Sure, "no hidden variables" is interesting/weird. And interference is interesting/weird. And both of those things happen independently from entanglement.

But entanglement itself seems very not-weird to me once you buy into those other things.

What you're on to is that all of the big popular examples of "quantum weirdness" (uncertianty, entanglement, tunneling) emerge from a very small and elegant set of axiomatic postulates. That's the beauty of physics.

One such group of postulates that chemists like to use can be found at http://vergil.chemistry.gatech.edu/notes/quantrev/node20.htm... . You can probably beat the elegance of those if you're willing to step further from what's actually used in calculations, but that's not what chemists like to do.

Here's a better shot at being axiomatic and elegant, but it's a lot less clear (from a lay-perspective) how they relate to reality: https://en.wikipedia.org/wiki/Dirac%E2%80%93von_Neumann_axio...

I find Lucien Hardy's discussion enlightening:

Quantum Theory From Five Reasonable Axioms

https://arxiv.org/abs/quant-ph/0101012

Yes, but the time displaced version is more like cause and effect. Non local correlations between variables separated in time is a generic feature of classical mechanics. Frankly I think this paper exploits hype and naivete but what do I know I only have a pnas paper on quantum Dynamics.

As you're the only person so far on this thread who seems to know about this, is my understanding correct that non-locality of entanglement is because all the entangled entities are described by a single hamiltonian which means the energy expressed in each of their degrees of freedom must sum to zero, so only certain combinations of measurements are possible of the system as a whole