

A realist interpretation will always involve a commitment to some metaphysics not resolvable by measurement.

Sure, but its preferable to have a description of the system when its not being measured if you are going to make that speculation, otherwise imo it becomes more difficult to argue against the idea that the formulation itself entails no more than a phenomenology description of the measurement process. And I think thats important because Barandes has been marketing it more or less as a formulation that implies an interpretation so it kind of backfires if people can argue that one doesn't imply the other.