A tweak to Bohmianism

I think there is a sense in which it is correct to say that:

1. Bohmian quantum mechanics is only known to work empirically if we suppose that the initial configuration of the particles is fine-tuned.

Yet there are famous results that show that:

2. For typical initial configurations, Bohmian quantum mechanics yields standard quantum Born rule predictions, which we know to work empirically.

It seems that (1) and (2) contradict each other. But that is not so. For the typicality in (2) is measured using a typicality measure P^ψ defined in terms of the initial wavefunction ψ of the universe (specifically, I believe, P^ψ(A) = ∫_A|ψ(q)|²dq for an event A). And a configuration typical relative to P^ψ₁ need not be typical relative to P^ψ₂. In fact, if ψ₁ and ψ₂ are significantly different, then a P^ψ₁-typical configuration will be P^ψ₂-atypical.

The fine-tuning I am thinking of in (1) is thus that the initial configuration of particles needs to be fitted to the initial wavefunction ψ: a configuration typical for one wavefunction is not typical for another.

I think there is an interesting solution to the Bohmian fine-tuning which I haven’t heard discussed, either because it’s crazy or because maybe nobody else worries about this fine-tuning or maybe just because I don’t talk to philosophers of quantum mechanics enough. Suppose that the wavefunction of the universe (or, more precisely, the aspect of physical reality that is representated by the mathematics of the wavefunction) has a special causal power in the first moment of its existence, and only then: an indeterministic power to produce a particle configuration, with the power’s stochastic propensities being modeled by P^ψ.

This adds a little bit of metaphysical complexity to the Bohmian story, but I think significantly increases the explanatory power in two ways: first, by giving us a proper stochastic ground for the statistic probabilities and, second, by unifying the cause of the initial particle configuration and the cause of the dynamics (admittedly at the expense of a complexity in that in that cause there is a causal power that goes away or becomes irrelevant).

(Maybe this is not necessary. Maybe there are, or can be, some typicality results that don’t require fine-tuning to the initial wavefunction. Or maybe I just misunderstand the framework of the typicality results. I don’t know much about Bohmianism.)