[ibab]

In the Everett/Many Worlds interpretation the appearance of randomness can be explained as an emergent phenomenon resulting from not being able to predict which part of the wave function we will end up in before running an experiment.

[Jweb_Guru]

The Everett/Many Worlds interpretation cannot reproduce the predictions of quantum mechanics without extra assumptions (e.g. the Born rule) that don't have any physical basis within the context of MWI.

[ibab]

Yes, you are right to point this out. There are some important details that are still being debated. Personally my impression is that the debate has advanced enough to the point where MWI can’t be outright dismissed based on this argument. There are multiple plausible explanations and the remaining difficulties have more to do with philosophy than physics.

Edit: To give one example of an approach that I think is promising: We start by describing the observer and environment through a density matrix (a probability distribution over possible wave functions) and introduce an interaction with a quantum system (e.g. a spin). Given a reasonable interaction, you can show that the entanglement in the combined state (observer, environment and spin) leads to the system approaching a state that is a probability distribution of entangled states where each probability corresponds to the Born rule. Interestingly in this case the probabilities emerge from our lack of knowledge about the microstate of the observer/environment, so it’s actually thermodynamic uncertainty.

[Jweb_Guru]

I'm not dismissing MWI, I'm just saying that current formulations either don't reproduce quantum mechanics or don't really address the existence of randomness within quantum mechanics.

[Jweb_Guru]

While I intuitively like the statistical approach you mention, under it the Born rule holds only approximately, so it should be theoretically possible to observe entangled states which we have never done--i.e. it produces different predictions from the Copenhagen interpretation of quantum mechanics, which means it's not strictly a different interpretation, but its own falsifiable theory. Like I said in another comment, if we ever do observe entangled states directly, people will jump on board one of these alternate explanations like lightning. But until we do, the question of why we never ever observe anything that doesn't look like collapse still needs mathematical justification.

[eigenket]

I am not aware of any interpretation that has the Born rule without assuming something equivalent to it. For example de Broglie–Bohm theory requires you to assume the original distribution of the particles follows the Born rule. QBists just postulate it, consistent histories just postulates it etc.

I am not particularly a many-world proponent, but I do not think it is fair to level this accusation as an issue for many worlds without bringing up that every other interpretation has the same "flaw".

[Jweb_Guru]

AFAIK it can in fact be derived through Gleason's Theorem under the assumption of noncontextuality, so I don't think it's fair to say that nobody can derive the Born rule without assuming it (many people have issues with noncontextuality but that's very much a philosophical thing). The thing you have to demonstrate is that a probability measure actually connects to physical observables in some way, and this is the part that is difficult (and as far as I can tell MWI does nothing to resolve this conundrum).

[eigenket]

Gleason's theorem also makes a big assumption when you require that the measurement outcomes are associated with POVM elements (or projection operators if you don't like POVMs). I lumped that in with "assuming something equivalent to it" since Gleason's theorem (at least by my understanding) is exactly the statement that assuming non-contextuality+POVMs/POMs is equivalent to assuming Born's rule.

Although its really cool I don't think Gleason helps you tie any particular interpretation to the Born rule, since you still have to make a jump to tie your measurement outcome to a POM/POVM element.

As far as your last sentence goes, this is sort of what I was trying to argue in my comment above. The "part that is difficult" that you identify as being unresolved by MWI is also completely unresolved by pilot wave theory, or qbism or consistent histories or any other interpretation (as far as I am aware).

[Jweb_Guru]

I think we're in agreement there (though IMO it's highly nonobvious that noncontextuality+POVMs automatically get you the Born rule, so I don't think it's "cheating" to assume that--obviously any set of axioms that let you derive Born will have such a property!). I was mostly saying, I don't think MWI helps us understand where the probabilities come from any more than any other interpretation--you need something more. And if you can't identify where the probabilities come from, then saying your theory is "deterministic" rings fairly hollow to me.