There are many classical systems that have properties we consider real that are nevertheless not practically measurable. For example, grains of sand have definite position and momentum, yet you can't in reality measure them for each grain of sand when you want to describe the flow of a sand in an hourglass. So the practical ability to measure something is not required for us to consider something "real".

Now, Bell's inequalities show that any theory of local hidden variables independent from the measurement apparatus is inconsistent with QM and with experimental observations. However, that still leaves the possibility of non-local hidden variables possible, and it also leaves open the possibility that the experiments have been flawed - that the measurement decision was somehow correlated with the result.

The Copenhagen interpretation is BOTH non-real and non-local, so I don't find a real non-local theory a priori problematic. Whether pilot wave theory can be made consistent with at least special relativity is still open as far as I know, but perhaps there is some equivalent of the no-communication theorem that will be found.

Superdeterminism is also seeing a resurgence - I can't claim to understand how it could be made into a real scientific theory, but perhaps there is something that is escaping me and we will see a successful theory come out of it.

Now, the matter of whether something can be considered "real" but fudamentally un-measurable (as opposed to just being practically un-measurable) is in the end a problem of definitions.

I would also note that there is no fundamental quantum randomness - quantum phenomena behave according to a linear equation, so they are fundamentally deterministic. It is only measurement (the interaction between quantum systems and classical systems) that introduces randomness - the superposition of all the solutions to the Schrodinger equation is replaced with a single position&momentum with some probability, and with error bars that are subject to the uncertainty principle.

> Whether pilot wave theory can be made consistent with at least special relativity is still open as far as I know

It can be made consistent, namely, adding a foliation (a notion of a canonical present moment) makes it work out fine. The foliation is not detectable, it gives the right predictions, it is mathematically sound, etc.

But it does feel philosophically sketchy and not fundamentally relativistic. However, there is a paper https://arxiv.org/abs/1307.1714 which explores how to derive foliations from the wave function itself and thus would be as relativistic as in theory involving the wave function.

The article also points to other articles with a variety of ideas how to deal with nonlocality in Bohmian mechanics.

> grains of sand have definite position and momentum

No, they don't. The uncertainty principle applies just as much to grains of sand as it does to electrons. The only reason they appear to have definite position and momentum is that their masses are large, so a very small velocity produces a very large momentum which gives them a very small wavelength, much smaller than their physical extent. But the uncertainty principle still applies. With the right technology you could do a two-slit experiment on grains of sand. See: https://www.wired.com/story/even-huge-molecules-follow-the-q...

To be fair, the parent was talking about "classical systems," not about the applicability of quantum-mechanical principles to macroscopic objects.

But there is in reality no such thing as a classical system. The world we live in is quantum. Its behavior approaches that of a classical system as the number of entangled degrees of freedom grows, to the point where classical physics becomes a damn good approximation. But reality never actually becomes classical. The wave function does not actually collapse. And grains of sand do not have actual positions and momemta.

Whether this is actually true or not remains an open question, but it is indeed the expected consequence of QM. However, there is as yet no experiment showing any kind of quantum behavior for huge objects (closest is a few hundred million atoms as far as I know).

Still, the point was about a classical model, not about physical reality being classical or quantum. To rephrase, my point was that even in a classical model there are quantities that can't practically be measured (even though classical mechanics as a model assumes all objects have definite positions and momentums), and that doesn't stop us from accepting in such a model that they are 'real'. So, the idea of property that is 'real' but not really measurable already exists in classical physics, it is not an invention of exotic interpretations of QM.

The Bohmian model is that particle positions are an intrinsic part of the evolution of the theory. This is in contrast to, say, the Copenhagen interpretation in which the particle position is not a part of the evolution of the system. In the CI, wave functions are real (I guess) and we need something external to the model, called measurements, which mathematically do some complicated operation to the wave function of putting it in an approximate eigenstate (it can't do it exactly nor is the approximate nature specified and the timing of this is generally specified but not really clear about time of arrival measurements in scattering experiments).

In the Bohmian model world, particle positions would be real. They may not be measurable to the inhabitants to infinite precision (assuming quantum equilibrium, i.e., the particles are distributed according to psi-squared), but the particles have definite postions in this world. It has in it no need to postulate anything about measurement. Observables and all that are deduced from the theory.

It is important to ask what in a model has a fundamental existence, what has an implied existence, and what is just a useful term for something secondary to all that. In Bohmian mechanics, particles (things with position) have a fundamental existence, the wave function has an implied existence because that is how the particles move about, and spin has a secondary existence since it does not have a separate existence from either of those two objects, being solely deduced from the motion of the particles.

The Bohmian model is well-defined and has an easy correspondence between the entities that are real and our experience (stuff has position). It does not require observers to be complete. A Bohmian world could happily exist without PhDs, humans, mammals, life forms, etc.

What's real in CI? Not really sure, but I guess the wave function and measuring devices? It does require something that corresponds to measurements and the evolution of that classical world is distinct and separate.

This is the context of calling BM a realist theory. I would just call it an actual theory.

Bohmian mechanics illuminates the quantum randomness, allowing it to be analyzed. The theory happens to be deterministic (ignoring creation/annihilation), but it derives the apparent randomness from all that and it clarifies the meaning of psi-square.

> What's real in CI? Not really sure, but I guess the wave function and measuring devices? It does require something that corresponds to measurements and the evolution of that classical world is distinct and separate.

The wave function and any of its behaviors are not considered Real in CI, quite the opposite. CI posits that the wave function / schrodinger equation is just a mathematical tool that can be used to model the behavior of quantum phenomena - it is merely a tool that we can use, together with the Born rule, to predict the outcome of measurements. The measurements are the only things that are real. That's why CI is also sometimes summarized as "shut up and calculate" :).