Yep. Great stuff, eh? And measurement theory is even weirder, especially when considered in the context of non-locality and causality. Just where in the light cone *does* the wavefunction collapse?

That's a very cool theorem! How come nobody told me about it before? When did Bell publish it?

Before I say any more, I'd like to check my understanding of what is meant by the statement "quantum mechanics is non-deterministic". Does the following look correct?

We describe the state of a quantum mechanical system in terms of a probability distribution (PD). The behaviour of the PD is, by definition, deterministic: all non-determinism is enclosed within this PD.

If you will forgive my lapsing into CompSci terminology, we might consider the PD as a layer of abstraction that allows us to disentangle the non-deterministic and deterministic aspects of quantum mechanics. I might even go so far as to suggest that, without it, quantum mechanics would be caught in the same kind of mathematical quagmire as string theory.

But now I have some questions. You mentioned some properties that a theory may or may not have, and that there can arise interesting relationships between these properties. Are there other properties that are just as interesting? For instance, would you place time symmetry or Galilean / Einsteinian Relativity on a level with the three that you mentioned?

I'm also intrigued by what you might have had in mind when you mentioned causal non-determinism arising from acausal determinism. I'm imagining something like a spreadsheet in which circular references are allowed and are, somehow, guaranteed not to generate errors or infinite loops, but at the expense of predictability.