pines-demon said:
You said before that one could be agnostic given the state of the theory. Now you are eager to defend there is some interpretation.
There are layers to interpretation and this goes for all interpretations not just Barandes' formulation. For instance, Bohmian mechanics and Many Worlds are both distinct interpretations defined by certain interpretational features. But within these interpretations there are disagreements like whether the Pilot wave is a physical object or not, or you could be agnostic. Barandes can be agnostic about the underlying mechanisms behind an indivisible stochastic process whilst still endorsing the interpretation of an indivisible stochastic process where particles are always in one position at any time and the wavefunction is real; these latter two features are unambiguously in the area of interpretation but we can still be ambiguous about the specific mechanisms for why the system behaves as it does. You can be a Bohmian and believe particles go along definite determinate trajectories but be agnostic about whether the pilot wave is a physical object. You can advocate Many Worlds and be agnostic about their ontological status (bizarrely, but I read a philosophy of science encyclopedia article that suggests there are different ways of looking at Many Worlds). There are layers to all interpretations.
pines-demon said:
Bohmian mechanics also has one configuration at a time, superdeterminism does to.
Yes, but they are also unambiguously not identical to Barandes' interpretation mathematically or interpetationally.
pines-demon said:
I do not think it is worth it unless he provides more content about it.
That's completely fair.
I just disagree; even ignoring other stochastic formulations, the idea of particles being in definite positions still has attractive implications even if you don't know exactly why they behave the way they do - definite positions gets rid of all of the measurement problem issues and it complements the way we view the world, not just at an everyday level but in almost every other field in science outside of quantum theory.
The quantum interpretation problems came about because we couldn't figure out how to reconcile quantum theory with the pre-quantum, classical-like view of the world. So I would argue that if a formulation appears that reconciles the quantum and pre-quantum, it kind of takes away the very reason people started looking at different interpretations. Barandes' formulation claims it is at least consistent to describe quantum systems in a pre-quantum way, giving a route to the aforementioned reconciliation even if not all the interpretational details are there.
Obviously, you could argue that Bohmian mechanics does exactly the same thing as said here. But I think there is a subtle difference in that Bohmian mechanics effectively postulates quantum mechanics then adds particles separately on top while Barandes' idea can be seen as deriving quantum mechanics from the behavior of a more general kind of system that already has definite configurations and so does not require the additional Bohmian step.
pines-demon said:
He is proposing some stocastic force that permeates space and allows to bypass Bell's theorem. In most cases that would mean that his theory is nonlocal.
It depends what you mean by nonlocal I guess. Barandes' theory would presumably be Bell nonlocal if it establishes a direct correspondence between quantum and stochastic behavior. But quantum mechanics is already nonlocal anyway. Quantum mechanics is already weird so even if you cannot rule out a weird underlying explanation to Barandes' theory, I still don't think this is necessarily a strong argument against it since all quantum interpretations so far have been a bit weird in certain senses.
At least in the area of entanglement, I think the Barandes theory does suggest memory of local interactions (as opposed to overt communications like say in the Bohmian theory) is a
sufficient mechanism which additionally explains many other aspects of the system's evolution, whether in the case of single or multiplr systems. So adding an explicit non-local communication to this doesn't seem parsimonious, at least in the case of entanglement, imo. Obviously this is all dependent on whether Barandes is actually correct or not.
pines-demon said:
People have tried to break the axioms of probability before to get quantum mechanics without amplitudes but that does not mean it is easier to comprehend or to interpret. Is Barandes proposal even a stochastic process at this point? We really need a simple example, hopefully a classical one.
I think there are plausible ways of viewing these things that aren't completely unintuitive. In post #282, I talk about indivisibility in terms of joint probability violations (and link pages from a source). The system has no unique joint probability distribution. But this doesn't necessarily mean that the statistics don't exist at all, just that they exist on different mutually exclusive probability spaces - mutually exclusive because of context-dependence. Various authors I have read talking about this include Dzhafarov, Khrennikov, Abramsky, Pitowsky and other people analyzing Fine's theorem.
I cite the second paper in #282 by Sokolovski as being a nice picture of indivisibility because it is clearly talking about the indivisibility of path integral "trajectories" in a similar kind of sense - trajectories evince different statistical probability spaces that are mutually incompatible and depend on measurement... or rather - to put it in Barandes' terms - depending on the statistical coupling to other systems, because the measurement disturbance properties in Barandes' formulation (and I believe in quantum mechanics generally) are properties any kind of physical system can have via interaction. Measurement is just a special case.
Can ignore below in red since based on misreading of passage on page 8 which I talk about in future post #380
You get something similar in the first paper I link in post #282, by Milz and Modi. I feel like I have to read between the lines a bit here but they state elsewhere that if processes are indivisible then they cannot be Markovian. So this should apply to indivisibility. (
but non-Markovian processes can actually be divisible)
** (comment at end)
on page 8:
"
It is always possible to write down a family of stochastic matrices for any non-Markovian process. Given the current state and history, we make use of the appropriate stochastic matrix to get the correct future state of the system. In general, for Markov order m, there are at most dm distinct histories, i.e., μ ∈ {0, ... , dm−1 − 1};
each such history (prior to the current outcome) then requires a distinct stochastic matrix to correctly predict future probabilities ... On the other hand, such a collection of stochastic matrices for a process of Markov order m could equivalently be combined into one d × dm matrix"
So it seems to be talking about non-Markovianity in the sense that different histories have different statistics - like different context-dependent probability spaces or ensembles, like in the Sokolovski paper. When you have a unique joint probability distribution satisfying consistency conditions in the form of Chapman-Kolmogorov Markov property, all the statistics can be fit onto one probability space (with unique joint probabilities) which determines the evolution through time in a history-independent way.
So maybe indivisibility just means the statistics are context-dependent on the history and can be disturbed or changed by interactions with other systems or contexts, but the statistics of the system's behavior do exist. This doesn't seem that bizarre or unintuitive to me even if the reason for the indivisibility may be unknown or even strange.
** (This following note might actually be irrelevant but I put in anyway because the idea of a non-markovian divisible process actually seems weirder to me than an indivisible process. Clearly the different kinds of stochastic systems that can exist are quite complicated.)
On page 15 of that Milz / Modi source they mention that divisible systems can be non-Markovian (my impression that such systems are a bit unusual as they have even been described as 'pathological' before, quoted in arXiv:2401.12715v1) and then give the following note as a citation [43]:
"Due to this inequivalence of divisibility and Markovianity, the maps t : s in Eq. (38) cannot always be considered as matrices containing conditional probabilities P(Rt|Rs)—as these conditional probabilities might depend on prior measurement outcomes—but rather as mapping from a probability distribution at time s to a probability distribution at time t [36,398]. This breakdown of interpretation also occurs in quantum mechanics [190]. In the Markovian case, t : s indeed contains conditional probabilities."
So to me they are suggesting this is kind of like a special case of a divisible system but where history-dependence again precludes context-
independent probabilities unless the system is Markovian.
When they say quantum case in that quote I believe they are talking about quantum stochastic processes (based on the source) which is a bit of a different topic despite the name.