The branching is an artifact of quantum mechanics still being formulated using classical mathematics when all the evidence, including macroscopic evidence, indicates nature is fundamentally analog and what is required, at the very least, is some sort of fuzzy logic variation on the excluded middle. That includes modern quantum mechanics which are formulated as wave mechanics according to the Schrodinger Equation. — wuliheron
Yep. But then MWI seems to be an example of applying fuzzy logic interpretations to those successful mathematical formalisms. Which would be ironic.
So the maths can't provide an actual (ie: real) wavefunction collapse. Your interpretive choice then is whether (1) to affirm that there must be a collapse to one-world classicality that so far has escaped out mathematical models, or (2) argue for a no-collapse reality and ride that to wherever it logically leads, like MWI, or (3) argue for strong agnosticism about the true nature of reality as with an instrumentalist version of Copenhagen.
And we are seeing MWI being defended in very fuzzy terms with talk of interactions, correlations, interferences, branches, and other such stuff happening causally across world lines. So concrete sounding mechanisms are being invoked, while at the same time the latest decoherence versions of MWI seem to get squirrely about what any of this talk means in a definite physical sense. The other worlds "don't really exist", just as the collapse "doesn't really happen".
So the charitable view is that MWI is part of the exercise of giving up fairly completely on our classical expectations about how reality works. In some way, the whole of existence is a thermal ensemble of evolving possibility with an emergently classical character. But nothing can be completely pinned down or localised.
So in some sense the very notion of "to exist" has to reflect that reality is fundamentally contextual and can feel the shadowy presence of all its alternatives - all its possible worlds - even as it hovers fitfully around some general emergent equilbrium balance of that ocean of possibility.
In that light, both hard and definite collapse scenarios, and hard and definite no-collapse/many real worlds scenarios, are too strong as interpretations. Existence is to be found somewhere between the bounds of the one and the many.
An approach to MWI I find appealing is Chad Orzel's -
http://scienceblogs.com/principles/2008/11/20/manyworlds-and-decoherence/
He emphasises that in a twin slit experiment, every photon has a slightly different thermal history or context as it passes through the array.
What you get depends on exactly what went on when you sent a particular photon in. A little gust of wind might result in a slightly higher air density, leading to a bigger phase shift. Another gust might lower the density, leading to a smaller phase shift. Every time you run the experiment, the shift will be slightly different.
So at a deep level, every photon has a spooky "completely entangled' connection. Yet at the emergent quasi-classical level, the world is varying enough to wash away the effect of these entanglements. Although you can arrange your experiment to also stop the entanglements being washed away and - now tilting the statistical ensemble the other way - present an accumulation of photon events that have the spooky connected pattern.
So the warring interpretations want to have it clean cut as being one or the other. Either there is one world spun of definite collapses, or many worlds spawned because of no-collapse. But a thermal realism says no world is perfect for any actual photon. It is always either relatively strongly entangled or relatively weakly entangled, depending on the amount of "perfect control" there is over the identicality of real world conditions.
That is, the context itself is varying or fuzzy at all times. Only an impossibly perfect and regular context could "manufacture" the kind of pure spookiness that hard-line approaches to MWI would demand. The "world" is itself never certain enough to justify the ontic demands of the no-collapse camp, just as much as an actual collapse view yielding a single classical world is also out of the question.
A parallel in thermodynamics might be the opposing notions of absolute thermal order that would be represented by the two possible minimum entropy organisations of a perfect gas. A highest state of order would be all the particles collected in the one corner of the jar - from where they would spread out randomly. But then the opposite perfect bound would be to start with every particle having an exact grid-like spacing - spread out as regularly as possible. Again, as soon as released, randomness would scramble that initial state very quickly (and much more quickly in fact that if the gas has to diffuse from one corner).
So that is an example of how real thermodynamics is about equilibrium states that are some thermal balance which is measured relative to two opposing perfect bounds. And with MWI, the collapse vs the no-collapse positions on quantum maths represent the single perfectly classical world and the unlimited perfectly entangled quantum world-lines of which our own world is the messy actual reality that exists between two impossible states of perfection.
There is huge uncertainty/contextuality at the local particle event level. But also that context has an always present residual uncertainty itself.
So as Orzel argues, we have to both accept spookiness as fundamental, but then not jump to treating it as itself something that has absolutely definite existence. Even the spookiness is relative to what emergently exists. The world in effect exists by suppressing the spookiness. It is not the spookiness that rules in a way that produces some unlimited number of actually branching world-lines, with their then fundamentally mysterious multiple "observers" experiencing different "collapses".
Orzel again...
Why do we talk about decoherence as if it produced “separate universes?” It’s really a matter of mathematical convenience. If you really wanted to be perverse, and keep track of absolutely everything, the proper description is a really huge wavefunction including that includes pieces for both photon paths, and also pieces for all of the possible outcomes of all of the possible interactions for each piece of the photon wavefunction as it travels along the path. You’d run out of ink and paper pretty quickly if you tried to write all of that down.
Since the end result is indistinguishable from a situation in which you have particles that took one of two definite paths, it’s much easier to think of it that way. And since those two paths no longer seem to exert any influence on one another– the probability is 50% for each detector, no matter what you do to the relative lengths– it’s as if those two possibilities exist in “separate universes,” with no communication between them.
In reality, though, there are no separate universes. There’s a single wavefunction, in a superposition of many states, with the number of states involved increasing exponentially all the time. The sheer complexity of it prevents us from seeing the clean and obvious interference effects that are the signature of quantum behavior, but that’s really only a practical limitation.
Questions of the form “At what point does such-and-so situation cause the creation of a new universe?” are thus really asking “At what point does such-and-so situation stop leading to detectable interference between branches of the wavefunction?” The answer is, pretty much, “Whenever the random phase shifts between those branches build up to the point where they’re large enough to obscure the interference.” Which is both kind of circular and highly dependent on the specifics of the situation in question, but it’s the best I can do.