Demystifying Born's rule

It would be tiresome to go through all the proposals listed in that article, identifying how they work, the resultant limitations, and then speculating whether they might nonetheless help us understand reality one day. Or at least, I think I would save that kind of analytical effort, for an audience of physicists interested in ontology. 

But let me just discuss one example. The proposal discussed in the most detail, is due to Dürr et al. The article straight out says that they rely on the existence of a "preferred foliation" of spacetime. That means that to define their "relativistic" Bohmian mechanics, they still need a particular decomposition of spacetime into a stack of spacelike hypersurfaces. Their trick is to then say, well, we don't need to use a coordinate system in which those hypersurfaces are all "t = constant". We can do a relativistic boost, and switch to a new coordinate system with a new time coordinate, in which those hypersurfaces are tilted with respect to the time axis. 

That's formally true, but nonetheless, their pilot wave and their equations of motion are only defined with respect to one specific foliation, which de facto defines a notion of absolute simultaneity. 

The point is that all these "extensions to relativity" involve some kind of trick, or they only work in an artificially narrow setting, or they meander off in some eccentric direction. There is certainly no relativisitc Bohmian mechanics known, that can deal with all the known phenomena of field theory, like pair creation and gauge invariance. 

I admit that I did not word that very well. Honestly don't know how to concisely express how much Copenhagen interpretation makes no sese at all, not even as an interpretation. 

What happens if the branch "you" are in gets cancelled with another branch?

One doesn’t invoke the term “different branches” unless they are macroscopically different, and if they’re ever macroscopically different, then they will remain macroscopically different forever, thanks to entropy (and the related fact that macroscopic events leave countless little persistent traces in the environment). Even moreso if we’re talking about human observers, who form memories of what they’ve seen in the form of changes to the structure of their brains. Macroscopically different branches can’t “cancel” and more generally macroscopically different branches can’t interfere in a way that has any measurable effect.

(For any quantum observable O that’s relevant in practice, $⟨\psi |O|\varphi ⟩\approx 0$ if $|\psi ⟩$ and $|\varphi ⟩$ are macroscopically different—e.g. the geiger counter loudly clicked in $|\psi ⟩$ but not $|\varphi ⟩$.)

See also: https://www.lesswrong.com/posts/7A9rsJFLFqjpuxFy5/i-m-still-mystified-by-the-born-rule#Q1__What_hypothesis_is_QM_ [LW · GW]

Solomonoff inductors are a bit of an odd case because they don’t & can’t exist in the universe. But leaving that aside (let’s say we’re implementing AIXItl or whatever):

Every time the computer makes an observation, we learn some stuff about the universe, and we also learn some indexical information about where we-in-particular are sitting within the universe. This has always been true, but it’s especially true about MWI because we will never stop getting indexical updates (unlike a deterministic universe where you can learn that you’re in a particular room on earth and then there’s no more indexical information to learn). In MWI, if we observe that a pixel is bright, then we have learned that we are in a branch of the wavefunction wherein the pixel is bright. There might or might not be other branches wherein the pixel is dark, but if there are, we now know that those branches are “not where I have found myself”, and we can ignore those branches accordingly. You can still have hypotheses, but they will incorporate born-rule indexical uncertainty about which branch I will find myself in in the future, on top of whatever other indexical uncertainty you have for other reasons.

What happens if the branch “you” are in gets cancelled with another branch?What happens if the branch “you” are in gets cancelled with another branch?

That can only happen if the "branches" or "worlds" are still in a coherent superposition.

There is an approach to MWI based on coherent superpositions, and a version based on decoherence. These are (for all practical purposes) incompatible opposites, but are treated as interchangeable in Yudkowsky's writings.

The original, Everettian, or coherence based approach , is minimal, but fails to predict classical observations. The later decoherence based approach, is more emprically adequate, but seems to require additional structure, placing it's simplicity in doubt

Coherent superpositions probably exist, but their components aren't worlds in any intuitive sense. Decoherent branches would be worlds in the intuitive sense, and while there is evidence of decoherence, there is no evidence of decoherent branching, as opposed to decoherence.