What exactly are interpretations of quantum mechanics?

[Ilja]

If MW fails in a non-circular way to derive the Born rule, that isn't actually an inconsistency. A theory is inconsistent if it allows the derivation of a contradiction, but failing to derive something doesn't imply inconsistency.

Ok, let's add that common sense essentially assumes that there is only one world which would actually happen.

 

[stevendaryl]

Ok, let's add that common sense essentially assumes that there is only one world which would actually happen.

Well, "common sense" really amounts to a naive theory of physics that is good enough for practical purposes. There is no logical reason to think that something being common sense makes it true.

If a theory is logically consistent and is also consistent with our experience, then we can't rule it out on the grounds of logic alone. We can rule it out based on aesthetic criteria of being more convoluted than it needs to be to account for the facts, but that's not really conclusive. Why should we expect nature to be simple? It's nice for us if it is, but why should it be?

To me, it's ultimately a practical matter. We don't have time to investigate every possible theory, since there are infinitely many of them, so we confine our attention to the ones that are simple enough that we can hope to make some progress on. But it's ultimately subjective, how we choose which theories are worth considering, and which ones are not worth our time.

 

[Ilja]

Well, "common sense" really amounts to a naive theory of physics that is good enough for practical purposes. There is no logical reason to think that something being common sense makes it true.

Yep, the point was the following:

Common sense presupposes single world. The derivation of Borns rule presupposes common sense. MW, if it uses this derivation, therefore, presupposes common sense, therefore presupposes a single world, logical contradiction.

Of course, there is a lot of room for disagreement, for the simple reason that common sense is much too vague. The "common sense" which presupposes the single world, in principle, may be different from the "common sense" used to derive Borns rule. But I see no way for this, Born's rule requires probabilities, and I see no base for probablity in many worlds.

 

[Jazzdude]

But I see no way for this, Born's rule requires probabilities, and I see no base for probablity in many worlds.

Subjective probability in the frequency sense arises naturally from the branching idea. That's why the first approach for deriving Born's rule was based on branch counting. Of course, the result of that counting cannot depend on the weights of the branches and therefore the rule cannot be recovered. That's why Everett introduced a cutoff that, if chosen adequately, results in the right statistical prediction. It's not hard to see that his derivation is arbitrary and wrong. Later attempts to fix this didn't give much better results. Other problems with branch segregation arose in addition and led the community to believe that branch counting is inherently flawed, as branches are already an ill-defined concept.

That's where the story of MWI ends for me. Without the concept of branches and the natural way of introducing probability by branch counting, there is no way to have any natural notion of probability in the interpretation. All attempts to introduce it must lean just as far out of the window as any other interpretation and instantly kill all the appeal of Everett's approach.

With this preamble I agree with your statement. There's no satisfying way of speaking of probability in MWI.

Cheers,

Jazz