Ok, so you tell me, what does it run on? Intrinsic curvature and virtual particles, or what?
As for how the curvature of spacetime fits with all that, that is an open question that has yet to be resolved. Well, constructing a quantum field theory within a given curved spacetime is fine, but we don’t know how exactly GR and QFT fit together.
I expect that your response is going to be to call these “abstractions” or something, as if this does anything more to discredit them than complaining that any idea is “just an idea”. But these are measurable things. That which can be measured is a real thing.
But this is just mystifying measurement. It's a convention that's been adopted because we've had to regress on the question of what is a real thing. It's not something you can look at or hold in your hand, it's not even something with material reality necessarily, it's just something that can be measured, or rather something that can be inferred to exist given the measured behavior of other things - i.e. gravity. You make it sound like it's a given, but this definition is a position that's been arrived at by progressive regression.
But what does this mean concretely? Do you believe there is a real field out there with a value at each point in space time? What's it made of, what is the value a value of? If there no real field where is the accounting done and by what? I understand that when we run it through our models that assume a field like thing we get the right predictions, but what's the mechanism out there?
Even setting that aside, I wouldn’t expect the state to be an eigenstate for that even if the “value of the field at this location” was an actual observable rather than a like, operator valued measure, so, even then I wouldn’t expect the value to be determinate, no.
If spacetime turns out to be discrete, that would resolve the “the distribution over the values for the field are distribution valued, not valued in genuine functions” issue, (and the other reason for it not having a determinate value is actually normal) but it is hard to see how this would fit with our non-observation of violations of Lorentz invariance.
I don’t know what you are asking for when you ask about a mechanism. Do you mean a classical mechanism? Nature isn’t classical.
If there is no inside to a box, then knowing everything about how the box interacts with things outside the box, is pretty much everything there is to know about the box, yeah.
The study of physics concerns only that which we can observe/measure. Now, like I implied before, I’m not a scientific materialist, and I don’t claim that all-that-there-is is amenable to understanding through the lens of physics. So, like, I guess the answer is “No, I don’t expect physics to tell us everything I want to know about the nature of the universe, just all of it that is accessible to experiment.”.
Yeah, that's kind of a biggie. And kind of the point. It's not just some box somewhere, it's the thing we've been trying to figure out since the beginning. If physics can't tell us the fundamental nature of the universe, then what is it doing?