You may wanna check out this:
(and in the description it gives titled links to particular sections of the interview)
Jacob Barandes presents a completely realist interpretation of quantum mechanics. Its one version of what you would call a stochastic interpretation of quantum mechanics.
The basic idea is that particles move along trajectories where at any time they are always in a definite position. The caveat is that their motion is kind of random. Closest analogy in everyday experience is probably something like a dust particle bobbing about in a glass of water, the water molecules pushing it one direction then another. This analogy isn't necessarily
precisely how we should view quantum behavior but it displays within it precisely what I mean when I say that the particle always has a definite position but is being subject to random motion making it change directions.
It is important to note that in this view, the wavefunction is not real, it is just a proxy for a statistical description of particle behavior. The particle and the wavefunction in this interpretation are completely separate things: the wavefunction spreads about in space and evolves deterministically, the particle is hidden underneath this description (but is compatible with Bell non-locality) and is always in a definite point of space like the dust particle in water and it moves randomly. The wavefunction is entirely a formal object that carries information about particle statistics when you repeat an experiment many, many times - it is a predictive tool like how probabilities in statistics are not physical objects but predictive tools that you apply to things. This is important to emphasize because in many interpretations, people automatically assume the particle and wavefunction are the same thing and so they make arguments against a stochastic interpretation under this kind of assumption. From my experience, it is really difficult for people to stop thinking in this kind of way and entertain the alternative. You can still use collapse in this theory but the implication is that it isn't a real event, it is just something a statistician could do if they wanted to describe behaviors of a statistical system when assuming some measurement event definitely occurs or has occurred - effectively this is just equivalent to throwing some of the data away.
Similar interpretations to Barandes' one (e.g. the main other one is called Nelsonian stochsstic mechanics) have existed literally since quantum mechanics was invented and what is nice about them is they are all - including the one by Barandes in the video - justified by and constructed in math. They prove that just starting from assumptions about particles randomly moving about, you can derive all quantum behavior. These interpretations have never been popular though. Probably partly because the mathematical formulation of these things can seem convoluted (Barandes' formulation appears to be a simpler statement of these kinds of interpretations though). They have had some unanswered questions too (though most major questions seem to have been directly addressed in the last couple years). Maybe partly they are unpopular because the news was never spread that well. Maybe because of bias and a preconception that these kinds models
shouldn't be able to work (but they do). Maybe because some people just like quantum mechanics to be mysterious.
In Barandes formulation, it seems to be suggested that entanglement is due to memory effects, i.e. there is a local interaction which causes a correlation and the correlation is remembered over time and space... it is non-local in the formal sense invented by Bell and Bell's theorem, but the non-locality is due to memory and not direct communication over space - I give an example of this kind of thing in a paper further down. Because it is simpler, Barandes' formulation doesn't really describe why quantum mechanics would have this weird behavior at all - it is agnostic about that - it just describes some formal conditions. The Nelsonian stochastic mechanics is more complicated but imo it gives a bit more depth to exactly what is causing quantum behavior. But it doesn't strictly explain the whole hog either.
Interestingly, there are classical models (called hydrodynmic pilot-wave models) and experiments which
seem to show quantum-like behaviors. They are very different - physically and descriptively - from what stochastic interpretations say, and they are very far from perfect models of quantum behavior; but they actually broadly share some mechanisms that seem to be proposed as explaining quantum mechanics in both the Barandes and Nelsonian models. Barandes says that particle behavior display a particular breed of behavior called non-markovianity (behavior with memory). The most straightforward interpretation of the Nelsonian math is that particles get their behavior from interacting with some kind of background field in a particular kind of way. Both of these suggestions seem to be present in a loose way in the hydrodynamic pilot-wave model (though not exactly in the same way given that the classical model is only an analogy with a very different description to the stochastic interpretations of quantum mechanics). The model is basically an oil droplet (i.e. the particle) bouncing on a bath (i.e. analogous to the Nelsonian background).
I can only see the abstract of this following paper but what it appears to be describing is actually very similar to the Barandes description of entanglement but in the same hydrodynamic droplet-bath model that's been mentioned:
https://scholar.google.co.uk/scholar?cluster=11815274735010691195&hl=en&as_sdt=0,5&as_vis=1
An interaction causes droplet correlations that are remembered even after the droplets are isolated.
The interesting coincidence between these hydrodynamic models and stochastic interpretations suggests that this may be a possible way of looking at how quantum behavior occurs... in a way that is completely realistic and classical. Obviously the connection between the bath and the stochastic interpetations isn't proven in any sense, the analogy imperfect, and the suggested mechanism is still not very intuitive imo - so I am not necessarily expecting people to see this and immediately find it convincing in any way. But to me, this is my leading avenue or direction of enquiry about what quantum mechanics actually means. I also imagine that the idea of particles moving in and interacting with some background that fills all of space may seem weird too but something like this already exists in quantum field theory (stochastic interpretation versions also exist of quantum field theory) where empty-space (i.e. the vacuum) always has energy fluctuations going on and these can actually interact with regular objects. So its not really adding anything weirder than what is already in quantum theory; it may not be adding anything at all if it were to turn out that the stochastic interpretation background and quantum vacuum fluctuations could be shown to be inextricably connected in some way.
https://en.wikipedia.org/wiki/Quantum_fluctuation
https://en.wikipedia.org/wiki/Zero-point_energy
I have to emphasize though that Barandes hasn't explicitly acknowledged the background explanation because it isn't explicitly part of his model - it is only something that has been inferred in the other Nelsonian theory. I think he is just agnostic about why quantum behavior is like it is; but the main takeaway is that in proving that quantum behavior follows from certain assumptions about stochastic behavior (e.g. particles moving randomly), you no longer have to view quantum mechanics in a way that isn't realistic, even if you don't know exactly why it does what it does. According to the Barandes model (the Nelsonian one too), you can in principle simulate all quantum mechanics with particles always in definite positions even when they are not being measured or observed.