Ackshually, many worlds is wrong
Thank you to Justis Mills for proofreading and feedback. This post can also be found on LessWrong.
I mentioned that I disagree with the many worlds interpretation of quantum mechanics in a comment, and I thought I should clarify my position. I title the post "ackshually" because it is a very pedantic objection that I don't think is very important. But I found the philosophy interesting/enlightening when I thought of it.
The TL;DR is that many-worlds theory is a way to embed a quantum system into a non-quantum system, whereas it seems more natural to assume that the world is just Inherently Quantum. To understand what I mean by "embedding a quantum system", it may be clearest to start with an analogy to stochasticity.
The many-worlds theory of stochasticity
To me, the notion of "true randomness" is philosophically coherent. Like yes, it's conceivable that we happen to live in a deterministic universe, but I don't think it's objectionable for the True Generator Of Physics to be a nondeterministic Markov Chain or whatever.
How can we model randomness? One option is sampling. If your modelling tool supports randomness, then you can turn the randomness of the system you're modelling into randomness in the tool itself, for instance in programming you could define an interface like such:
trait Distribution[A] {
def sample(): A
}
val uniform = new Distribution[Double] {
def sample() =
/* somehow produce a stochastic number in [0, 1], using True Randomness */
}... with the property that each time you call uniform.sample(), you get a new random number.[1]
Sampling is not the way randomness is usually modelled in mathematics, partly because mathematics is deterministic and so you can't model randomness in this way. Instead, it is usually modelled using probability, which in the finite setting we can think of as a function P:A→ℝ. This means that to each possible value a:A, we have a real number P(a) quantifying the "realness" of this A.
Now, what happens if we take P literally? It seems like it is postulating "many worlds" of A, with quantifiable levels of realness. This isn't true if the universe is truly stochastic. It's also not true if the P is modelling uncertainty. One could perhaps say it's sort of true if the P is modelling propensities, but even then it's sort of a stretch. Maybe the place where it's most true is in frequentism, where the P is modelling long-run frequencies.
Pros and cons of the many-worlds theory of quantum mechanics
Quantum mechanics is sort of like stochasticity, so if I'm to feel like the universe can be Inherently Stochastic, it also seems like I should feel like the universe can be Inherently Quantum. I used to think the many-worlds interpretation of quantum mechanics was literally just that, but the comparison to the many-worlds interpretation of stochasticity makes me think it is not. The main mathematical difference is that we swapped out ℝ and ℂ.
The many-worlds theory of quantum mechanics says that the wavefunction simply is the objective underlying reality, much like the many-worlds theory of stochasticity says that the probability function simply is the objective underlying reality. But a wavefunction is just a way to embed any quantum system into a deterministic system, so that seems like an assumption that the universe is Inherently Deterministic, rather than Inherently Quantum.
On the other hand, the possibility of destructive interference introduces a strong distinction between quantum mechanics and stochasticity, so maybe one could say that True Stochasticity is conceivable in a way that True Quantum Mechanics are not. That is, under True Stochasticity, after you sample one value from the nondeterministic dynamics, the other potential samples have no effect on what happens afterwards, whereas there is a sense in which this is not true for quantum mechanics. (On the other hand, the principle of superposition is a sense in which it is true...) So I could see the point in wanting to embed True Quantum Mechanics in a way that one wouldn't want to embed other systems.
Embedding Quantum Mechanics using wavefunctions also introduces confusion around the Born probabilities. This becomes clear with the example of True Stochasticity vs The Many-Worlds Theory of Stochasticity:
A Truly Stochastic System has a built-in weighting of realness, as there is one real outcome which depends on the probabilities. Meanwhile, if you evolve a probability mass function over time, the relationship between the numbers and the realness is kind of weakened. For instance if you store it as a hash map which maps outcomes with nonzero probability to their probabilities, then computationally, all possible outcomes are equally real, and the probabilities are just epiphenomenal tags. (This is basically quantum immortality, but for the many-worlds theory of stochasticity.) But this is not the only way to store it, and assuming you weight "true realness" by the number of different computations that result in a given state, different representations could yield just about any distribution of realness.
Collapse interpretation as an embedding of quantum mechanics into stochastic foundations
If the simplest assumption is that the world is just quantum mechanical, and the many-worlds interpretation is the assumption that the world is deterministic, then the collapse interpretation is the assumption that the world is Truly Stochastic.
That is, the collapse postulate is a way of turning wavefunctions into randomness, and when interpreted in a realist way, it is interpreted as occurring stochastically. Given that the world is quantum mechanical, the collapse postulate is arbitrary, with variants of it being continually falsified as quantum computers prove larger and larger superpositions to be stable.
The main advantage of the collapse interpretation is that it provides a bridge rule, where if the rest of your model is a first-person stochastic model, then you can embed third-person quantum-mechanical models into it. Meanwhile the many-worlds interpretation suffers from the problem that it is hard to bridge to experience, because nobody uses a third-person quantum-mechanical model for navigating their day-to-day life.
I think lots of many-worlds theorists actually agree with this?
Like, the point of many-worlds theory in practice isn't to postulate that we should go further away from quantum mechanics by assuming that everything is secretly deterministic. It's that we should go closer to quantum mechanics by assuming that postulates like "collapse" are mathematical hacks to embed the true quantum mechanical systems into our false models.
Many-worlds theory is "directionally correct" in this sense, but multiple incompatible theories can be "directionally correct" in the same sense, and theories that try to address different things can be directionally correct for different things. (E.g. maybe the pilot-wave model is directionally correct in the sense of informing us about the nature of knowledge?)
In practice, most software libraries that use randomness use pseudo-random number generators, which would make it a hidden-variable model rather than a Truly Stochastic model. But let's pretend there's an exception, somehow.