The distinction between epistemic vs ontic (also known as aleatoric in other contexts) uncertainty is critical for understanding the difference between the standard interpretations of QM (e.g., the Copenhagen interpretation and Hilbert space approach) and the pilot-wave approach.
Epistemic uncertainty reflects our own lack of knowledge about the true underlying state of the system, but, critically, excludes any actual “true randomness” arising from the stochastic behavior of the system itself, that would obtain even if we had (counterfactually) perfect knowledge of the underlying state of the system. This latter type of uncertainty is the ontic (“ontologically real”) or aleatoric (derived from the latin word for dice) variety.
If the quantum wave function is largely (or even partially) reflecting epistemic uncertainty, then it seriously challenges the pilot-wave framework in a way that does not affect the purely probabilistic Copenhagen approach. How would it make any sense for an epistemic wave of uncertainty to be guiding the real physical positions of particles as they move about the world?
By contrast, the Copenhagen interpretation already takes a laissez-faire epistemic-level approach to the wave function in the first place: it is all just a big untouchable ball of mystery until you do a measurement anyway, so it might as well be epistemic or whatever! The Quantum Bayesianism (QBism) approach takes this to its logical extreme, with an entirely subjective epistemic treatment of the wave function (Fuchs et al., 2014; Mermin, 2018).
Fortunately, Pusey et al., 2012 have shown that a purely epistemic account contradicts quantum theory, so there is good reason to believe in the central premise of wave reality (see also the double-slit experiment).
Nevertheless, there is clear evidence from within the pilot-wave approach itself that a not-insignificant portion of the pilot-wave actually does represent epistemic uncertainty, because many different possible initial starting states must be modeled to capture our very real uncertainty about the precise starting state of any actual experimental configuration.
The Heisenberg uncertainty principle dictates that there is a fundamental limit to which we can simultaneously determine all of the relevant degrees of freedom about a physical system, and in practice we almost certainly have well less certainty than this lower limit, because it is very difficult to make any kind of precise measurement of microscopic quantum-scale systems.
The incorrect incorporation of epistemic uncertainty in the standard Schrodinger pilot-wave framework is also evident in the inevitable spreading out of the wave function over time. In the epistemic case, this spread represents a very sensible increase in uncertainty about where something might be located, given more time since the last time its position was known. But given that the pilot-wave model maintains exact locations of each particle over time, it really doesn’t seem to make sense for the wave function to spread out in this manner, at least for variables associated with particle positions.
In summary, this quote from E. T. Jaynes (Jaynes, 1990) particularly apropos here:
“But our present QM formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature — all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that the unscrambling is a prerequisite for any further advance in basic physical theory. For, if we cannot separate the subjective and objective aspects of the formalism, we cannot know what we are talking about; it is just that simple.”
From this perspective, one could make the following reasonable claim about the pilot-wave approach: it provides a very powerful demonstration in principle that QM is compatible with a “realistic” underlying world where particles always have definite positions. Nevertheless the specific formulation in terms of the Schrodinger wave function operating in configuration space is very likely conflating epistemic and ontic uncertainty, and a more realistic wave function that only reflects whatever “real” aspect of the wave function remains after the epistemic part is subtracted away should be used instead.
A recent paper has attempted to disentangle the epistemic vs. ontic contributions to the wave function using a novel analytical technique, and concluded that different quantum behavior can be associated with each of these contributions (Budiyono & Rohrlich, 2017). However, their approach assumes that the uncertainty principle is purely epistemic, which is inconsistent with its fundamental basis in the basic properties of waves. As usual, any analysis is only as good as its assumptions. As a consequence, they reject the pilot-wave approach because of its “incorrect” use of a purely epistemic uncertainty wave (under their assumptions) to guide real particle trajectories.