I agree MWI is the minimal "version" (don't get hung up on that word) of quantum mechanics. I take it as a given and consider the way we experience/interpret the universe as an insight into how the brain works.

Totally agree

I don't think you get to claim simplicity for the theory that results in an exponential explosion of entities. Simplicity isn't just about descriptive simplicity.

That's not the right way to frame MWI, there's no explosion of entities at all, just a single wave function that evolves. The wave function starts out being a function of n variables, evolves according to a differential equation and remains a function of n variables.

It is strange given my physics training to read this discussion.

Physicists do not directly apply Occam's razor in most circumstances, and we certainly don't do bookkeeping on how many “entities” there are, and your comment illustrates precisely why: how you count is not a given.

Here is something that did happen in classical mechanics: we transitioned from F_i = m a_i to Lagrangians even though they have roughly similar explanatory power. Here is an argument that was not made: “Lagrangians are truer because you don't have to postulate three equations of conservation of momentum and one of conservation of energy, you just have one law of least action.” Nobody even declared a confident end to the tyrrany of Newton's third law as Lagrangians no longer need it.

Furthermore nobody said that classical field theory was “better” per Occam's razor merely because you were no longer bound by the tyrrany of the least action principle and could now consider essentially a world in which F_i = m a_i was not universally true, to be replaced with a philosophical interpretation by some bloke Neverett who declares the fields on-shell “typical” and derives the least-action principle as a statement that “if you find yourself in a typical universe then almost surely your retroactive reconstruction of events satisfies the least action principle.”

No, many worlds interpretation is thriving precisely because it calls physicists attention to the importance of decoherence calculations in the understanding of various physical phenomena. It gives you an idea for how to model measurements that are somehow partial, or being continuously performed. Occam doesn't enter into the discussion in the first place.

You're right that you can't just count the number of postulates naively because there is generally not a well defined way to do so. A great example is the one you give: three laws of motion vs one law of least action. However, if I told you that it was possible to reproduce all of mechanics with only the first two of Newton's laws, then surely you'd agree that there wouldn't be a need for the third law and in that sense the new system of postulates would be simpler.

In other words, because MWI is obtained by removing a postulate from the usual formulation of QM, I think it's fair to say it's simpler. If, instead, MWI had been obtained by formulating all of QM in some other distinct framework where there was no mention of wave functions, measurements, or the Schrodinger equation etc, and it had one fewer postulate, then yes I would agree that you can't arbitrarily say that it's simpler.

Put another way, suppose you have some linear dynamical differential equation in n variables that you solve somehow. Then, take that solution and expand it in some set of basis functions (e.g. a Fourier series). You wouldn't throw your hands up in the air and say "wow that's so complex, look at all those infinite terms in the solution!". The complexity isn't really there, it just appears to be there because you've chosen to expand your solution in a basis that makes it appears really complex. Similarly in the MWI we see something that looks complex simply because we've chosen to expand the solution in a set of states that makes sense to us (state1 = particle at location 1, state2 = particle at location 2, ...)

With the Fourier example, there is a constant amount of information in the system, and so the apparent complexity in the Fourier basis representation is an illusion.

Is that the case with MWI? Is there a constant amount of information at time t and t+1? Note that I see a fundamental equivalence between information and entropy (of the computational sort), and so an exponential growth of computation required to get from t to t+1 is an inescapable theoretical burden.

To put it a different way, MWI seems to reify possibility. But the state of possibility grows exponentially in time, and so the theoretical entities grow exponentially.

Yes, there is a constant amount of information in the system. In fact, that's part of the beauty of MWI in contrast with Copenhagen. In MWI, the state at any point in time can be used to reconstruct the state at any other time. However, because of the collapse, that's not the case for Copenhagen. In other words, measurement in Copenhagen actually destroys information. As far as computational complexity goes, the same happens in classical mechanics. Start with 10^23 particles far apart but moving toward each other. Then simulating the first second is simple, but once they get close together, it gets hard with the computational complexity growing as time progresses (or alternatively the error growing for fixed computational resources).

I still don't follow. There is a constant amount of information as input into the system, but (from my understanding) the "bookkeeping" costs grow exponentially with time. This is different than the classical case where the complexity is linear with respect to time. A quick google search says that simulating quantum mechanics is NP-hard, which backs up this take. This bookkeeping is an implicit theoretical posit of a QM formalism. We can think of different ways to cash out this bookkeeping as different flavors of MWI, but we shouldn't hide this cost behind the nice formalism.

Comparing MWI to collapse interpretations, collapse is better regarding this bookkeeping as collapse represents an upper limit to the amount of quantum bookkeeping required. MWI has an exponentially growing unbounded bookkeeping cost.

Yes, that's right but that has to do with entanglement in QM and is not specific to MWI. In classical mechanics, a system of n particles is specified by 3n different functions of time - the three coordinates for each of the n particles. The complexity in terms of e.g. memory then scales linearly with the number of particles.

In QM by contrast we have entanglement, which essentially means that we can't describe one particle separately from all the other particles (if we could, then QM would be just as "easy" to solve as classical mechanics). Instead of 3n functions of time, we instead have a single function of 3n variables (plus time). The complexity of these functions does not scale linearly with n (imagine e.g. a Fourier series in one variable vs one for two variables)

So, you're right that QM is an exponentially harder problem to solve compared to classical mechanics, but this is because of entanglement and has nothing to do with Copenhagen vs MWI.

We don't like it because it can make no actual predictions about the physical world if it doesn't include measurements. And when you include them it's no longer that simple.

You can make predictions if you assume that you are in (weighted) randomly selected world.

Well rather than a single world, I think that the perceived identity exists in multiple highly similar and interacting worlds seen as an entity. Just like we have a size in physical space we also have a non-zero "size" in probability "space".