Could you touch on why many worlds is more parsimonious than pilot wave? I'm not sure that I understand that reasoning. Is it because a given "universe" is locally simpler? Would it be accurate to describe the comparison as an infinite number of universes (separated via some higher dimension) vs. a single universe that is holistically connected throughout spacetime?
The theory is more parsimonious. Whether it generates untold amounts of parallel universes is immaterial to its own Kolmogorov complexity.
Many worlds basically says "the wave function is real". You just take what the math says at face value, and the math says there's a blob of amplitude where the cat is alive, and another blob of amplitude where the cat is dead, and those blobs do not interact.
Copenhagen adds something on top of the math: a kind of "collapse" where the blob you did not observe gets mysteriously zeroed out. There's only one universe, which looks simpler, but the theory itself is more complex, because you just added that collapse.
Pilot Wave (of which I know nothing) seems to add a similar complexity. There's no collapse, but there's this additional non-local "wave" that's laid out on top of everything, and determines which of the blobs is real (the dead cat blob or the live cat blob).
Think Chess vs Go. Chess has rather complex rules, with an initial position, moves for 6 different pieces, and a couple special cases. Go's rules on the other hand can fit on one page. So, Go is simpler. However, in terms of possibilities, the universe generated by the Go rules is orders of magnitudes bigger than Chess'. Simpler rules can lead to more diverse possibilities. Quantum physics interpretations are similar: Many Worlds have the simplest rules, but it also describes the biggest universe.
Actually, configuration space have an infinite number of dimensions. Current physics, (or at least QM) doesn't describe our universe as having 3 spatial dimensions. That's a projection, the classical illusion —which is a logical consequences of the underlying physics of course.
Imagine 2 pearls on a thread. You have 2 ways to represent them: the obvious one is 2 points on a line. A less obvious (but just as valid) is a single point on a plane: the X axis would represent the first pearl, and the Y axis would represent the second pearl. Similarly, 2 billiard balls on a billiard can be represented by a single point in a 4 dimension configuration space. And the entire universe require many many more dimensions than that.
Many worlds is parsimonious in some ways in that all the stuff allowed by the equations happens and that's it (sort of in theory at any rate - not sure it really gives the Born rule). With pilot wave or Copenhagen you have to tack on a wave or observer respectively. On the other hand all the stuff is a lot of stuff.
The complexity of a theory is in how long the theory itself is, not how big the objects it generates are. The peano axioms are extremely simple, despite generating an Infinity of numbers.
