[lmm]

> Not really, because in Bohmian mechanics the wave function is nomological, ie. not real, and merely describes a law of motion.

I don't see that that's a meaningful/objective distinction? The wavefunction is certainly physically meaningful in the sense that you can't predict experimental results without computing its behaviour (or something equivalent to it). I don't think that you can reduce your number of postulates by declaring parts of your theory "not real" - given that elementary particles are not directly observable, couldn't we just declare that e.g. electrons are "not real" and merely describe a law of experimental results?

> Since you mentioned Bohmian mechanics, the Born rule was derived from the postulates a long time ago

It's not really derived, rather something equivalent to the Born rule is included as one of those postulates. At some point you have to go from wavefunction to probability distribution, and you either make the rule for that an outright postulate or have some plausible but unsatisfactory argument about how dynamical evolution makes this the "right" rule. Different interpretations do this at different points, but they all have to do it somewhere.

[naasking]

> The wavefunction is certainly physically meaningful in the sense that you can't predict experimental results without computing its behaviour (or something equivalent to it).

The wavefunction in Bohmian mechanics is just as interesting and unreal as the Hamiltonian in classical statistical mechanics. Which is to say that, sure, you still need something like it to calculate outcomes and what you observe will conform to it, but that doesn't make it real. The particles are real here, and they just follow a law of motion described by the wave function.

> given that elementary particles are not directly observable, couldn't we just declare that e.g. electrons are "not real" and merely describe a law of experimental results?

Sure, that's what ontology is all about: define what's real (base axioms), and derive what else we observe in terms of what you consider real. This needs to fit into a coherent total picture, and you want one that's general and parsimonious.

For MWI, the wavefunction is real and the grooves are real worlds that evolve in parallel, and the particles don't have any independent existence. In Bohmian mechanics, the particles are real and follow a law of motion described by the wave function, but the latter doesn't have any physical existence.

> It's not really derived, rather something equivalent to the Born rule is included as one of those postulates.

I don't think that's correct. To my knowledge, distributions conforming to the Born rule [1] are guaranteed in all but highly anomalous initial configurations, akin to how thermodynamics ensure that entropy always increases except again, in highly anomalous initial configurations. And even for the majority of anomalous distributions, evolution under the Bohmian dynamics is very likely to converge to the Born rule anyway [2].

Because this quantum equilibrium is a hypothesis and not a postulate, this leaves open the possibility that Bohmian mechanics can be experimentally differentiated from orthodox QM, but no one has figured out a way to actually create such distributions.

Anyway, this is all an interesting academic exercise and I don't think Bohmian mechanics is nearly as problematic as some physicists think, but it's unlikely to go anywhere given the little investment it receives.

[1] https://arxiv.org/abs/quant-ph/0308039

[2] https://arxiv.org/abs/1103.1589

[lmm]

> For MWI, the wavefunction is real and the grooves are real worlds that evolve in parallel, and the particles don't have any independent existence. In Bohmian mechanics, the particles are real and follow a law of motion described by the wave function, but the latter doesn't have any physical existence.

Obviously I'm coming at this from a partisan perspective, but that really does seem like more postulates - either you calculate your wavefunction evolution and predict your experimental results from that or you calculate that same wavefunction evolution, calculate your particle state ensemble from that, and then predict your experimental results from that.

> I don't think that's correct. To my knowledge, distributions conforming to the Born rule [1] are guaranteed in all but highly anomalous initial configurations, akin to how thermodynamics ensure that entropy always increases except again, in highly anomalous initial configurations.

I tried to skim through the 60 page paper but couldn't find the part you're claiming. Most modern presentations of Bohmian mechanics take the probability rule as a postulate. Bohm did initially present it with a statistical fluctuation and dynamical evolution argument, but most people find that unsatisfactory, and you can (and people do!) make the same argument in an Everett-style many worlds setting as well. (Admittedly people tend to find it even less convincing in a probability-branches setting than a particles-following-a-probability-distribution setting, but I suspect that's an artifact of similarity to classical thermodynamics rather than because it's objectively more plausible there).