How valid is the indivisible interpretation of quantum mechanics?

[Morbert]

No. For example, Bohmian QFT (Struyve-Westman or Dürr-Goldstein-Tumulka-Zanghì) constructs stochastic processes where field configurations are the state variables, and the process is Markovian only in the extended (φ, Ψ[φ]) space and non-Markovian in the field configurations alone.

So what is meant by "The non-Markovianity in Barandes' correspondence comes from projecting this onto particle-configuration variables"?

 

[danieltanfh95]

So what is meant by "The non-Markovianity in Barandes' correspondence comes from projecting this onto particle-configuration variables"?

Projection to any configuration space produces the non-Markovianity, particles or fields. Barandes uses particle configurations, so I named that specifically, but the mechanism is the projection itself, not the particle choice.

 

[Fra]

I've tried to understand what your objection really is... I wonder if the disagreement is on terminology after all.

The issue is that the "true value" of the configuration of a subsystem plays no role, even in the temporal evolution of the same subsystem.


This is not true for the reasons I explained above. Of course, this is something Barandes is aware of. In his work 10.31389/pop.186 (arxiv.2302.10778), he wrote:

"To the extent that quantum theory is empirically adequate, the higher-order conditional probabilities are then unobservable in experiments and will be left unspecified in this paper (...) Whether there exists some theoretical principle that picks out one set of higher-order or whole-trajectory probabilities from all the various possibilities is a question that will be left to future work."

Lucas.

I would like to participate in the discussion, as I have an objection to Barandes' formulation (we already talked a little about that in other threads), and I'm not sure if it's related to the one @iste is pointing out.

My objection to Barandes' interpretation lies in the fact that he postulates the existence of "things" that are not physical, in the sense that they play no role in his own theory. To understand what I mean, it's worth noting that, given the stochastic-quantum correspondence, Barandes' formalism could be described by saying that, between division events, the position of a particle at each instant in time is a well-defined variable whose probability is given by the square of the wave function. As we've already discussed in another thread, this allows for cases like a particle entering through one slit and exiting through the other in the two-slit experiment. This doesn't have to be a problem in itself, the issue is that these values for the position of a particle are not physical, in the sense that they don't appear in the equations of the theory!

Another way to look at it is by examining how this same issue is addressed in other $\psi$-epistemic interpretations. For example, in RQM, it's argued that, in general, $P(c|a) \neq \sum_i P(c|b_i) P(b_i|a)$. Since assigning a value to $b$ has no physical meaning, it is assumed that it does not (physically) exist. In contrast, what Barandes does is start from the fact that it is possible to define the probabilities of a variable taking one value or another at time $t$ and, from this, conclude that that variable must take some value at that moment.

In a way, this might seem to contradict well-known no-go theorems, such as Bell's and/or Kochen-Specker's. One way to see how Barandes' interpretation is able to overcome this type of no-go theorems is to think that these implicitly assume a divisible temporal evolution, but the truth is much simpler: Barandes's interpretation assigns a value to the variables at each instant in time, but these values are not physical, they play no role in the theory, and they aren't even mentioned in it!

Lucas.

When I read this again it sounds like your definition of "physical" is something that must constitute an objective beable? and that constitutes a partition of the sample space?

Indeed this is not how the configuration space works, if that is your objection? you are of course correct.

/Fredrik

 

[iste]

the issue is that these values for the position of a particle are not physical, in the sense that they don't appear in the equations of the theory!

I'm not sure I understand what you mean by this if these values have probabilities given by the central correspondence equation of the theory. You don't have to interpret the inequality you give as b not having any physical meaning - a measurement of b just disturbs c, like Bohmian effective collapse as talked about in David Albert's commentary on Barandes.

 

[Sambuco]

I'm not sure I understand what you mean by this if these values have probabilities given by the central correspondence equation of the theory.

As you correctly point out, the theory provides probabilities for the different values a variable can take at different times. However, the actual value that this variable takes at a specific instant between two division events is not included in the theory. In other words, the probability of a system's configuration taking a particular value at a given time depends exclusively on the system's configuration at the last division event and, of course, on the Hamiltonian.

To be more specific, let's consider a well-known example: the double-slit experiment. Given the events $a$ = "the source emitted a particle," $b_i$ = "the particle passed through slit i," and $c$ = "the particle was detected on the screen in a particular region," the only way to compute the probability of the last event is through the equation $P(c,t) = \Gamma_{ca}(t←t_0) P(a,t_0)$, where $\Gamma_{ca}(t←t_0) = P(c,t|a,t_0)$. According to most $\psi$-epistemic interpretations, such as RQM, the particle doesn't have a defined value for its position at any intermediate time between $t_0$ and $t$, so the event "the particle passed through slit i" lacks physical meaning. Instead, Barandes postulates the existence of well-defined values for the system's configuration at all times, even if these configurations don't appear in the equations of the theory, i.e., they don't play any (physical) role. In my opinion, this is a metaphysical prejudice that arises from the fact that, in our everyday experience, this kind of assumption holds true.

In comparison, this is completely different from what happens in Bohmian mechanics, where particles possess well-defined positions at every instant, but these positions appear in the equations of the theory.

You don't have to interpret the inequality you give as b not having any physical meaning - a measurement of b just disturbs c, like Bohmian effective collapse as talked about in David Albert's commentary on Barandes.

Of course, but the key difference is that the measurement of $b$ represents a different context, which is reflected in the hamiltonian. For the two-slit example I mentioned above, a measurement at the slits modifies the dynamics in such a way that decoherence occurs and this measurement becomes a division event, so the particle's position enters the equations.

Ultimately, it's a matter of interpretation, but personally, I don't like it.

Lucas.

 

[Sambuco]

When I read this again it sounds like your definition of "physical" is something that must constitute an objective beable? and that constitutes a partition of the sample space?

Indeed this is not how the configuration space works, if that is your objection? you are of course correct.

I believe my post #125 should have cleared things up. Do you think it did?

Lucas.

 

[iste]

In my opinion, this is a metaphysical prejudice that arises from the fact that, in our everyday experience, this kind of assumption holds true.

Yes, 100%. The aim of serious Bohmians and Barandesians might be partly to see if what we find intuitive can hold in quantum theory, which would arguably make a simpler solution to both measurement problem and classical limit. From my perspective, measurement disturbance would itself could provide a good reasoning for why there may exist Bohmian or Barandesian "hidden variables" but these don't show up in quantum theory. They make trajectories epistemically inaccessible in-principle because out only means of looking at them would be disturbing.

In comparison, this is completely different from what happens in Bohmian mechanics, where particles possess well-defined positions at every instant, but these positions appear in the equations of the theory.

I only read this part after writing the above. I don't understand what you mean when you say they featute in Bohmian mechanics but not Barandes. I don't see the particle position entering only at division events; you have transition probabilities for the position at all times.

 

[Sambuco]

The aim of serious Bohmians and Barandesians might be partly to see if what we find intuitive can hold in quantum theory, which would arguably make a simpler solution to both measurement problem and classical limit. From my perspective, measurement disturbance would itself could provide a good reasoning for why there may exist Bohmian or Barandesian "hidden variables" but these don't show up in quantum theory. They make trajectories epistemically inaccessible in-principle because out only means of looking at them would be disturbing.

I completely agree!

I don't understand what you mean when you say they featute in Bohmian mechanics but not Barandes. I don't see the particle position entering only at division events; you have transition probabilities for the position at all times.

In Bohmian mechanics, given the guiding equation, the particle's future position can be obtained using its current position. For example, in the double-slit experiment, it is important whether the particle passes through the upper or lower slit; depending on which slit it passes through, the particle will be detected in the upper or lower half of the screen. There is nothing similar in Barandes' formulation. Whether the particle passes through the upper or lower slit does not alter in the slightest the probability of its detection in any region of the screen.

Lucas.

 

[Fra]

I agree with alot of what you write, but it seems this is the key issue...

I believe my post #125 should have cleared things up. Do you think it did?

Barandes postulates the existence of well-defined values for the system's configuration at all times, even if these configurations don't appear in the equations of the theory, i.e., they don't play any (physical) role. In my opinion, this is a metaphysical prejudice that arises from the fact that, in our everyday experience, this kind of assumption holds true.

So You and iste seem to be questioning the point of saying configurations are real if they do not generate future evolution in the usual trajectory-law sense. You also seem to see this as a metaphysical prejudice of Barandes.

I see it differently! I think the more serious prejudice is the assumption that physical law must be a flow on some objective state space: an initial/boundary-value problem, perhaps with added constraints. But how is such a law physically supposed to be enforced? How exactly does an initial condition “cause” the future flow? It seems to me that the usual paradigm leaves this enforcement question largely unexplained. Mathematics itself does not enforce anything in nature.

For me, the key point of the indivisible stochastic picture is that it questions this conventional picture of fundamental dynamical law and causation.

I am thinking like this.... If the configuration is the system, then there is no additional internal structure that also has to encode its own whole history or future path. The current configuration simply evolves stochastically, one transition at a time. To me this looks like a more physically defensible enforcing mechanism.

The relevant residual question is not: What hidden path generates the future? The relevant question is: What constrains the next admissible transition?

That constraint here is Gamma. The stochastic evolution depends on both the current configuration and the transition constraint. But I think Gamma cannot be generated by the hidden path through intermediate configurations. Rather, I would understand it as the limiting form of a stochastic relation between configurations, constrained by the wider physical context or environment. In this reading, Gamma can be understood as implicitly encoding information about historical interactions between the subsystem configuration and its environment; these stabilize the subsystem.

This is why I do not think the configuration path belongs in, or fits into any primitive law. The path can not be what not what enforces the stochastic evolution; Gamma does together with current state. The only “memory” relevant to the transition lies in the stochastic constraint, which is not encoded in the subsystem alone; it must be relational to the environment; not in the form of "formal paths" in subsystems configuration space.

My personal intuition is that Gamma would conceptually have to emerge from somelike like stable stochastic relations between subsystems and their environments, but no one knows how, and Barandes does not elaborate it. But thinking about it like this, helps me appreciated the picture, that is my point.

So the real missing question is not “why have configurations if they do not generate trajectories?” The deeper question is: how is Gamma physically enforced, evolved, or constructed? To understand how Gamma, as a kind of stochastic relation, is constructed becomes very strange if one does not understand configurations as real. It is like trying to define relations while denying the reality of the relata. I think they must co-emerge. One without the other makes no sense.

Ultimately, it's a matter of interpretation, but personally, I don't like it.

We agree on this, except I personally like it - even given it generates new questions (but that isn't a bad thing).

/Fredrik

 

[iste]

I completely agree!


In Bohmian mechanics, given the guiding equation, the particle's future position can be obtained using its current position. For example, in the double-slit experiment, it is important whether the particle passes through the upper or lower slit; depending on which slit it passes through, the particle will be detected in the upper or lower half of the screen. There is nothing similar in Barandes' formulation. Whether the particle passes through the upper or lower slit does not alter in the slightest the probability of its detection in any region of the screen.

Lucas.

Fair enough, that sounds similar to my criticism in the thread.

 

[Sambuco]

So You and iste seem to be questioning the point of saying configurations are real if they do not generate future evolution in the usual trajectory-law sense. You also seem to see this as a metaphysical prejudice of Barandes.

I don't object to the configurations between division events being considered real because "they do not generate future evolution in the usual trajectory-law sense," but because these configurations do not appear at all in the equations of the theory.

In fact, I would say that I almost completely agree with the rest of your post, given that I sympathize with relational interpretations.

Lucas.

 

[Morbert]

I don't object to the configurations between division events being considered real because "they do not generate future evolution in the usual trajectory-law sense," but because these configurations do not appear at all in the equations of the theory.

Unless I am misunderstanding, take some configuration $i$: $p_i(t) = \sum_j \Gamma_{ij}(t\leftarrow t_0)p_j(t_0)$. This is equation (4) in the correspondence paper.

 

[Sambuco]

Unless I am misunderstanding, take some configuration $i$: $p_i(t) = \sum_j \Gamma_{ij}(t\leftarrow t_0)p_j(t_0)$. This is equation (4) in the correspondence paper.

Yes, I know. And, given the stochastic-quantum correspondence, that equation can also be written as $p_i(t) = |\Psi_i(t)|^2$, which is eq. (23) in the paper. Now, let's compare a traditional $\psi$-epistemic interpretation, such as that of Copenhagen/RQM/QBism, with Barandes' interpretation. According to the former, this equation represents the probability of the system being in that configuration only if it interacts with another physical system. In Copenhagen, the other system will be a measuring instrument; in RQM, it will be any other system; and in QBism, it will be an agent. In contrast, in Barandes' interpretation, this equation allows us to calculate the probability of the system having a definite configuration even if it is a closed system that does not interact with anything. My objection is that this assumption is an addition to the mathematical formalism, since the fact that the system reaches a certain configuration and not another plays no role in the theory as formulated by Barandes. The only way in which the configuration of a system at a given instant has any relevance is if it interacts with another system, causing, at least partially, a division event.

Lucas.

 

[Fra]

Before i comment more.. one question.

I don't object to the configurations between division events being considered real because "they do not generate future evolution in the usual trajectory-law sense,"
but because these configurations do not appear at all in the equations of the theory.

Do you mean, it is not enough for you that "only" the probability of configuration is there? Ie you want the explicit config vs timr in there? Not its probability. Is that it?

/Fredrik

 

[Fra]

the probability of the system being in that configuration only if it interacts with another physical system. In Copenhagen, the other system will be a measuring instrument; in RQM, it will be any other system; and in QBism, it will be an agent. In contrast,

Id say in Barandes view another fellow susbsystem takes this role of instrument/agent.

in Barandes' interpretation, this equation allows us to calculate the probability of the system having a definite configuration even if it is a closed system that does not interact with anything.

we can "calculate" in any view. But we can only verify under certain conditions.

My objection is that this assumption is an addition to the mathematical formalism, since the fact that the system reaches a certain configuration and not another plays no role in the theory as formulated by Barandes. The only way in which the configuration of a system at a given instant has any relevance is if it interacts with another system, causing, at least partially, a division event.

Just like a stochastic agents "actions" will not be changed until it is informed of a change. The stochastic constraint (if we understand it as a stochastic relation between environment and system) will not change until the relations are revised due to the system interaction with something in thr environment that makes info available.

I still think they way one understands causation or law here is the key.

An agent for example can not revise his state due to information not at hand. This is why its the subsystems expectation/knowledge that determinea a stochastic better. Paradoxally the process does not care about the "true state". Only information about it matters.

/Fredrik

 

[Sambuco]

Do you mean, it is not enough for you that "only" the probability of configuration is there? Ie you want the explicit config vs timr in there? Not its probability. Is that it?

Yes, something like that. My objection is similar to the one raised against some modal interpretations. I would like to add two brief comments on this matter:

1. It is not surprising that Barandes' interpretation has points in common with modal interpretations, given the work he has done on this in the past. From that perspective, what he has achieved is to formulate an interpretation where the role of the wave function as a "dynamical state" is less important than in existing formulations.

2. The second issue concerns the true novelty of this interpretation compared to existing ones. Personally, I consider it very similar to Rovelli's relational interpretation, but with an ontology centered on the system's configuration, which takes definite values at all times, rather than an ontology based on discrete and sparsed "quantum events".

Id say in Barandes view another fellow susbsystem takes this role of instrument/agent.

Yes, this is a point of agreement with the relational interpretation.

Paradoxally the process does not care about the "true state". Only information about it matters.

I completely agree! My position is somewhat more radical: a "true state" (the "value state" of modal interpretations) only exists when there is information about it.

Lucas.

 

[Fra]

Personally, I consider it very similar to Rovelli's relational interpretation,

I agree that Barandes view has similarities with RQM, but many interpretations are similar.

My own critique of Barandes is that he does not give a first-principles construction of Gamma. In that sense the stochastic-quantum correspondence is still a correspondence, not yet a deeper explanation.

But I would make a similar criticism of RQM. Rovelli correctly emphasizes that there is no absolute view and that different views can only be compared through physical interaction. But that comparison process is still just a quantum-mechanical interaction he says. So RQM uses QM to glue together the relational perspectives; it does not explain the origin of the quantum structure itself.

Where I see novelty in Barandes is that he gives a different handle on the nature of physical law. The primitive is not a global wavefunction evolving on an objective state space, but a stochastic transition structure between configurations. Rovelli does not, in my view, offer a similarly useful handle on the nature of law itself.

An agent for example can not revise his state due to information not at hand. This is why its the subsystems expectation/knowledge that determinea a stochastic better. Paradoxally the process does not care about the "true state". Only information about it matters.

I completely agree! My position is somewhat more radical: a "true state" (the "value state" of modal interpretations) only exists when there is information about it.

When I used the word paradoxically I was trying to express the following point of your reasoning.

If one thinks of laws of nature as acting on an objective state space of facts or truth-values, then it gets paradoxal to say that the process cares about information rather than the “true state.” But in a picture of interacting evolving subsystems, the current information state is precisely what determines how a subsystem can react. No subsystem can update its behaviour on information it does not have.

So the “real truth values” of other systems are always shielded behind layers of interaction(or inference which makes it more clear what i mean). This also should also shields the stochastic constraints. What a subsystem actually has is information about something else, and that information is represented by a probability measure or predictive state.

But I see an important trick here. My information state about something else can itself be my true state of information. And this is my configuration state. A subsystem may encode an uncertain probability distribution about another configuration, but that encoded distribution can still be a definite configuration of the subsystem itself. In that sense, uncertainty about one configuration can map onto certainty in another configuration space.

This is why I think configuration space should be understood abstractly, not merely in terms of particle properties. The configuration space of a subsystem can be its encoding microstructure. A true memory configuration state can represent an uncertain state of some other transformed configuration. That is one way to bridge the gap between “true state” and “information state.”

So I partly agree that if no subsystem has information about something, then it does not exist anywhere. Ie. if not a single observer anywhere in the universe has see it, it seems fair to say it does not exist.

When that information is later revealed, it makes a physical difference. Nearby systems update their configurations, and the relevant effective transition constraints Gamma change as well. This is similar to measurement. Before which-path information is available to the environment, the process is indifferent to the “actual value” in the public classical sense, and interference remains. Once the information is recorded in the apparatus/environment the context changes and interference disappears.

So I distinguish between true and objective. A true state is a fact, or ontological configuration state, relative to one subsystem. An objective statement is something stabilized across subsystems through interaction, and requires emergence, it is not a single "configuration".

If “exists when there is information about it” you means exists only when it is macroscopic shared information, or when all context can confirm it, then that sound like classical logic of objective beables.

/Fredrik

 

[Sambuco]

My own critique of Barandes is that he does not give a first-principles construction of Gamma. In that sense the stochastic-quantum correspondence is still a correspondence, not yet a deeper explanation.

Absolutely. If his theory is intended to be more fundamental, one would expect not only a correspondence, but a reconstruction of the Hilbert's space quantum formalism.

Where I see novelty in Barandes is that he gives a different handle on the nature of physical law. The primitive is not a global wavefunction evolving on an objective state space, but a stochastic transition structure between configurations. Rovelli does not, in my view, offer a similarly useful handle on the nature of law itself.

I disagree with this. In relational quantum mechanics, the wave function is considered merely a mathematical tool that allows us to calculate the probability of an event occurring given information about another event; that is, the transition probabilities between events.

If “exists when there is information about it” you means exists only when it is macroscopic shared information, or when all context can confirm it, then that sound like classical logic of objective beables.

Good point. When I said "exists when there is information about it," I meant a notion of physical information à la Shannon, so to speak. Quoting Rovelli in a recent paper: "

“"Information” is understood here in its purely physical sense, namely as correlation: a system has information about another system if the number of possible states of the two systems is less that the product of the number of possible states of each."

As an additional comment, there is a reconstruction of the quantum formalism associated with the relational interpretation, such as Höhn's work, based on an informational approach.

Lucas.

 

[Fra]

Absolutely. If his theory is intended to be more fundamental, one would expect not only a correspondence, but a reconstruction of the Hilbert's space quantum formalism.


I disagree with this. In relational quantum mechanics, the wave function is considered merely a mathematical tool that allows us to calculate the probability of an event

This was my point, the entire discussion here is to seek understanding of the descriptive mathematics. Ie. to map the mathematical structures to some explanatoty insightful picture of reality. Without this Rovellis just matches two pictures but does not explain its emergence.

Any, the final vision for me is of course NOT, only to just reproduce quantum theory exactly. They purpose would be to explain more, unification of all forces. This is where the "no law", and emergent constraints are the conceptual good match. Recovering standard QM is not the goal, is is just a "consistency check" in the limite of small systems relative to a dominant well evolved/equilibrated dominant context. Which is explicitly NOT the conditions valid for, General relativity for example. And Barandes correspondence offers this, without referring to hilbert space and hamiltonian notions.

As an additional comment, there is a reconstruction of the quantum formalism associated with the relational interpretation, such as Höhn's work, based on an informational approach.

The spirit of the paper; to explain quantum mechanics from the agents rational inferences about a system - subject to some constraints of information preservation etc, is exactly what i conceptually refer to. So that is a good reference relevant to the discussion!

But too many things are assumed in the paper, the biggest issue is that if one has en external description of O and S, we have violated the instrinsic construction already from this "background" context. That will still serve as an exampl, but it misses the key point. How O and S evolve and emerge, and how the information capacity of a system can change, and how objectivity emerges from interacting subsystems, but without using an external description (superspace) where there is a fixed microstruture for the subsystems. (this is the background independnence). So one needs to start the other way around, without "classical observers", without a external view. (OF course QM as it stands does RELY on an external massive observer O, so in this sense, the premises are correct. But as i mentioned, the goal for me isnt "just" to recover QM from an idealisation one, but to extend the explanatoty value so that in that process we gain new insight on gravity and how all other interactions and spacetime emerge)

From other "reconstructions" of quantum probabilitity i have seen before another big problem is that respectless introduction of real numbers. This is easy to miss, but just assuming there is a background context where you can assign real numbers to things, is a massive "background" context from the inferential perspective. This index allows indexing with infinite precision. And if this has no physical basis to the agent (which I think it hasnt) then we contanimated the model with mathematical degrees of freedom that is guaranteed to mix up with thingsn and cause confusion. (for example a kind of "mathematical entropy", inconsistencies in counting, infinities etc).

The paper says

"In this work, we therefore do not address the measurement problem: we simply assume a division between the system S and a ‘classical’ observer O and shall neither explain the origin and nature of this ‘classical’ O, nor why S gives definite answers (i.e., yields definite measurement outcomes) upon being asked some Qi ∈ Q by O. This will nevertheless allow us to derive the quantum formalism for qubits relative to this O."
-- https://arxiv.org/abs/1511.01130

/Fredrik

 

[Sambuco]

Without this Rovellis just matches two pictures but does not explain its emergence.

And Barandes correspondence offers this, without referring to hilbert space and hamiltonian notions.

Personally, I see no difference between the two interpretations. RQM can also be framed/interpreted as a stochastic process, with the caveat that the variables only have values at certain times. In any case, we can agree to disagree on that point.

From other "reconstructions" of quantum probabilitity i have seen before another big problem is that respectless introduction of real numbers. This is easy to miss, but just assuming there is a background context where you can assign real numbers to things, is a massive "background" context from the inferential perspective.

Interesting. To be honest, I'd never stopped to think about it.

Lucas.

 

[Fra]

Interesting. To be honest, I'd never stopped to think about it.

Although this is diverging from the topics, this is critical IMO to any "relational picture", if you require that the relata must be able to encode their relations. Here assuming that a primordal relata can index things in a continuum, is a very huge jump/omission in reconstructions. So this is a MAJOR issue that needs to be solved and it takes is to the foundations of probability theory itself. The question one may ask, what is the physica basis for the [0,1] contiuum? what kind of physical relata can even encode that? The simplest solution seems to be to think that, none can - and therefore the continuum as well as probability itself must also be emergent from the discrete formalism.

Most papers that are in the spirit of "physics from inferences", also various entropic reasonnings, ariel caticha and others make this jump/omission, and this is the point where i stop reading the rest of the paper.

/Fredrik