[monktastic1]

The only explanation I've ever seen of when worlds split is when decoherence has become "effectively irreversible." That's not a well-defined physical event, and so it's hard to say that worlds "actually" split.

For your unentangled state on the left, Sean Carroll explicitly describes it as a state that doesn't have two worlds yet. I can find the post if you like, or maybe we already agree and I'm misunderstanding.

[gpsx]

If you have can find a post I'd like to see it. I don't quite follow.

In what I am describing, the two "worlds" don't really separate. It is possible that they can interact, theoretically. However, you can't construct an experiment to detect the different parts of the wavefunction interacting because of decoherence. You just can not make a coherent quantum system that invovles real people (to my knowledge). So in practice you can not do the experiment.In anything we observe, the two resulting observers (in a measurement with two choices) are effectively isolated.

In other words, decoherence is automatic. Also, it is inherently irreversible.

But, I am sure he (or whoever wrote that post) is saying something sensible so I would be interested in seeing it.

[monktastic1]

I just mean like this: http://www.preposterousuniverse.com/blog/2014/06/30/why-the-...

"We wouldn’t think of our pre-measurement state (1) as describing two different worlds; it’s just one world, in which the particle is in a superposition. But (2) has two worlds in it. The difference is that we can imagine undoing the superposition in (1) by carefully manipulating the particle, but in (2) the difference between the two branches has diffused into the environment and is lost there forever."

(State 1 is when the particle is in a superposition by itself and state 2 is when it's entangled with a macroscopic apparatus.)

My issue is that he uses words like "forever" and "impossible." These convey a sense of finality, but the decision of where to draw the boundary is subjective. The worlds can in principle (and under certain cosmological models, must) recohere.

See, for example: https://arxiv.org/abs/1105.3796

"Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment"."

See in particular Section 3.2 (Failure to irreversibly decohere: A limitation of finite systems)

(Edit: I should mention that I am not a physicist, by a long shot. Just a curious amateur.)