A little bit of googling reveals that I am not the only person to have this question.
To summarize some answers:
a) Energy is conserved by anyone performing an actual observation, therefore energy is conserved. (I suppose this is the 'shut up and calculate' answer.)
b) MWI worlds are actually entirely separate non-interacting universes that just happen to have the exact same history up to the moment of 'divergence.' Therefore energy is conserved.
(But why does world B exist in the first place, waiting around for this specific point of divergence? Are there just so many universes lying around that we're guaranteed to be able to find two that reflect both sides of a given coin flip? Or are the many-worlds realizable as the 'closure' of events from any given world-line?)
But I suppose all of this points at MWI being internally consistent but deeply unsatisfying. Any attempt to chase implications puts you in 'we can't answer why' territory.
I’m very much a layperson in this context but those seem like nonsense answers.
a) If we’re proposing that we need an observer then this is certainly no simpler than the Copenhagen interpretation.
b) I fail to see how this works. There happen to be an infinitude of parallel worlds that only shows up to make individual calculations convenient. It doesn’t seem consistent that those universes would exist to make calculations convenient until the movement of “divergence” and then suddenly they no longer affect later calculations.
For (b), imagine a set S of all possible universes. Then the two universes that agree perfectly up to the chosen event and then diverge are certainly both in S. And since they are non-interacting, there's no problem with energy conservation.
FWIW, the existence of infinite universes to justify calculations also strikes me as deeply unsatisfying...
I don’t have any trouble with the two universes, conceptually. I have trouble with the infinite others. I don’t understand the idea that the two convenient universes are represented by the wave function, but the infinite inconvenient ones are not.
But maybe the answer is that all universes are somehow represented by the wave function and I just don’t understand the implications. This might indeed be the case.
I tend to agree that this is deeply unsatisfying, regardless. Many worlds is interesting but also feels extremely far fetched. It honestly feels a little bit like “we don’t understand this yet, must be magic”.
We’ve invoked an extremely complicated phenomenon to answer a gap in our understanding. And maybe it’s true, but that’s what ancient astronomers thought about the wild paths planets took, too. “The math works out with circles in circles. Occam’s razor, amiright Ptolemy?”
To summarize some answers:
a) Energy is conserved by anyone performing an actual observation, therefore energy is conserved. (I suppose this is the 'shut up and calculate' answer.)
b) MWI worlds are actually entirely separate non-interacting universes that just happen to have the exact same history up to the moment of 'divergence.' Therefore energy is conserved.
(But why does world B exist in the first place, waiting around for this specific point of divergence? Are there just so many universes lying around that we're guaranteed to be able to find two that reflect both sides of a given coin flip? Or are the many-worlds realizable as the 'closure' of events from any given world-line?)
But I suppose all of this points at MWI being internally consistent but deeply unsatisfying. Any attempt to chase implications puts you in 'we can't answer why' territory.