I Carroll interviews Barandes on Indivisible Stochastic QM

[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.

 

[Morbert]

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

It's a term I'm borrowing from Barandes himself. For Bohmian mechanics it is the hypothesis that the configuration of a systems evolves in accordance with a wavefunction and guiding equation. Early versions interpreted the wavefunction as something real but modern versions treat it as nomological.

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.

From https://arxiv.org/pdf/2302.10778 :
"Note that the target time t is treated here as a real-valued variable that can be zero, positive, or negative, so there is no assumption of any fundamental breaking of time-reversal invariance."

I read this to mean, if the particle position is measured by the slit detectors at time $t'$, we can presumably evolve a distribution backwards: $p(t) = \Gamma(t\leftarrow t')p(t')$ where $t < t'$, and infer the likelihood that the particle passed through a slit, given that it was (or was not) detected by the adjacent detector. And since $\Gamma(t)$ is continuous, it means the closer the detector is to the slit, the more likely the detected particle passed through that slit.

Maybe there is a unistochastic equivalent to Vaidman's two-state formalism with $$\Gamma_{ijk}(t\leftarrow 0) = p(i, t | j, 0 \land k, t') = \mathrm{tr}(\Theta(t'\leftarrow t)P_i\Theta(t\leftarrow 0)P_j\Theta^\dagger(t\leftarrow 0)P_i\Theta^\dagger(t'\leftarrow t)P_k)$$so that the distribution can be conditioned on both the preparation division event and measurement division event.

 

[Morbert]

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.

There is a description of the system when it is not being measured.

The stochastic process spits out a distribution at all times. I.e. The directed conditional probabilities are sparse, but the unconditioned probabilities are not.

 

[iste]

There is a description of the system when it is not being measured

Then make rebuttles to my points: e.g.

The unistochastic marginal probabilities are just the Born probabilities: i.e. measured probabilities in QM.

The stochastic-quantum correspondence matches the unistochastic transition properties to a Hilbert space representation in terms of projectors for a specific time + initial time that would clearly be referring to measurements in the quantum description.

The unistochastic process requires a measurement device as a subsystem. The video I link again he also explicitly talks about how the measurement device is required. He explicitly says the phase in the complex description is a proxy for the measurement device. I also recall him in the Scott Aaronson video, and maybe the lecture video with the other Biologist, acknowledging that the formulation doesn't talk about what going on unmeasured, and his defence being that orthodox QM doesn't either.

The distribution that the stochastic system spits out at all times is clearly one that occurs only in the presence of a measurement device. Its describing nothing more than what would happen if you performed a single measurement at t1, t2, t3, t4 ... . Indivisibility comes from attempts to make multiple measurements.

 

[Morbert]

The unistochastic marginal probabilities are just the Born probabilities: i.e. measured probabilities in QM.

The stochastic-quantum correspondence matches the unistochastic transition properties to a Hilbert space representation in terms of projectors for a specific time + initial time that would clearly be referring to measurements in the quantum description.

The distribution that the stochastic system spits out at all times is clearly one that occurs only in the presence of a measurement device. Its describing nothing more than what would happen if you performed a single measurement at t1, t2, t3, t4 ... . Indivisibility comes from attempts to make multiple measurements.

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.

The unistochastic process requires a measurement device as a subsystem. The video I link again he also explicitly talks about how the measurement device is required. He explicitly says the phase in the complex description is a proxy for the measurement device. I also recall him in the Scott Aaronson video, and maybe the lecture video with the other Biologist, acknowledging that the formulation doesn't talk about what going on unmeasured, and his defence being that orthodox QM doesn't either.

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.

The stochastic process spits out a distribution at all times. I.e. The directed conditional probabilities are sparse, but the unconditioned probabilities are not.

 

[iste]

Well, I guess there is nothing more to be said. I can only reiterate that with Barandes' stochastic-quantum dictionaries like the one given at the bottom of Morbert's #51 having PVMs baked into the correspondence, I find it hard to justify that the unistochastic transition probabilities can be used to describe an unmeasured system without making additional assumptions that do not exist in the current formalism (because its too sparse compared to, say, Bohmian mechanics). Without that, the interpretation of what is physically happening seems uninformative at best and generally unintelligible to me, personally.

While I don't think Bohmian mechanics is the correct interpretation, I do think that what I believe is the way that Bohmian mechanics produces indivisibility in terms of measurement disturbance is the correct way, and implied by orthodox QM itself. I don't think its possible to interpret the meaning of the interference equations in the Barandes approach in this way while assuming the unistochastic transition probabilities can be describing behavior when no measurement device is present.

 

[gentzen]

The transition matrix is continuous. In the limit of $t\rightarrow t_0$, we have $\Gamma(t\leftarrow t_0) \rightarrow \Gamma(t_0 \leftarrow t_0) = \mathbb{1}$.

But here, $t_0$ is a division event. Together with your "I read this to mean" below, you get some sort of connection around division events, but even that connection is ambiguous or unreliable, without further clarifications or ontological commitments.

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.

What has the "definiteness of the configuration at each time" to do with "continuity"? I guess I read this the wrong way around, i.e. you probably mean that the "continuity of the transition matrix" somehow gives rise to an evolution of the configuration.
But this is only true as long as the transition matrix is exactly the identity. As soon as the configuration is allowed to jump around arbitrarily, there is no longer an evolution.

However, I realized that it is good that you try to defend Barandes' proposal, because Barandes himself "lacks the time" to do it. This gives people like me the opportunity to present their quibbles as clear as possible. I still try to bring across two concrete "fixable"/"doable" things.
However, I came to realize now that beyond those, there might be a deeper issue common to all "reconstructions of quantum mechanics". Namely, QM is predictive, but I am no longer sure whether Barandes' "reconstruction" is still predictive, and whether other existing "reconstructions of quantum mechanics" fail to preserve this "QM is predictive" part too.

Here is your "I read this to mean":

From https://arxiv.org/pdf/2302.10778 :
"Note that the target time t is treated here as a real-valued variable that can be zero, positive, or negative, so there is no assumption of any fundamental breaking of time-reversal invariance."

I read this to mean, if the particle position is measured by the slit detectors at time $t'$, we can presumably evolve a distribution backwards: $p(t) = \Gamma(t\leftarrow t')p(t')$ where $t < t'$, and infer the likelihood that the particle passed through a slit, given that it was (or was not) detected by the adjacent detector. And since $\Gamma(t)$ is continuous, it means the closer the detector is to the slit, the more likely the detected particle passed through that slit.

So according to your reading, the measurement at time $t'$ tell us both something about what was before the measurement, and about what is after the measurement. This is interesting, because the word "measurement" is often used ambiguously: A POVM for example only tells us what was before the measurement. And "filtering" (imagine for example a double slit with polarization filters at both slits) only tells us something about what is after the "filtering"/"measurement".

 

[Morbert]

But here, $t_0$ is a division event. Together with your "I read this to mean" below, you get some sort of connection around division events, but even that connection is ambiguous or unreliable, without further clarifications or ontological commitments.

What has the "definiteness of the configuration at each time" to do with "continuity"? I guess I read this the wrong way around, i.e. you probably mean that the "continuity of the transition matrix" somehow gives rise to an evolution of the configuration.
But this is only true as long as the transition matrix is exactly the identity. As soon as the configuration is allowed to jump around arbitrarily, there is no longer an evolution.

The ontological and nomological commitments are straightforward: The system is in a classical configuration, and evolves stochastically along a trajectory in configuration space, with dynamics given by directed conditional probabilties. Stochastic doesn't mean arbitrary.

However, I came to realize now that beyond those, there might be a deeper issue common to all "reconstructions of quantum mechanics". Namely, QM is predictive, but I am no longer sure whether Barandes' "reconstruction" is still predictive, and whether other existing "reconstructions of quantum mechanics" fail to preserve this "QM is predictive" part too.

The correspondence is exact, so there is exact agreement with experiment.

So according to your reading, the measurement at time $t'$ tell us both something about what was before the measurement, and about what is after the measurement. This is interesting, because the word "measurement" is often used ambiguously: A POVM for example only tells us what was before the measurement. And "filtering" (imagine for example a double slit with polarization filters at both slits) only tells us something about what is after the "filtering"/"measurement".

I'm using the word measurement, but measurement has no fundamental significance in this formalism. If a system is highly correlated with the environment at some time $t'$, and we marginalize over the environment, the dynamics of the system will contain directed conditional probabilities at $t'$. Measurement, POVMs etc are all derived features.

 

[Fra]

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

I think there shouldnt be.

The idea that there even can come to exist rational description of something, without having interact with it ~ without "observer"/"mesaurement device" is to me a total breakdown of mandatory inference rules. That would we completely pull out of the blue, and would be deeply intellectually unsatisfactory and also not falsifiable even.

In Baranders view, the measurement is not "prepared" as a choice of an external observer in macroscopic realm, it rather happens spontaneously, and is even unavoidable. The only difference between measurement and interactions is that Baranders consider some qualifications on the complexity level and efficient communication with the environment.

This is a pretty major shift in perspective.

But it's indeed unsatisfactory until we complete this line of reasoning, by remove the qualification of what subsystem constitutes a measurement device(generalization). This is an open issue. And this for sure would deviate from unistochastics and quantum mechanics.

The new quest would then be to try to explain, why regular objectivity is attained (unistochastics receovered) as you scale the arbitrary system up to what qualifies as a macrosocpic measurmeent device - but without resorting to explanations of the usualy type where you imagine the state of the whole universe where you just marginalise out most of it. It would come with extreme fine tuning and lack explanatory value, if we think that quantum mechanics would be some limit of sometihng more general.

This more general thing is what I want to understand, and for this an interpretation that is "constructive" as in helpful to move forward, is what I seek. Not an interpretation that would pretend that if we just apply it all mysteries are gone. Such interpretation does not exist at all to my knowledge.

Edit: In general a good "interpretation" to me is not one that pretendes to solve and cover up all problems, or pretend they don't exist, it's on that implicitly suggest a whole researh program, so actual progress can be made.

/Fredrik

 

[iste]

The idea that there even can come to exist rational description of something, without having interact with it ~ without "observer"/"mesaurement device" is to me a total breakdown of mandatory inference rules.

But surely this happens all the time elsewhere in science?

 

[Fra]

But surely this happens all the time elsewhere in science?

The Ad hoc reasoning we have all seen? Sure. But it is elegant and something to strive for?

And even if an ad hoc model can later be fitted empirically to data, it will qualify as an effective description, but it has almost no explanatory value.

A major part of this whole discussion is not just about finding an effective model, that we can fit to experimental data(for most subatomic physics, we have one alredy, but most dont understand it conceptually), but construct a model that makes sense and adds explanatory value and insight.

Here I think the role and nature of the "probe" to the system under observation is key, and while it is annoying that the probe is not uniqe, it makes no sense to try to do away with it completely.

To go further here brings us into philosophy of the scientific method and the subtopic of hypothesis generation. Anyway, there are all guiding principles at least for me, in the quest of understanding things.

/Fredrik