I A new realistic stochastic interpretation of Quantum Mechanics

[PeterDonis]

This transition implies the following assumptions:
- $A(a, b, \lambda) =\pm 1, B(a, b, \lambda) = \pm 1$ (aka determinism assumption)

Yes, Bell assumes that the measurement results are predetermined, so his theorem only applies to models for which that is true.

- $A(a, b, \lambda) = A(a,\lambda), B(a, b, \lambda) = B(b,\lambda)$ (aka locality assumption)

Yes. As I said before, I was calling this assumption "factorizability", but Bell does use "locality" to refer to the underlying rationale for it--basically that A's measurement settings can't affect B's results, and vice versa.

- $\rho(a,b,\lambda) = \rho(\lambda)$ (aka, no enhancement, free-will assumption)

No, this is not an assumption. The joint probability being calculated is for measurement results $A$ and $B$ given measurement settings $a$ and $b$. There is no integration over $a$ and $b$, and $\rho$ is not a function of them; $\rho$, as Bell explicitly states, is the probability distribution for $\lambda$, which is the only thing that is integrated over.

 

[Fra]

It's much simpler than you appear to be trying to make it.

Finally something we agree on.

The question is, if reality is as simple as the ansatz in Bells paper? I think not.

I thought it was obvious that I am reconsidering the premises of Bell's assumptions. In particular what is NOT explicitly there, by either beeing implicit and not elaborated or simply overlooked by Bell or both.

My firm opinion is that the "simpler picture" simplifies things too much, and from my perspective (not Bell's original) seems to have a too simple mental model of the nature of micro-causality in interactions between parts of the system. You are correct that this is not explicitly mentioned in Bell's paper.

Baranders picture here gives another perspective. But it is painfully clear how hard it is to convey, and perhaps we need to await the explicit reconstruction from the other perspective, to convinced everyone. That does not exist yet, which is why I try to convey it conceptually.

Yes, I am saying that in order to correct your understanding of what lambda includes.


That's also included in lambda. You still don't seem to get the point: lambda includes everything that is common to both entangled particles and might affect the measurement results.

If you and Bell holds the simpler "mental model" that the outcomes can be partitioned by "common factors", some of which we as physicists are ignorant; then that clearly illustrates the oversimplification, that perhaps satisfieds some, but not me. This is exactly the problem, and also why I think what I say makes no sense to you.

The difference beweteen "ignroance" and variables that are known only to parts, is why certain hidden paramters, isn't compatible with the preparation, and thus don't commute in the information processing chain. This is why the simple form of partitioning is an oversimplification. And this is also at the heart of Baranders indivisibility, but you can put it in different ways, but it's related.

/Fredrik

 

[PeterDonis]

The question is, if reality is as simple as the ansatz in Bells paper? I think not.

So far I have not seen from you a correct description of the ansatz in Bell's paper. I think you need to get that right first before trying to form an opinion about it.

If you and Bell holds the simpler "mental model"

We don't. Once more, this "mental model" is something you're reading into Bell's paper that simply isn't there. Bell does not have any specific "mental model" underlying his assumptions; his theorem applies to any model whatever that satisfies the assumptions.

 

[martinduclocher]

sorry to disturb you, but in the barandes approach, knowing that there is no accessible phase and that only the transition probabilities are accessible due to the squaring of the unit matrix. So it's not possible to reconstruct the wave function experimentally ? and have access to phases and amplitudes, which puts its approach in tension with what can be done experimentally . I'm an amateur, so what I say may be inaccurate.

 

[pines-demon]

sorry to disturb you, but in the barandes approach, knowing that there is no accessible phase and that only the transition probabilities are accessible due to the squaring of the unit matrix. So it's not possible to reconstruct the wave function experimentally ?

There is no wave function in Barandes approach...

 

[martinduclocher]

Yes, but the fact that we can experimentally reconstruct the wave function and see that the way it interacts, for example in this experiment, or the way the wave functions interact with each other, dictates the polarization of the material. How can we understand this in the vision of barrrandes? https://arxiv.org/abs/2102.02266
Similarly, how can we understand phenomena such as the bose-einstein condensate in barrandes' vision if there are no more physical waves? Sorry in advance if my porpos is confusing but I would like to understand

 

[pines-demon]

Yes, but the fact that we can experimentally reconstruct the wave function and see that the way it interacts, for example in this experiment, or the way the wave functions interact with each other, dictates the polarization of the material. How can we understand this in the vision of barrrandes? https://arxiv.org/abs/2102.02266
Similarly, how can we understand phenomena such as the bose-einstein condensate in barrandes' vision if there are no more physical waves? Sorry in advance if my porpos is confusing but I would like to understand

That's what this thread is about. I'm not sure that any of us understand what Barandes interpretation really means (I think he is lacking ontology). However we know what are the rules of the game from his stochastic-quantum correpondence. In his dictionary, the wave function is just an operator that when squared tells you about the conditional probabilities. You can always construct such an operator from any given set of probabilities, it is only that in Barandes' formulation "it is no longer wavy".

What you want to understand is how interference arises, like the interference in a double slit experiment or in interacting Bose-Einstein condensates (which is usually a wave like phenomenon). For the double slit this is what Barandes says:

According to the approach laid out in this paper, the particle really does go through a specific slit in each run of the experiment. The final interference pattern on the detection screen is due to the generic indivisibility of time evolution for quantum systems. One cannot divide up the particle’s evolution into, firstly, its transit from the emitter to the slits, and then secondly, conditioned on which slit the particle enters, the particle’s transit from the slits to the detection screen. The interference that shows up in the double-slit experiment may be surprising ,but that is only because indivisible stochastic dynamics can be highly nonintuitive. In the historical absence of a sufficiently comprehensive framework for describing indivisible stochastic dynamics, it was difficult to recognize just how nonintuitive such dynamics could be, or what sorts of empirically appearances it could produce.

After having read and listened to Barandes, I still do not have a clear toy model in my head on how indivisibility gives rise to quantum stuff.

 

[Sambuco]

$\Gamma_{i,j}(t)$ doesn't need to be non-locally updated because, according section H on entanglement in the arxiv:2302 paper you linked, the non-Markovian transition matrices store statistical information cumulatively extending back to the initial locally interacting composite state at time 0. At the level of Barandes' formalism, non-local updating isn't needed because the system just somehow remembers the correlation created at the earlier time even though its subsystems may be spatially distant.

Thanks for your answer @iste!

I don't fully understand how this happens in Barandes' formulation. Given the quantum-stochastic correspondence, after an interaction between two subsystems, the composite system's transition matrix cannot be factorized, which seems to be equivalent to the non-separable (entangled) wave function. Therefore, if the transition matrix is supposed to play the role of a "dynamical law" as he repeatedly acknowledges throughout the paper, measuring one of the susbystems should "afect" the entire transition matrix.

Lucas.

 

[martinduclocher]

thank you for your reply, but if I understand correctly, the barrandes approach in the context of Bec would no longer be a wave phenomenon? That's right, but it's becoming complex to explain the topological effects linked to the wave function.

 

[iste]

Thanks for your answer @iste!

I don't fully understand how this happens in Barandes' formulation. Given the quantum-stochastic correspondence, after an interaction between two subsystems, the composite system's transition matrix cannot be factorized, which seems to be equivalent to the non-separable (entangled) wave function. Therefore, if the transition matrix is supposed to play the role of a "dynamical law" as he repeatedly acknowledges throughout the paper, measuring one of the susbystems should "afect" the entire transition matrix.

Lucas.

When a measurement happens, the entangled system is no longer entangled - a division event occurs - which I believe might be linked to why there is no signalling. The non-separability is lost whenever the system is disturbed so the measurement device can only interact with the part of the formerly entangled system in its local vicinity, without affecting the distant part.

 

[PeterDonis]

When a measurement happens, the entangled system is no longer entangled

This depends on which interpretation of QM you use. In no collapse interpretations, like the MWI, measurements do not remove entanglement; they extend it to include the measuring devices.

 

[Sambuco]

When a measurement happens, the entangled system is no longer entangled

Yes (in a single-world interpretation, as @PeterDonis clarifies), but for the measurement results to be Bell-correlated, the state of the remote particle must "collapse" into a specific state, depending on the measurement result obtained on the other particle. Otherwise, the correlation would not hold. "Translating" this into the language of Barandes' formulation, the transition matrix $\Gamma(t)$ changes discontinously. I don't see how to avoid that and at the same time reproduce Bell correlations.

Lucas.

 

[iste]

This depends on which interpretation of QM you use. In no collapse interpretations, like the MWI, measurements do not remove entanglement; they extend it to include the measuring devices.

Yes, I was just describing the Barandes entanglement; but there is some at least partial overlap since he explicitly requires inclusion of measurement devices so the loss of entanglement for the measured system coincides with entanglement between a measurement device and one of the measured subsystems. Neither is there collapse for Barandes.

 

[iste]

Yes (in a single-world interpretation, as @PeterDonis clarifies), but for the measurement results to be Bell-correlated, the state of the remote particle must "collapse" into a specific state, depending on the measurement result obtained on the other particle. Otherwise, the correlation would not hold. "Translating" this into the language of Barandes' formulation, the transition matrix $\Gamma(t)$ changes discontinously. I don't see how to avoid that and at the same time reproduce Bell correlations.

Lucas.

This is only the case if you interpret the wavefunction as the particle. But in the Barandes formulation, there is no physical wavefunction - instead it represents statistics of particles when you repeat an experiment many times. But in any given repetition of the experiment, the particle always is in one definite configuration, in one definite position, moving along a definite path.

Collapse in the Barandes formulation is just statistical conditioning which is physically meaningless; physical collapse is unecessary because the particles that exist always have definite configurations anyway. Everything meaningful to say about the quantum behavior is in the long run statistics, even when something ends up in a state with probability 1. Rather than a measurement causing a delocalized superposition to collapse into two matching configurations, particle's statistical behaviors became correlated at a local interaction, and their correlated behaviors just continue over time as they travel, until measurement. I may do a follow up post a bit later.

 

[Fra]

Rather than a measurement causing a delocalized superposition to collapse into two matching configurations, particle's statistical behaviors became correlated at a local interaction, and their correlated behaviors just continue over time as they travel, until measurement.

I think this a good description, and it is the point: it's not the outcomes that are predetermined (this is only a presumed argument based on the local realist dynamics), it's the correlations. And that is tentatively accomplished by means of pre-correlated transition matrixes of the correlated systems; this is the same to say that the two correlated systems have "correlated behavioral responses", and this IMO is what explaines the correalation, but NOT each individual outcomes as the idea is with the non local system dynamics.

When the two systems have become correlated, the indeed "remember" and this is the kind of "hidden variable" that explains the correlated behaviour, so that their interactions with respective detector is correlated regardless of detector settings. This is how I see it. This "memory effecty" is simply hard to model with system dynamics in a intuitive way - it unavoidably "shows up" as weird non-local stuff, but when it's in fact not necessarily non-locally mediated.

To understand the difference between "behaviour" and pre-correlated output, I find the agent based model conceptually superior to system dynamics, because instead of modelling the whole happening as a deterministic evolution of a state as per a fixed dynamical law; we can interacting parts that in principle are autonomous - but can become correlated in their behaviour - because they share a history.

So it seems to me that non-locality is an artifact from the system dynamics paradigm. A no-go theorem that are related to local system dynamics theories (where by construction the hidden variables are global), hardly apply to theories based on agent based models where hidden variables can be shared between a couple of agent only. It's generally considered that agent based models form a larger theory space than system dynamics.

I can't help but associating Baranders stochastic guided process, byt the stochastic learning process of an "agent"(ie any subsystem), but Barandes description of the agent are still not intrinsic, they are extrinsic, which is I think why he manages to get the actual correspondende to QM. I think a true intrinsic "agent" would only have a correspondence to quantum mechanics in a limiting case. This is the relation to Baranders picture and my own preferred perspective. If someone suggests there is a similar no-go theorem also for any agent based model theories, then I would be deeply confused and i have never seen it.

But what makes this still hard to accept conceptually, is that Baranders only (but it's a good start) provices a correspondence, there is stil no indepdent first principle explanation of WHY we have these indivisible general stochastic sytems, and in particular from where we get this time dependent stochastic matrices; which I see as the key to unification progress. I personally like it, but you have to fill in the gaps on your own. It's just acorrespondence after all, not a full reconstruction. But in such a possible reconstruction Baranders correspondence will likely be an importance "correspondence checkpoint" between paradigm.

/Fredrik

 

[iste]

This "memory effecty" is simply hard to model with system dynamics in a intuitive way - it unavoidably "shows up" as weird non-local stuff, but when it's in fact not necessarily non-locally mediated.

To understand the difference between "behaviour" and pre-correlated output, I find the agent based model conceptually superior to system dynamics, because instead of modelling the whole happening as a deterministic evolution of a state as per a fixed dynamical law; we can interacting parts that in principle are autonomous - but can become correlated in their behaviour - because they share a history.

I am not familiar with your agent-based model to understand how this would work; e.g., how would the autonomy work? But I actually think the "memory effect" can be given a reasonably intuitive description, at least from my interpretational perspective.

I believe the "memory effect" is described by these papers by Wharton et al. and Sutherland examining spin weak values that carry information about the intermediate time before a final spin measurement. These spin weak values (both real and imaginary parts) are constant through intermediate times and only depend on the spin directions at initial and final times, which each fix a spin component of the weak value:

"For each possible result, the smallest vector that conforms to both of these constraints, without changing between measurements, is precisely Re(w±)" (Wharton et al.).

The spin weak value calculations in Berry (2011) [section 2] also gives a picture of constant spin values only constrained by pre- and post-selected spin directions. So this seems to be the memory effect - a constant spin vector between initial preparation and final measurement. But the problem is that it kind of looks like retrocausal influence from measurement settings to intermediate times.

But we can look at what they are saying directly from a stochastic mechanical perspective because stochastic mechanical current and osmotic velocities are identical to the real and imaginary momentum weak values, respectively, including for spin. Current velocities (the real part) are constructed using expectations from ensembles of particle trajectories, as explicitly depicted by de Matos et al. (2020) here:

https://images.app.goo.gl/cC2oj

Osmotic velocities (imaginary part) describe the tendency of particles to climb the probability gradient. The expectations of the quantum mechanical momentum and spin operators directly correspond to expectations of stochastic mechanical current velocities (e.g. de Matos, 2020) [section 4.3] - i.e. weak values in the orthodox formalism: Hiley (2012) (6th equation); Hosoya & Shikano (2010) [equations (3)].

In the orthodox picture, spin is a property of an individual particle which then changes at the point of measurement, which is difficult to reconcile in a locally realistic manner. But in stochastic mechanics, spin clearly cannot be identified with any individual particle; it is only meaningful  statistically on the level of ensembles of particle trajectories. This opens up the possibility that different measurement orientations just partition whole (counterfactual) ensembles of intermediate trajectories, associated with an initially prepared spin, in different ways that have different spin statistics in accordance with the current and osmotic spin velocity fields. If you think about it, what Malus' Law cos^2θ when applied to photons is telling you is just how particles will be distributed across two ensembles in terms of relative frequencies / probabilities. Stochastic mechanics is then just saying that the related spin or polarization directions are to do with the statistics associated with each ensemble as a whole.

In the Wharton et al. qubit example you also see that:

"the weighted average of w+ and w− (using their Born-rule probabilities) is exactly (0, 0, 1), with no imaginary part surviving. This average matches ˆi [the initial spin]".

This description seems to be related to how before I said quantum mechanical spin expectations can be described as expectations of weak values, Wharton et al. earlier mentioning this themselves in the paper:

"Nevertheless, in the usual situation where the result of the final measurement is unknown and a weighted average is taken over the possible outcomes, the weak value Re(W[A])(t) can then be shown to be exactly equal to the usual expectation value ⟨A⟩(t)".

From the stochastic mechanical view, the quotes are then saying that the initially prepared spin statistics are related to the statistics of its post-selected components by just a very conventional expectation. That seems to me exactly what you would expect if the final spin outcomes just came from partitioning an ensemble of intermediate trajectories into different subsets which each have different statistics - like any other kind of post-selection in statistics. Its then difficult for me to understand from this perspective why some extra weirdness like retrocausality would be needed (I don't think retrocausality even makes any sense to be honest).

Because any sub-ensemble's statistics at preparation are "remembered" up to final measurement, then in an entanglement scenario you can get the Bell state correlations by having a perfect correlation locally fixed between any and all sub-ensembles of entangled pairs. Obviously, the correlation can actually only be physically, methodologically imposed on particles one pair at a time that go through the experimental set up; experimental repetition then would build up (sub-)ensembles with the appropriate statistics.

 

[Sambuco]

Rather than a measurement causing a delocalized superposition to collapse into two matching configurations, particle's statistical behaviors became correlated at a local interaction, and their correlated behaviors just continue over time as they travel, until measurement.

You're right, measurement does not collapse the configuration of the system. Instead, "collapse" means that the measurement causes the system's transition matrix to change discontinously. Let me give an example. Suppose two particles interact at time $t_0$ and become entangled. Then, Alice measures particle A at $t_1$, while Bob measures particle B at $t_2$ ($t_2 > t_1$). For $t_0 < t < t_1$, the system's transition matrix does not factorize, i.e. $\Gamma_{A,B}(t) \neq \Gamma_A(t) \otimes \Gamma_B(t)$. When Alice measures particle A, as you said in post #640, a division event ocurrs and the system is no longer entangled. So, for $t_1 < t < t_2$, the transition matrix factorize. But the question is: What is the transition matrix $\Gamma_B(t)$ for time evolution of particle B after Alice measured particle A, but before Bob measures particle B. Given the "dictionary" that Barandes introduced to construct the Hilbert space from his stochastic formulation, $\Gamma_B(t)$ after Alice's measurement should correspond to the wavefunction of particle B, which results from the "collapse" of the global wavefunction, according to the remote measurement outcome obtained by Alice. Otherwise, I don't see how Bell correlations could be satisfied. In addition, if we don't know which outcome Alice obtained, we have to consider a statistical mixture.

Collapse in the Barandes formulation is just statistical conditioning which is physically meaningless; physical collapse is unecessary because the particles that exist always have definite configurations anyway.

I slightly disagree. Collapse is just statistical conditioning in information-based interpretations, such as Copenhagen and relational QM where the system has no definite configuration between measurements. Instead, Barandes interprets the system's transition matrix as a dynamic law that plays a nomological role. So collapse is conditioning, as you said, but it's more than that. That's why, in post #638, I made the analogy with the modern view on Bohmian mechanics à la Dürr-Goldstein-Zanghi (https://arxiv.org/abs/quant-ph/9512031). In that sense, we can also say that the effective collapse in Bohmian mechanics can be interpreted as "conditioning", in the same way Barandes say that, after a measurement (division event), "system's density matrix $\rho^S(t)$ can equivalently be expressed as a probabilistic mixture of the conditional density matrices $\rho^{S|\alpha',t'}(t)$ statistically weighted by the measurement probabilities $p_{d(\alpha')}^D(t')$".

Lucas.

 

[Fra]

Got buried in other stuff for a couple of days.

I am not familiar with your agent-based model

I was not referring here to any specific agent-based model as that would get into explicit speculation, I was speaking more of the different paradigms, just to highlight that herein is room for explanation.

In system dynamics, we have a state space, initial conditions and dynamical laws, in differential form; this i essentially timeless, as the future state follows from the initial state and law in a computationally trivial way.

In agent based models, there is not one state space, but more like a "population of statespaces" (ie population of "agents") and there are, initial conditions for each state space, and some rule for how the agent evolves, and interacts with the environment and other agents. The actual evolution of this system is highly non-trivial, and perhaps even computationally irreducible, so one can conceptualize evolution as an "irreducible computation", which is more like a cosmological kind of time; much different than the "parametertime" that you have in system dynamics; which is trivial in comparasion.

In agent based models relations to other agents can be fully emergent, so instead of an external spacetime embedding, relations can emergent - but in a non-trivial way that can't be captured by dynamical law. So certain "mechanism" might be possible to simulate in agent based paradigm, but not necessirly in system dynamics. After all the advantage of agent based models is the focus on mechanism and emergence, rather than overall system evolution. So the notion of "loca causality" needs to be different, one can in ABM note DEFINE it with respect to the external embedding - instead the conditional probabilities independence as Baranders defines it seems the way to go, but t here is still the detail of wether you consider objective or subjective bayesian probabilities.

So the crude idea is that agent based models are more general than sytem dynamics, and can model more heterogenous and non-continous systems, and has natural emergence. Thus I think - a nogo theorem for theoreis in system dynamics paradigm, is not automatically a nogo theorem for theories in agent based models.

Agent-based computational models and generative social science​

Tutorial on agent-based modelling and simulation​

to understand how this would work; e.g., how would the autonomy work?

Conceptually "agents" would be a priori independent stochastic processes or have independent "time evolutions".

But as the interact, they influence each others future even after they "separate". Ie. they are both affected by a common past in a broad sense. There are two kinds of memory I see; one from the actual interaciton(LOCAL hidden memory) and memory with common environment(global shared memory). Entanglement would be like a common past event which happens between two agents now, and as long as they are not disclosed, interacting with all OTHER agents (and in particular the environment, detectors) would be an inteacting between agents that is informed about the preparation proceduire only - (ie "statistics") and the agent that has a hidden variable.

To explain the exact details satisfactory from more agent first principles one would need an explicit toy model, including a toy model for the emergent space, which is why "locality" itself is challenged.

/Fredrik

 

[iste]

Given the "dictionary" that Barandes introduced to construct the Hilbert space from his stochastic formulation, ΓB(t) after Alice's measurement should correspond to the wavefunction of particle B, which results from the "collapse" of the global wavefunction, according to the remote measurement outcome obtained by Alice. Otherwise, I don't see how Bell correlations could be satisfied. In addition, if we don't know which outcome Alice obtained, we have to consider a statistical mixture.

This doesn't happen. It has to be emphasized that in Barandes' formulation, measurements don't produce results. The coupling of the measurement device to a sub-system of an entangled pair is not a one-shot event that causes an outcome, its a statistical description of two statistically coupled systems. So there is then no obligation to change what is going on at the otherside of the now-factorized transition because invoking the measurement device doesn't single out a result. You can invoke statistical conditioning but thats not physical, it is what a statistician does at his desk.

So yes, I think Barandes' theory doesn't consider anything more than statistical mixtures, and there is no inherent problem with this. People describe systems out in the world statistically like this allthe time. I think in quantum mechanics though there is just this extremely strong, in-grained intuition that the theory should be about the behavior of a single particle that tells you what its doing and exactly where it is at some specific moment. But the kind of stochastic interpretation by Barandes or others explicitly does not view quantum theory like this. And historically, I believe collapse is an extra postulate. Its not even an intrinsic part of the theory, its something that was put there because people found the interpretation of the formalism confusing.

In that sense, we can also say that the effective collapse in Bohmian mechanics can be interpreted as "conditioning",

Well surely effective collapse is somethg more than conditioning because its involving the pilot wave or wavefunction or whatever. But in the Barabdes formulation we are just talking about random variables so it is in fact straightforwardly just statistical conditioning like in any other statistical topic. And because Bohmian mechanics explicitly has non-local instantaneous influence, its very difficult to say that it is local without having a very good way of explaining away the formalism itself. But in the Barandes formulation I don't believe such non-local influence has been seen to arise like it does in Bohmian mechanics as of yet.

 

[PeterDonis]

in Barandes' formulation, measurements don't produce results

Does that mean that Barandes is using the MWI? Note that in standard statistical interpretations, such as Ballentine's, measurements do produce results. The quantum state is not interpreted as describing individual systems in these interpretations, only ensembles, so the collapse process in the math doesn't correspond to an actual physical state change on an individual systems. But Barandes, though he talks about statistics, does not appear to be using such a statistical interpretation: he appears to be interpreting the state as describing individual systems, not ensembles. In that context, "measurements don't produce results" seems to me to imply the MWI.

 

[iste]

Does that mean that Barandes is using the MWI? Note that in standard statistical interpretations, such as Ballentine's, measurements do produce results. The quantum state is not interpreted as describing individual systems in these interpretations, only ensembles, so the collapse process in the math doesn't correspond to an actual physical state change on an individual systems. But Barandes, though he talks about statistics, does not appear to be using such a statistical interpretation: he appears to be interpreting the state as describing individual systems, not ensembles. In that context, "measurements don't produce results" seems to me to imply the MWI.

Maybe "don't produce results" is poor choice of words. What I am try to talk about is my belief (at least my impression) that when people think about measurement they automatically think of a model of some event ongoing in time which latches onto one outcome.

But in a stochastic system, statistics could only be realized in ensembles of experimental repetitions - an empirical distribution. The measurement device is also a stochastic system here, so the measurement device is treated in the same way in terms of ensembles of whatever the measurement device reads. From Barandes' dictionary, the quantum state translates to a statistical description using transition matrices; but physically, these statistics are only realizable if you repeat the experiment many many times.

The description of a system evolving in time is then a description of the statistics evolving in time so you will never see a single outcome singled out in the description of the system's time-evolution unless either: 1) you artificially do an exercise in statistical conditioning at your own discretion, 2) the system somehow evolves to a state where only one outcome will occur statistically on repetition due to some other reason unrelated to the act of measuring and seeing an outcome. The evolution of the measurement device is also an evolution of its read-out statistics which may or may not be coupled to the statistics of another system.

 

[PeterDonis]

the quantum state translates to a statistical description using transition matrices; but physically, these statistics are only realizable if you repeat the experiment many many times.

The description of a system evolving in time is then a description of the statistics evolving in time

These two statements contradict each other. The first is something like the standard statistical interpretation as it appears in, say, Ballentine. But it's very important to understand that the statistics described by the quantum state correspond to a specific preparation process. That's how the abstract ensemble that the quantum state describes is defined. (Ballentine discusses all this quite clearly.)

But on that interpretation, there is no such thing as "the statistics evolving in time" in the sense you mean. In order to compare the predictions of your QM model against experiment, you have to run the same experiment many, many times, with the same preparation process each time, and therefore the same underlying statistics each time. If the statistics are "evolving with time", that means your preparation process is changing, and so you're not running the experiment correctly and the data you get is useless for comparing with theory.

 

[iste]

But on that interpretation, there is no such thing as "the statistics evolving in time" in the sense you mean.

You can have an initial preparation, a final measurement, and whatever is going on in the intermediate times. At every point in time the system is described statistically. The statistics then can change over time, but you can only realize this by repeating the experiment over and over again, the particle sampling a definite configuration randomly at every point in time between initial preparation and final measurement.

 

[PeterDonis]

You can have an initial preparation, a final measurement, and whatever is going on in the intermediate times. At every point in time the system is described statistically.

No, this is not correct. Please read Ballentine. The statistical interpretation does not work the way you are thinking.

The statistics then can change over time, but you can only realize this by repeating the experiment over and over again, the particle sampling a definite configuration randomly at every point in time between initial preparation and final measurement.

If you do this, you're not running one experiment. You're running multiple experiments, with different measurements done at different times after the initial preparation, that result in different statistics, and correspond to different statistical ensembles in the theoretical model. Of course the different statistical ensembles are not unrelated; but you are still not testing "how the statistics evolve in time" in the way you are trying to use the term in describing Barandes's approach.

 

[iste]

No, this is not correct. Please read Ballentine. The statistical interpretation does not work the way you are thinking.

I am not talking about the statistical interpretation. I am talking about a stochastic one like Barandes; a stochastic interpretation is necessarily statistical because a stochastic process is just random variables. You cannot observe the statistics of ransom variables, of stochastic processes without realizing their outcomes repeatedly and looking at the empirical distribution, or hypothetically, an infinite ensemble of sample paths. That is just the nature of the stochastic process. If you have a stochastic interpretation of quantum theory then it is going to work in exactly the same way.

If you do this, you're not running one experiment. You're running multiple experiments, with different measurements done at different times after the initial preparation, that result in different statistics, and correspond to different statistical ensembles in the theoretical model. Of course the different statistical ensembles are not unrelated; but you are still not testing "how the statistics evolve in time" in the way you are trying to use the term in describing Barandes's approach.

I don't see the issue. Barandes' formulation will give you statistics for every point in time given an initial time. It then makes perfect sense to be able to talk about how those statistics change as time progresses. At the same time, were you to sample a given time via a measurement, you can't know those statistics for that particular time unless you repeated the experiment over and over again.

Edit:

I do see your point about the different ensembles but ultimately all my original point in that post was about was conveying that the formulation is only about statistics that can only be realized by repeating an experiment. If there is a description of the systems behavior at any point in time, it is a statistical one that can only be realized by repeating an experiment. And naturally you have different statistics at different times even if probing how it got there disturbs the system. If you want to start saying that different measurements are different experiments, I don't see how that really changes my original point or the fact that for any given measurement, you will only know the statistics by repeating that particular experiment.

 

[PeterDonis]

a stochastic interpretation is necessarily statistical because a stochastic process is just random variables. You cannot observe the statistics of random variables, of stochastic processes without realizing their outcomes repeatedly

Yes, which means outcomes have to be realized. Just as in the statistical interpretation of, say, Ballentine, where outcomes have to be realized in order to even do statistics to compare the results of experiments with theory. But you said a few posts ago that outcomes aren't realized in Barandes's interpretation; that's what prompted my question about whether Barandes is using the MWI. So which is it? You can't have it both ways.

Barandes' formulation will give you statistics for every point in time given an initial time. It then makes perfect sense to be able to talk about how those statistics change as time progresses.

Which is just another way of saying, as I said, that you're running different experiments when you sample the statistics at different times.

were you to sample a given time via a measurement, you can't know those statistics for that particular time unless you repeated the experiment over and over again.

Yes--repeat the same preparation process, and then repeat the same measurement the same amount of time after the preparation, multiple times.

So far nothing here is any different from the standard statistical interpretation. And everything only makes sense if outcomes are realized. But you've said that Barandes is not using the standard statistical interpretation, and in his interpretation outcomes are not realized. So I don't understand what you think Barandes's interpretation actually is. Again, you can't have it both ways.

 

[iste]

But you said a few posts ago that outcomes aren't realized in Barandes's interpretation; that's what prompted my question about whether Barandes is using the MWI. So which is it? You can't have it both ways

Yes, and I addressed that in the following posts, and the first thing I said was: "Maybe "don't produce results" is poor choice of words".

And everything only makes sense if outcomes are realized. But you've said that Barandes is not using the standard statistical interpretation, and in his interpretation outcomes are not realized. So I don't understand what you think Barandes's interpretation actually is. Again, you can't have it both ways.

The main difference to a statistical interpretation is that the system you are measuring takes definite configurations even when it isn't measured. A God's eye view would see these definite outcomes, just humans cannot obviously, and Barandes' formulation doesn't give you any statistics for those unmeasured paths. It does this because the unmeasured system is still a stochastic process so it actually does have something a bit more than the statistical interpretation. What I am saying the formulation is is what Barandes says it is. You can see in his interviews he looks at his formulation as an interpretation where particles or whatever other ontology always are in definite configurations when unmeasured.

But I do think that the fact it doesn't tell you about unmeasured stuff is a major criticism of the formulation; in many ways it kind of just looks like a phenomenological model of what happens when you measure a quantum system. Obviously to Barandes it doesn't look that way, but if the formulation or interpretation is agnostic about why quantum behavior occurs or what happens beneath the hood, as they say, then I guess his formulation won't provide him with strong weapons to defend that criticism. Sure, maybe he could say that it shows that quantum theory could plausibly be instantiated in a stochastic system, but because it is so general that can plausibly be used to describe various other things that may be unrelated to physics, he can't as of yet demonstrate exactly how quantum theory would be instantiated in a stochastic process. If you can't do that then I guess people are in their rights to be skeptical about whether his formulation actually is metaphysically plausible, even though it in principle it has the advantages of giving a very straightforward solution to the measurement problem and a relatively conventional, common sense view of reality, at least compared to most other interpretations.

 

[PeterDonis]

The main difference to a statistical interpretation is that the system you are measuring takes definite configurations even when it isn't measured.

In the standard statistical interpretation, individual systems don't have "definite configurations", in the sense of "quantum states", even when they are measured. The quantum state does not describe individual systems at all; it describes abstract ensembles (or, equivalently, preparation processes, as Ballentine makes clear).

If Barandes's "stochastic" interpretation is statistical, as you said it was (though not the "standard" statistical interpretation), then the above property should apply to it as well. But you seem to think that in Barandes's interpretation, individual quantum systems (as opposed to abstract ensembles) do have quantum states. That means Barandes's interpretation can't be statistical. If it's "stochastic", then that must mean something different than "a particular kind of statistical interpretation".

Note that there already is a model in the literature that is "stochastic" in a non-statistical sense--the GRW stochastic collapse model. Which, AFAIK, has been falsified by experiment.

 

[iste]

In the standard statistical interpretation, individual systems don't have "definite configurations", in the sense of "quantum states", even when they are measured. The quantum state does not describe individual systems at all; it describes abstract ensembles (or, equivalently, preparation processes, as Ballentine makes clear).

I mean this description is more-or-less the same as for Barandes' interpretation since the configurations of particles are not the same as the statistics that describe them. What is translated into the quantum state is the statistics. The configurations of particles are therefore not the same as the quantum state and what you have described basically what holds in the Barandes' formulation.

But you seem to think that in Barandes's interpretation, individual quantum systems (as opposed to abstract ensembles) do have quantum states.

There are particles that are in definite configurations at any one time; there are statistics that describe the behavior of those random particles were you to repeat an experiment; those statistics are what get translated into the quantum state, which is therefore not physical insofar that probabilities are not physical objects in the way particles would be.

 

[PeterDonis]

the configurations of particles are not the same as the statistics that describe them. What is translated into the quantum state is the statistics.

If "the configurations of particles" are not the quantum state, which is what you seem to be saying, on what basis are you saying that "the configurations of particles" exist at all? Where are they in the mathematical model? Where are they in the observations?