First off, thank you for taking the time to respond to this! I don’t think your reply was weird or messy at all. If you want weird and messy, keep reading!

Now, to have a precise frequency, you need a lot of wavelengths, so there’s a lot of places the particle can be. If you add together lots of different waves with different frequencies, you can get a sum wave with a single enormous peak, and the particle is localized. But now there’s many different frequencies, so the kinetic energy is uncertain.

This is great and I think it is core to my question. You are talking about how there is a probabilistic way to calculate the frequency, which, if I’m understanding correctly, means you can determine where the particle is as it is traveling down the path of the wave. So this is a model of the behavior of the particle.

However, it makes intuitive sense to me that the actual, objective location of any particular particle isn’t probabilistic. (It might, however, be completely unknowable.) It just exists at some point in space at some particular time. Instead, we are using the model as a way to understand the behavior of a particle. Which is why the quote above sparked my question: are we modeling reality or the way we think about reality?

You also said this:

It’s not a measurement error, the information literally doesn’t exist at that level of granularity.

Which might imply that my intuition is wrong and at the physical level particles fundamentally don’t behave the way I think they should. Or maybe you mean that the information is unknowable because of how we model the problem.

And it leads to all sorts of weird consequences like quantum tunneling. if you put a barrier between a particle and measure the momentum very precisely, the position can get uncertain enough that it could be on the other side of the barrier.

Again, is this a matter with the model or with reality? Are we essentially dealing with mathematical errors in the model that build up, but the particles actually have smooth trajectories in space? Or is there something more fundamentally random occurring?

I know that at a certain point we are dealing with questions so far beyond concrete human abilities that as far as we can tell the model is reality so maybe this is really a philosophical point. Furthermore, I hope that my line of reasoning doesn’t feel totally unreasonable and unsatisfiable.

Mathematically, any physical observation corresponds to a transformation of the wave vector. And the position and momentum transformations don’t commute, so mathematically measuring position-then-momentum must give a different result than measuring momentum-then-position.

That’s a neat detail!

and the experiments are fascinatingly subtle.

Hence my fear of not understanding the replies!

If you really don’t want probability in the underlying theory, the usual route is to go to Everett’s interpretation, which does away with a classical observer entirely. In that case the random chance we see is because we perceive ourselves as on one lobe of a bifurcating wave function.

Oh, no! My fears have been realized!

My issue isn’t really with having probability in the theory.* It’s that when people talk about quantum physics I can’t tell if they are talking about the model of quantum physics or how the world actually works. I know that might sound crazy: theory is supposed to be about how the world works! But sometimes theory is an incomplete picture of how the world works. It’s a particular view that solves particular problems. That’s not necessarily how theory is always talked about and it may be completely inaccurate here.

You have all sorts of pop sci articles that claim that objective reality doesn’t exist. I can’t tell how seriously I should take such claims. Are they misinterpreting experiments that demonstrate the defects of the model or is there actually a deeper more fundamental question being raised here?

I don’t want to sit here and ignore what might be very fundamental deviations from how I view the world, but I also feel the need to clarify how I should interpret these claims before accepting them.

• I don’t really really have an issue here besides my own ignorance.

Interestingly I find Software Foundations similarly dense / opaque.

As an example of a book in a similar vein that I was able to align with is Concrete Semantics. That is pretty close to what I’m talking about as being a good beginner book for formal methods. The only thing it leaves to be desired is that it’s very focused on language semantics and not so much of an overview of formal methods in general.