[tsimionescu]

> A more likely outcome means there are many more worlds with that outcome. You can calculate the percentage of worlds that have that outcome.

First of all, this is a new postulate of QM, you can't derive it from the Schrodinger equation. It is perfectly equivalent with the measurement postulate.

> Measurement, observer and classical shouldn't be part of a physical theory. The answer as to why things appear that way to us is decoherence.

This contradicts the other part, where you were talking about a notion of worlds that can be counted. If they can be counted, they have to be defined as classical worlds. Decoherence only explains why worlds can't interact with each other, it doesn't help define what they are without appealing to measurements. Even the notion of "the environment" is somewhat ill defined if we go down to the philosophical level.

[goatlover]

Measurements are interactions that result in entanglement. Atoms radioactively decaying in your body are interactions. The environment is the entire universe as it becomes entangled with a quantum event.

[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