[tsimionescu]

Entanglement is not enough to give you the properties of measurements. While it is often presented as "when a spin-0 particle decays into two particles, one must have spin +1 and the other spin -1", that is not what the math actually says.

What the math actually says is that the spin of each particle is a linear combination of |+1> and |-1>, and that their sum must be 0. For example, one of the entangled particles could have state 1/3|+1> + 2/3|-1>, and the other would have 2/3|+1> + 1/3|-1> (or something similar, I'm a bit fuzzy on the exact math). There is nothing that says that particles must be in pure states from their own perspective. And yet, we only ever observe pure states (with some probability) in our own perspectives. So, there must be some additional law that favors these states.

[goatlover]

Decoherence from entanglement with the environment interferes with the coherence of the supposition, so we only see the pure state as I understand Sean Carol's argument. At this point in the video below he goes over the spin states.

https://youtu.be/LGtimjuA5gA?t=2545