A new realistic stochastic interpretation of Quantum Mechanics

[iste]

We already know what such an interpretation of QM looks like: it looks like Bohmian mechanics. Which is about as far from stochastic as you can get.

Not at all; as I already said in that post, the trajectories of stochastic particles that take up definite positions in a stochastic interpretation are quite literally the physical realization of the trajectories in the path integral formulation. The fact that the path integral trajectories are generally non-differentiable is something also shared with Brownian motion - i.e. they look like particles traversing continuous paths but where their direction of motion is being constantly disturbed.

 

[iste]

So suppose there's a gap of two seconds between observations, and I want to think about what was happening one second after the first observation. Am I just not allowed to ask about probabilities for unobserved properties? Is that what indivisibility means?

Well indivisibility would apply to both unobserved and observed scenarios - observation consists in adding an additional stochastic subsystem whose role is as a measurement device. But yes, indivisibility means you would not be able to talk about probabilities for the intermediate time (one second) conditioned on the initial time. More specifically, it means there is no unique joint probability distribution that includes the intermediate 'one second' time from which you can construct transition probabilities for the 'two seconds' time.

The following paper which Barandes cites talks about this pg. 12 - 15 (where divisibility is also mentioned) and pg. 35-38. So the ability to construct marginal probabilities from unique joint probability distributions in stochastic processes is talked about in terms of Kolmogorov conaistency conditions / extension theorem here. Divisibility can be seen as a special case of that which breaks down in quantum mechanics.

https://scholar.google.co.uk/scholar?cluster=8084926175613713567&hl=en&as_sdt=0,5

I am not entirely sure what the unobserved case means but I think this paper, even just reading the abstract, gives I think a nice picture of what indivisibility means in quantum mechanics with measurements:

https://scholar.google.co.uk/scholar?cluster=251868338556687708&hl=en&as_sdt=0,5

And you see there that it is intimately related to contextuality because contextuality is characterized by similar kinds of joint probability violations to indivisibility.

 

[PeterDonis]

the trajectories of stochastic particles that take up definite positions in a stochastic interpretation are quite literally the physical realization of the trajectories in the path integral formulation.

But each individual particle only has one trajectory. It doesn't have all of them. And each individual trajectory is still deterministic, since, as you say, it's just one of the paths in the path integral. Which is exactly the same as Bohmian mechanics.

 

[iste]

But each individual particle only has one trajectory. It doesn't have all of them.

Yes, a particle would not go along all trajectories simultaneously, it can only take one. But then if you repeat some experiment or situation ad infinitum then you will see that eventually all possible trajectories will be taken over the course if repetition.That all possible paths will be taken exactly exemplifies the fact that it is not deterministic.

Which is exactly the same as Bohmian mechanics.

Not sure what you mean. Bohmian trajectoried are not the same as the ones that show up in the path integral formulation.

 

[PeterDonis]

That all possible paths will be taken exactly exemplifies the fact that it is not deterministic.

No, it does nothing of the sort. The same thing occurs in Bohmian mechanics. It has nothing to do with non-determinism in the particle trajectories. It only has to do with the randomness of the initial conditions: the initial positions of the particles are randomly assigned, so that over a large number of experiments, a random distribution of the possible initial positions, and hence of the possible paths, will be sampled.

 

[PeterDonis]

Bohmian trajectoried are not the same as the ones that show up in the path integral formulation.

Why not?

 

[iste]

It only has to do with the randomness of the initial conditions: the initial positions of the particles are randomly assigned, so that over a large number of experiments, a random distribution of the possible initial positions, and hence of the possible paths, will be sampled.

This may be the case in Bohmian mechanics with smooth deterministic trajectories but it is not the case for Path integral trajectories which zig-zag is around randomly and constantly. The fact that path integral trajectories are non-differentiable is inconsistent with the guiding equation of Bohmian trajectories. At the same time, the average velocity of path integral trajectories is the same as the velocity that deterministically guides and shapes Bohmian trajectories (i.e. the two formulation's trajectoried relate to the same velocity in very different ways). They cannot be the same object, and path integral trajectories are fundamentally stochastic as mentioned in passing in the paper below:

https://www.mdpi.com/1099-4300/20/5/367

There are some nice images in the following that depict how they look very different. Its comparing Bohmian and stochastic mechanics trajectories but stochastic mechanics trajectories are identical to path integral trajectories:

https://arxiv.org/html/2405.06324v1

 

[martinbn]

I don't know such an example, but I also don't know an opposite example, for which standard QM is better than BM. Do you?

No, I don't. My guess would be any example where in addition to the Schrodinger equations you need to work with the equations for the position, and they add difficulty to the solution. Or any problem that is better in any other basis than the position basis.

But why do you ask for such an example?

 

[martinbn]

There is indeed no physical problem that BM solves and QM not. However, David Bohm and Jeffrey Bub pointed out to their uneasy feeling with regard to the orthodox interpretation of QM. In their paper “A Proposed Solution of the Measurement Problem in Quantum Mechanics by a Hidden Variable Theory“ (Rev. Mod. Phys. 38, 453, 1966), they wrote:

“It is not easy to avoid the feeling that such a sudden break in the theory (i.e., the replacement, unaccounted for in the theory, of one wave function by another when an individual system undergoes a measurement) is rather arbitrary. Of course, this means the renunciation of a deterministic treatment of physical processes, so that the statistics of quantum mechanics becomes irreducible (whereas in classical statistical mechanics it is a simplification – in principle more detailed predictions are possible with more information).”

To me that shows that they had a problem accepting that nature can be probabilistic. But nature could be that way, and all we know so far suggests it is that way. So this is more their problem than a problem of QM.

 

[Demystifier]

But why do you ask for such an example?

Because you think that standard QM is better than BM, so I wondered if you could back that up with an example.

 

[pines-demon]

It is frustrating how Barandes can be so eloquent and at the same time not give straight answer to what is the mental picture to have here. If he cannot do that, then it is just another obscure rewritting of QM that does not allow for interpretations. Like ok, you are allowed to violate Bell's inequalities but how should I think of it? He ask us to exchange the wavefunction and collapse for an all permeating fluctuating force. Does this force updates faster than light to produce entanglement results? Or is there a memory effect from the past over large regions of space that allows us to measure QM-like effects (conspiracy, superdeterminism)?

It would be really helpful if Barandes just gave a course solving an example with a single qubit and then and two entangled qubit example. His formalism seems very general, it does not depend on fundamental objects being qubit, particles or fields, and the non-classicality is encoded in his indivisibility. So it also does not give any new insight on the fundamental nature either.

Edit: thinking more about it, I think Barandes just stumbled into duality, it could be helpful if it can be used to to solve non-Markovian problems with quantum mechanics and viceversa. Nevertheless, calling it an interpretation is flawed at this stage, it is like calling a Wick rotation an interpretation.

 

[martinbn]

Because you think that standard QM is better than BM, so I wondered if you could back that up with an example.

This is a question for someone else, most physicists may be. But it is a strange question! QM was developed first, then came BM. So it is BM that need to show what new it has to offer. Any way I gave you two reasons why QM is better. 1) It doesn't have huge number of additional equations and 2) It ca work in any basis not just the position basis. Don't you think these are advantages?

 

[PeterDonis]

path integral trajectories are non-differentiable

Are they? Don't they still have to be solutions of a differential equation?

 

[Demystifier]

This is a question for someone else, most physicists may be. But it is a strange question! QM was developed first, then came BM. So it is BM that need to show what new it has to offer.

I cannot beat that argument, so I wrote this:
https://arxiv.org/abs/physics/0702069

Any way I gave you two reasons why QM is better. 1) It doesn't have huge number of additional equations and 2) It ca work in any basis not just the position basis. Don't you think these are advantages?

Yes, these are advantages. But BM has corresponding counter-advantages:
1) It doesn't have huge number of additional collapses (one collapse whenever a measurement happens).
2) It can derive the Born rule in any basis from Born rule in the position basis.
Don't you think these are advantages too?

 

[Demystifier]

Are they? Don't they still have to be solutions of a differential equation?

No, path integral trajectories are not solutions of a differential equation.

 

[PeterDonis]

No, path integral trajectories are not solutions of a differential equation.

Then what constraints do they have to obey? Do they just have to be connected?

 

[renormalize]

Don't they still have to be solutions of a differential equation?

No, since for a Feynman path integral, a general path is nowhere differentiable. Here's a recent reference that discusses this:
https://link.springer.com/article/10.21136/CMJ.2024.0493-22
Non-differentiability of Feynman paths by Pat Muldowney
Abstract:
A well-known mathematical property of the particle paths of Brownian motion is that such paths are, with probability one, everywhere continuous and nowhere differentiable. R. Feynman (1965) and elsewhere asserted without proof that an analogous property holds for the sample paths (or possible paths) of a non-relativistic quantum mechanical particle to which a conservative force is applied. Using the non-absolute integration theory of Kurzweil and Henstock, this article provides an introductory proof of Feynman’s assertion.

 

[PeterDonis]

for a Feynman path integral, a general path is nowhere differentiable.

Thanks for the reference--another thing to add to my already overloaded reading list.

This property of general paths is not one I have seen discussed in what I have read previously; I suspect that is because, in practice, the contributions of such paths to actual amplitudes is negligible, so they are mostly ignored. I don't know how that practical issue affects the interpretation under discussion in this thread.

 

[iste]

It is frustrating how Barandes can be so eloquent and at the same time not give straight answer to what is the mental picture to have here. If he cannot do that, then it is just another obscure rewritting of QM that does not allow for interpretations. Like ok, you are allowed to violate Bell's inequalities but how should I think of it? He ask us to exchange the wavefunction and collapse for an all permeating fluctuating force. Does this force updates faster than light to produce entanglement results? Or is there a memory effect from the past over large regions of space that allows us to measure QM-like effects (conspiracy, superdeterminism)?

It would be really helpful if Barandes just gave a course solving an example with a single qubit and then and two entangled qubit example. His formalism seems very general, it does not depend on fundamental objects being qubit, particles or fields, and the non-classicality is encoded in his indivisibility. So it also does not give any new insight on the fundamental nature either.

Edit: thinking more about it, I think Barandes just stumbled into duality, it could be helpful if it can be used to to solve non-Markovian problems with quantum mechanics and viceversa. Nevertheless, calling it an interpretation is flawed at this stage, it is like calling a Wick rotation an interpretation.

Yes, it is very general and minimalist but it gives interpretation at least in the following sense. Because we are talking about quantum mechanics as being stochastic systems, just this very fact, if it were true, would imply that the system is always in a definite configuration at any point in time. So at the very least you would have a picture of the universe full of particles that are always in one place at a time but they just move randomly. I would say that is definitely interpretational in a minimal way.

In two of Barandes' papers he mentions the mechanism for entanglement being the fact that correlations induced by local interactions between two different stochastic systems are remembered over time until the system is later disturbed (e.g. by measurement devices), after which it basically forgets what had happened in the past at the original local interaction. This is purely because the indivisible transition matrix is non-Markovian - divisibility or division events means it no longer has these memory properties. There is no superdeterminism because the correlation is solely due to the local interaction. Any correlations in the measurement devices are solely due to the fact that the correlation from the original local interaction is remembered; the devices do not causally influence each other over distances independently of this. It is very general though. His entanglement examples I don't think give strong insight to entangled polarization / spin experiments.

 

[Demystifier]

Then what constraints do they have to obey? Do they just have to be connected?

They are only constrained by their initial and final points. It is in fact somewhat wrong to think about them as paths. They are functions $x(t)$, a function can be totally weird, like $x(t)=0$ for rational $t$ and $x(t)=1$ for irrational $t$. The "path" integral is really the functional integral, i.e. the integral over all functions.

 

[Fra]

I think one reason this is hard to understand is because we implicitly but repeatedly confuse normative/guiding P of possibilities and descriptive P of what actually happened historically.

Histories don't interfere. Interference lies in how guiding probabilities account for possibilities and uncertainties of the future.

In inference its important to not mix the concepts. This is closely related to what barandes label the "category error" or "category problem".

Ie. If you keep thinkning of the transition probabilites as descriptive, it gets wrong. But if you think of them as guiding P for an agent taking stochastic actions, it makes more sense.

The flawed application of common cause in bells ansatz is easier to spot if you think in terms of guiding probabilities of agent/observer - which of course, like barandes thinks, is a physical system. One just have to not confuse this with thinking that means there is an exteral view of all this. It is beacause it does not, that makes the guiding view of P more fundamental.

/Fredrik

 

[Fra]

calling it an interpretation is flawed at this stage, it is like calling a Wick rotation an interpretation.

I partly agree with this. But I think he highlights important things, and changing stance that can make future development eaiser. He points out the obvious flaw in bells ansatz, that was there all along but which few speak of. Its in the talk RUTA posted way back in the thread sa well.

/Fredrik

 

[pines-demon]

In two of Barandes' papers he mentions the mechanism for entanglement being the fact that correlations induced by local interactions between two different stochastic systems are remembered over time until the system is later disturbed (e.g. by measurement devices), after which it basically forgets what had happened in the past at the original local interaction. This is purely because the indivisible transition matrix is non-Markovian - divisibility or division events means it no longer has these memory properties. There is no superdeterminism because the correlation is solely due to the local interaction. Any correlations in the measurement devices are solely due to the fact that the correlation from the original local interaction is remembered; the devices do not causally influence each other over distances independently of this. It is very general though. His entanglement examples I don't think give strong insight to entangled polarization / spin experiments.

You say it is not superdeterminism but as you put it, it sounds like it is. You say that measurement devices do not necessarily interact with each other instantaneously (so it is not some nonlocal faster-than-light interaction), but it is more of like past event thing

There is no superdeterminism because the correlation is solely due to the local interaction. Any correlations in the measurement devices are solely due to the fact that the correlation from the original local interaction is remembered

Does that means that all measurement devices interacted once in the past so measurements are not independent [a.k.a aka superdeterminism]? If it is not this, what is it? Is there a way I can think about it aside from "indivisible non-Markovianity"?

 

[Fra]

"Not statistically independent" does not imply superdeterminism. Superdeterminism is a special extremal case.

Just as in bell experiments, the "memory" explains the correlation - it does not determine the full results, because they involve detector settings too.

So the full interaction is then conceptually an interaction between
1. a system (that is remebers a relation to its correlates partner)
2. The detector that is ignorant about this, and thus acts stochastically based on "preparation info" only - which is "public"

The combination fo this will have elements of chance; and be influenced by detector choices; but also partially influenced by the "memory" of incoming system.

For me this is conceptually quite clear. What is missing is the mathematical modell of this from that perspective.

IMO, what prevents superdeterminism conceptually is that the memory of systems are limited; thus over time some model with lossy retention seems required. Only maybe an observer beeing a black hole can retain most without loss by growing mass.

But this is all future possible developments not lined out by Barandes. But de does say thar he thinks there may be link to this and future QG. It is in the same talk in rutas post.

/Fredrik

 

[pines-demon]

I partly agree with this. But I think he highlights important things, and changing stance that can make future development eaiser. He points out the obvious flaw in bells ansatz, that was there all along but which few speak of. Its in the talk RUTA posted way back in the thread sa well.

/Fredrik

I rewatched that part today and now I am more skeptic. To get Bell's inequality one needs several ingredients, mainly statistical independence (violations lead to superdeterminism) and factorizability. There are several ways to get factorizability. Bell had two different ways, one appears in Bell's later work and is called local causality. The other is indeed Reichenbach's common cause principle (not used by Bell). Either way, standard quantum mechanics violates this factorizability.

Barandes finds that his theory also violates this factorizability and claims that it is a violation of Reichenbach principle (it could very well be). But it could be very well that it is a violation of local causality making Barandes' interpretation nonlocal (in the Bell way, like in the case of Bohmian mechanics). In his lecture he conflates the Bell's local causality with Reichenbach' common cause (saying that is what Bell used) so I do not think he is into something there.

 

[pines-demon]

"Not statistically independent" does not imply superdeterminism. Superdeterminism is a special extremal case.

It is kind of the definition. That comment was aimed at iste who claimed that the correlations result from the the interactions of the detectors in the past . This is usually what superdeterminism claims (maybe iste did not meant that but to say interactions between the entangled particles instead).

 

[Fra]

It is kind of the definition. That comment was aimed at iste who claimed that the correlations result from the the interactions of the detectors in the past . This is usually what superdeterminism claims

Determinism means the future is predetermined. At least in principle - modulo deterministic chaos. Superdetermimism take this to include even choices of experimenters.

That is not what the memory thing implies. The problem with bells ansatz lmo does NOT(edit) save determinism.

/Fredrik

 

[pines-demon]

Determinism means the future is predetermined. At least in principle - modulo deterministic chaos. Superdetermimism take this to include even choices of experimenters.

While superdeterminism does imply determinism it is not exactly that what is meant by that term. At least in this context it is a statistical property, statistical independence (no superdeterminism) it is the ability to average out any correlations between the measuring devices (make many trials, create the measuring devices in different factories, put them far apart, make the setting dependent on nuclear random number generators). It is important in science because that's why experiments can be repeated. Mathematically, superdeterminism means that a representative distribution of your hidden parameters $\lambda$ depend on the settings $x,y$ of your measuring devices, i.e.
$$\rho(\lambda|x,y)\neq\rho(\lambda).$$
It is called superdeterminism because all measuring devices of the observable universe interacted at some point in the past if not in the Big Bang, so the correlations would be set from early in the past (conspiracy).
Edit: funny enough there are Bell tests that put constraints to superdeterministic theories by deciding the settings of the measurement devices based on thermal radiation from very distant galaxies.

 

[iste]

You say it is not superdeterminism but as you put it, it sounds like it is. You say that measurement devices do not necessarily interact with each other instantaneously (so it is not some nonlocal faster-than-light interaction), but it is more of like past event thing

Does that means that all measurement devices interacted once in the past so measurements are not independent [a.k.a aka superdeterminism]? If it is not this, what is it? Is there a way I can think about it aside from "indivisible non-Markovianity"?

No, measurement devices didn't interact in past. Particles interact in the past before they are measured, causing a correlation between them which is preserved when the particles are separated and subsequently measured. Measurement devices don't interact with each other or anything else before the measurement of the particles. But obviously this doesn't incorporate measurement settings so maybe it is missing something that could account for what you are possibly thinking about.

Barandes finds that his theory also violates this factorizability and claims that it is a violation of Reichenbach principle

From the paper, he seemed to suggest that its not so much that Reichenbach's principle is violated but it isn't applicable to the stochastic description because the third variable needed to formulate it doesn't exist in the stochastic description, even though the straightforward analysis is that the correlation between the particles can be directly attributed to an initial local interaction between the particles that is subsequently remembered even when they are moved far apart, purely because of the non-markovianity of the indivisible transition matrix.

I actually mentioned a source earlier that seems to display this mechanism in a completely different classical hydrodynamical model:

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.093604

Droplets interact in the same fluid bath and become correlated so that their dynamics are nonseparable. A barrier is erected which isolates the particles so they can no longer communicate in any way. But despite their isolation, their behavior still maintains correlations between them which can be attributed to the fact that they have been remembered by the now-isolated respective particle-bath systems. This description models quite closely to Barandes' description of entanglement only here it is expicit that there is no non-local communication because its a classical model of just a droplet in a bat which you could build an experiment about. Its not mentioned in the abstract I think but if you look at other sources for these pilot-wave hydrodynamic systems, the reason they have these quantum-like behaviors is that they are non-Markovian and retain memory of the past.

 

[iste]

They are only constrained by their initial and final points. It is in fact somewhat wrong to think about them as paths. They are functions $x(t)$, a function can be totally weird, like $x(t)=0$ for rational $t$ and $x(t)=1$ for irrational $t$. The "path" integral is really the functional integral, i.e. the integral over all functions.

What does weird mean here in terms of paths?

 

[pines-demon]

No, measurement devices didn't interact in past. Particles interact in the past before they are measured, causing a correlation between them which is preserved when the particles are separated and subsequently measured. Measurement devices don't interact with each other or anything else before the measurement of the particles. But obviously this doesn't incorporate measurement settings so maybe it is missing something that could account for what you are possibly thinking about.

Thanks for clarifying what you meant, I quoted a previous text of yours that seemed to suggest the opposite.

From the paper, he seemed to suggest that its not so much that Reichenbach's principle is violated but it isn't applicable to the stochastic description because the third variable needed to formulate it doesn't exist in the stochastic description, even though the straightforward analysis is that the correlation between the particles can be directly attributed to an initial local interaction between the particles that is subsequently remembered even when they are moved far apart, purely because of the non-markovianity of the indivisible transition matrix.

That does not cut it for me. He does not have factorizability that is fine, he can argue about Reichanbach principle all day, but Reichbach vs Bell causal locality is not settled. So he could also just have nonlocality built into it without knowing it. I mean again I would sell his work as a duality, it needs to be worked into an interpretation that can provide a picture of the phenomena.

I actually mentioned a source earlier that seems to display this mechanism in a completely different classical hydrodynamical model:

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.093604

Droplets interact in the same fluid bath and become correlated so that their dynamics are nonseparable. A barrier is erected which isolates the particles so they can no longer communicate in any way. But despite their isolation, their behavior still maintains correlations between them which can be attributed to the fact that they have been remembered by the now-isolated respective particle-bath systems. This description models quite closely to Barandes' description of entanglement only here it is expicit that there is no non-local communication because its a classical model of just a droplet in a bat which you could build an experiment about. Its not mentioned in the abstract I think but if you look at other sources for these pilot-wave hydrodynamic systems, the reason they have these quantum-like behaviors is that they are non-Markovian and retain memory of the past.

This for me would do the work [if understood], in the sense that if he can come up with a SIMPLE classical picture of his phenomena he would be able to provide an interpretation. However I cannot access or assess this paper and I would not be too surprised if real fluid systems have weird non-linear effects lead to wrong conclusions. That's why I think a toy model with a single qubit could clarify the situation.

 

[Demystifier]

What does weird mean here in terms of paths?

The $x$ attains only two values, 0 and 1, without ever attaining any value in between. Moreover, it jumps from 0 to 1 and back infinitely often. The velocity $dx/dt$ is not defined at any $t$.

 

[pines-demon]

The $x$ attains only two values, 0 and 1, without ever attaining any value in between. Moreover, it jumps from 0 to 1 and back infinitely often. The velocity $dx/dt$ is not defined at any $t$.

Just to be clear here the derivative is not defined but has some instantaneous momentum right?

 

[WernerQH]

Droplets interact in the same fluid bath and become correlated so that their dynamics are nonseparable.

But do these experiments produce anything resembling Bell-type correlations? Classical correlations have been understood for ages. It is misleading to wave your hands and talk about "nonseparable" dynamics.

 

[iste]

But do these experiments produce anything resembling Bell-type correlations? Classical correlations have been understood for ages. It is misleading to wave your hands and talk about "nonseparable" dynamics.

The Barandes entanglement example is very rudimentary. I was just implying that given the description of entanglement he gives, there is no need to add any underlying non-local influence; the paper then is an example since it is equally rudimentary. I see that someone may not be as convinced with regard to actual quantum experiments, or even that the indivisibility could be achieved without something else funny going on.

I would not be too surprised if real fluid systems have weird non-linear effects lead to wrong conclusions.

I do note in post #247 that these hydrodynamic models are superficially similar to the interpretation given by Nelson's stochastic mechanics, which is a predecessor that shares the same stochastic interpretation as Barandes' model. But yes, Barandes' model is agnostic of what kind of mechanisn would cause the non-Markovianity... or how weird the mechanism would be. I guess there could be an underlying non-local mechanism but to me it feels like that is like overkill in terms of parsimony by doubling the mechanisms in the picture.