A new realistic stochastic interpretation of Quantum Mechanics

[Fra]

There is something kind of like that in the stochastic mechanical interpretation though from a very different perspective to yours. The particle is interacting with a background which is hidden insofar that it is not mentioned explicitly in quantum mechanics. It would be conservative interactions between particle and background which are related to the indivisibility.

sounds like leading to via, embedding things in a bigger system. Ie. embedd the non-markovian interactions in a much larger system that is markovian?
for eample https://arxiv.org/abs/2005.00103 ?

This "type" of solution, which is also analogous to how one tries to make true evolution, as a simple entropic dynamics, has the same conceptual flaws and IMO will not solve the problem, without creating more and often bigger problems, which cripples the "explanatory value" of the constructions.

Yes; for Barandes, the external observer is explicitly modeled as part of the stochastic system.

Note sure what this means, did he elaborate more clearly on this somwhere that i missed when skimming?

For me "external observer" is an idealisation and fiction, it has a value to simplify models for small subsystem, but in realist, there are only internal obsevers.

But I think of "internal observers" as a kind of stochastic agents existing in and thus interacting with the environment, but the environment is unknown. But this observers is not "modelled" externally, only other internal observers can model other observers. And two internal observers have different views - non more right than the other one.

Rovelli has a nice quote in the context of this Relational QM (before he goes south...).

"Does this mean that there is no relation whatsoever between views of different observers? Certainly not..."
-- C. Rovelli, Relational Quantum Mechanics

"There is an important physical reason behind this fact: It is possible to compare different views, but the process of comparison is always a physical interaction"
-- C. Rovelli, Relational Quantum Mechanics

So the key question is again, what is the NATURE of this physical interaction? Rovellis answer, was - quantum mechanics. But this is a non-answer, as long as no-one understands quantum mechanics, but then again his interpretation served not to unifiy all interactions, it's mainly to build a quantum theory of gravity. (from there on he goes south IMO.. )

I think the key to the non-markovian nature here is the nature of this physical interaction. Embedding this in a bigger space, is cheating. We need to solve the problem without changing perspective, and that is how I envision a kind of stochastic process but taking place in an unknown space. So the space itself, is evolving as observer moves through it. Which is similar to how GR works. So there is interesting enough, conceptual similarities with the dynamics in space, and the evolution of space - and the stochastic processes in some space, and the evolution of this same space in the quantum foundations. Is it a coincidence? I suspect not? And this thing, is also I think exactly why the markovian divisibility isn't be true; there is "information" not only in the state, but in the state of the space as well, but I think not in the sense of a state embedded in a bigger one; that attempt of explanation totally misses the point of what is to be explained.

/Fredrik

 

[iste]

sounds like leading to via, embedding things in a bigger system. Ie. embedd the non-markovian interactions in a much larger system that is markovian?
for eample https://arxiv.org/abs/2005.00103 ?

This "type" of solution, which is also analogous to how one tries to make true evolution, as a simple entropic dynamics, has the same conceptual flaws and IMO will not solve the problem, without creating more and often bigger problems, which cripples the "explanatory value" of the constructions.

I don't know. I don't think so. It's just the most natural way of looking at the stochastic mechanics if you want an unextravagant description. The particles move randomly. Ideally, something must be causing their movement - like a dust particle getting disturbed by the background of molecules in a glass of water. The stochastic mechanical "osmotic velocity" directly corresponds to a component of momentum in quantum mechanics and got an interpretation due to comparison with Einstein Brownian motion - "velocity acquired by a Brownian particle, in equilibrium with respect to an external force, to balance the osmotic force". The external force is then attributed the background, causing the particle random motion. The particle naturally is acting back on the background (because where else is it going to go?) like your dust particle would in a glass of water, and the interplay leads to the osmotic velocity assuming that it leads to an equilibrium which would also conserve particle energy on average in its exchanges with its background environment. The osmotic energy is then mathematically responsible for quantum behavior and is required for energy conservation. This osmotic energy is just the same as the Bohmian quantum potential apart from the fact it is explicitly derived from the assumption of a diffusion which is non-dissipative, i.e. frictionless, time-reversible (albeit without explicit insight into an underlying microscopic model like for the dust particle suspended in water molecules - conservative diffusion seemingly seems sufficient as a constraint).

In the end what it looks like (crudely speaking) is: Lagrangian mechanics + noise = quantum mechanics, hence if you tone down the randomness, or alternatively are talking about objects that are far too big (purposefully ignoring their fine-grained descriptions) to noticeably feel random fluctuations of the background, you just get deterministic classical behavior.

So this background interaction thing is just a notable interpretation for what the mathematics in stochastic mechanics is saying. The classical hydrodynamic fluid bath mentioned earlier is a tempting way of looking at the stochastic mechanical background interaction because of how artificially countering viscous dissipation in those models leads the bath (i.e. background) to retain a memory of the events that interact with the bath, and leads to quantum-like, and seemingly non-local behavior. At the same time its an extremely tenuous link: these models still seem very different to the stochastic mechanical one, very less than perfect quantum analogs, highly fine-tuned with additional distracting components, not clear how similar it actually is at all - I very much have doubt. But the sentiment is vaguely similar to that of Ed Nelson in his book 'quantum fluctuations': "The particle doesn't know whether the other slit is open [or closed], but the background field does", and this isn't necessarily instantaneous either since these stochastic mechanical models seem to take finite amount of time for the system to settle into quantum equilibrium and show interference effects.

Note sure what this means, did he elaborate more clearly on this somwhere that i missed when skimming?

Well the observer is just referring to the measurement-dependence in quantum mechanics, right? In the Barandes model, that is all explicitly incorporated into the stochastic system so you have your observer system and whatever is being measured and then perhaps whatever else may be relevant, depending on scenario. Even though the observer disturbs the system it is observing (and momentarily reinstates Markovianity according to Barandes), there is only ever one definite classical-looking outcome (or set of outcomes) occurring at any given moment in time. The observer-dependence is just a special case of a phenonena that is generic to any interaction between different stochastic systems in the Barandes picture.

 

[mitchell porter]

Nelson's stochastic electrodynamics works because, like Bohmian mechanics, it's defined in configuration space, not physical space, so nonlocality is built in. Unfortunately from the discussion so far, I have no sense of how Barandes's mechanics works, what it lacks, and why he would think it enough to reproduce all the effects of entanglement...

 

[iste]

Nelson's stochastic electrodynamics works because, like Bohmian mechanics, it's defined in configuration space, not physical space, so nonlocality is built in. Unfortunately from the discussion so far, I have no sense of how Barandes's mechanics works, what it lacks, and why he would think it enough to reproduce all the effects of entanglement...

The assertion is that all quantum systems are equivalent to indivisible (also dubbed as 'generalized') stochastic systems - stochastic systems whose time-evolution cannot be arbitrarily divided up in terms of stochastic matrices for intermediate sub-intervals. Barandes' idea then is to show that any indivisible system is a subsystem of a unistochastic system, via something called the Stinespring Dilation Theorem. The unistochastic system can then be translated into a unitarily evolving quantum system in virtue of its definition. So the implication is that all of the behaviors of quantum systems should be expressible in terms of indivisible stochastic systems - or vice versa. For instance, the statistical discrepancy due to violations of divisibility  is interference, specifically corresponding to the kind of interference you would have for trajectories in the path integral formulation (I believe).

Barandes then describes a rudimentary entanglement entirely from the perspective of these indivisible stochastic systems that you can translate a quantum system into. Correlations from local interactions between different stochastic systems results in a non-factorizable composite system. The indivisibility of the composite stochastic system's transition matrix means that it cumulatively encodes statistical information so that the correlation is effectively remembered over time (even with spatial separation) until the composite system experiences a division event (i.e. decoheres and divisibility is momentarily restored) by interacting with another system. The mechanism of entanglement for the indivisibe stochastic system is then arguably due to non-Markovianity - memory - rather than some kind of overt communication.

 

[Fra]

Well the observer is just referring to the measurement-dependence in quantum mechanics, right? In the Barandes model, that is all explicitly incorporated into the stochastic system so you have your observer system and whatever is being measured and then perhaps whatever else may be relevant, depending on scenario. Even though the observer disturbs the system it is observing (and momentarily reinstates Markovianity according to Barandes),

The big problem in the inference picture not that the obserer distorts the system, but if you account for the systems back reaction on the observing context. This is trivial when the observing context is dominant. But when you add gravity, and want to understand unification without ad hoc fine tuning, this is the major problem; which I think suggest that we need to provide the other half of the story as well.

Ideally, something must be causing their movement -
...
The external force is then attributed the background, causing the particle random motion.

I get what you are saying and agree, but this is half the answer. My reactions are due to that we often seem that alot ot approached supply exactly that - only half the answer. This half of the answer represents the conventional external perspective, where "the whole macroscopic environment" observes a small subsystem (the quantum system). This conceptual framework works for small subsystems, which is where QM is corroborated as it stands.

But when the systems get big enough to cause non-trivial feedback into the "baground observer, macroscopic envirionment"; we tend to fall back to semiclassical models.

So half answer, can make us understand the action of small subsystem, embedded in a dominant context where we have perfect control; and the smaller subsystems we need to explain, the more finetuning to de need to make in the embedding, even to the point nwhere we can't handle it.

So the missing part of the answer is; what about trying to describe the situation from the inside. Then explanatory models can not be rooted in fictional background contexts. Randomness in this inside view rather does not need explanation, as somehow randomness is the "nullhypothesis", because the starting point is a simple stupid agent INSIDE a black box; not OUTSIDE the black box. On the contrary deviation from randomness is what needs to be "explained". And this is the missing part for me... and I couldn't see Barandes offering any new grips on this...

In my view, I do not think in terms of that "something" must be causing the random motion; I see this as artifacts of the external view.

I prefer to think that inside view is that the randomness is simply a manifestation of that the observes can not predict it - the obserever is indifferent to the cause because the mechanism can not be distinguished. This should even mean that the observers actions uncouple with these details; suggesting that that the phenomenology of interactions change as the observational scale does. The problem is that the explanatory power of normal renormalization flow works so that knowledge of a complex detailed microstructure of the macrostate "explains" the reduced interactions as you goto the macroscale. So it's redutionist in nature. But it offers littel insight into the emergence logic.

/Fredrik

 

[jbergman]

The assertion is that all quantum systems are equivalent to indivisible (also dubbed as 'generalized') stochastic systems - stochastic systems whose time-evolution cannot be arbitrarily divided up in terms of stochastic matrices for intermediate sub-intervals. Barandes' idea then is to show that any indivisible system is a subsystem of a unistochastic system, via something called the Stinespring Dilation Theorem. The unistochastic system can then be translated into a unitarily evolving quantum system in virtue of its definition. So the implication is that all of the behaviors of quantum systems should be expressible in terms of indivisible stochastic systems - or vice versa. For instance, the statistical discrepancy due to violations of divisibility  is interference, specifically corresponding to the kind of interference you would have for trajectories in the path integral formulation (I believe).

Barandes then describes a rudimentary entanglement entirely from the perspective of these indivisible stochastic systems that you can translate a quantum system into. Correlations from local interactions between different stochastic systems results in a non-factorizable composite system. The indivisibility of the composite stochastic system's transition matrix means that it cumulatively encodes statistical information so that the correlation is effectively remembered over time (even with spatial separation) until the composite system experiences a division event (i.e. decoheres and divisibility is momentarily restored) by interacting with another system. The mechanism of entanglement for the indivisibe stochastic system is then arguably due to non-Markovianity - memory - rather than some kind of overt communication.

I am in the process of skimming the paper and I for one would like to dig deeper into the math to see if what he is claiming is even correct before discussing the implications of it. Are you convinced that what he is claiming is true?