Although there are many versions of MWI, the general claim is that a single axiom (a unitarily evolving wavefunction) is sufficient to explain our observations of the universe. Without getting into what it means to "explain" something, it seems fair to demand that a sufficiently intelligent agent with no prior knowledge of our physics should be able to predict what the theory says about their future observations. However no one would be able to make any experimental predictions based on the above axiom. There's nothing there to suggest that if the agent becomes entangled with a quantum system then they would only experience a single branch of the entanglement. Even if you add that in, there's nothing to suggest which branch the agent will experience (this is roughly the preferred basis problem). Even if you add that in, there's nothing to suggest with what probability the agent will experience that branch.
You could always add in the above as additional axioms. You could postulate some physical content to the Born-rule, or to something weaker from which to deduce the Born rule. But this would break the illusion that MWI requires fewer axioms. Instead, a great deal of energy has been expended into deducing the Born rule purely from that single axiom. There have been many very clever attempts at this, but none convincing enough to settle the matter.
Isn't that obvious given that the particles of your brain can't interact with the particles of your brain in physically-different branches?
>it seems fair to demand that a sufficiently intelligent agent with no prior knowledge of our physics should be able to predict what the theory says about their future observations. ... Even if you add that in, there's nothing to suggest which branch the agent will experience
Don't you get that same problem with other interpretations that instead assume interactions can have a truly random result on some probability distribution?
Not immediately obvious to me. An agent could calculate the entangled state of themselves (including brain particles), the system and the measuring apparatus. This overall entangled state would in principle be pure, although the agent's own reduced state would be in a superposition which could be written in one of an infinite number of ways. What the agent should expect to experience in this situation is not at all clear, to me.
> Don't you get that same problem with other interpretations...
Most other interpretations have an explicit postulate relating physical probabilities to parts of the mathematical formalism. The agent can use this to make predictions about future observations.
So if it's right, it needs to rigourously exclude everything else.
So why X happens instead of Y?
1. Let's propose an unexplainable, unmodellable infinite entropy source under everything
vs.
2. X happens and so do Y, and one is observed at a certain probability due to anthropic principle - like this: https://www.youtube.com/watch?v=9R5OWh7luL4
The first is somehow psychologically less satisfying answer for me, although - of course - I accept that calculation works either way. The second at least not an unimaginable infinite, and in the end leaves me with less "why?".
Sorry if I'm underestimating your familiarity with MWI here; if I am, szemet has a much better response. I'm just a little concerned that some people in the thread don't realize MWI refers to something much more specific and grounded than what-if-multiple-universes, and I wanted to dispel that notion.
If you want a more layman's explanation of what sort of things would cause a branch and how the branches would differ: one simple example is that when an excited atom emits a photon, it doesn't emit it in a random direction, instead there's a superposition of it emitting the photon across all paths away from itself. In many of these paths, the photon will interact with particles differently than happens with other paths, and the paths will decohere into different branches of the world with separate consequences from the photon hitting in a different place in each branch. In one branch, the photon could hit a particle in the air and affect its temperature and velocity by the tiniest amount. In another branch, the photon could instead hit a receptor in a person's eye and immediately trigger a reaction that would not have otherwise occurred.
Small differences between the branches could build up into bigger differences over time, especially when you consider the sheer number of concurrent interactions that are creating overlapping superpositions which decohere in many different ways. It could be that there's enough branches that most things that could have reasonably happened by chance do happen in some branch.
(If you're wondering how we could know in theory that the world may branch like this, it's because branches where particles take different paths but then later have all of their positions line up together interfere with each other. See the two-slit experiment.)
The arguments against MWI from Occam's Razor are indeed weak. The stronger critiques are the difficulty of deriving the Born rule, or indeed quantum randomness at all, from the deterministic MWI. This is presumably what the authors hint at in their "doubtful it [pure Hamiltonian evolution] makes sense even there (in MWI)".