Bohmian Mechanics, also referred to as De Broglie-Bohm theory or pilot wave theory is often presented as a completely deterministic theory that matches all of the predictions of quantum theory. Strictly speaking this is true – all of the state variables of a Bohmian model evolve in a precise way specified by equations associated with the theory. No one doubts the validity of non-relativistic pilot wave theory, and while no universally accepted relativistic version yet exists there is good reason to believe one is feasible (see my references here, in particular the thesis by Boers).
However, simply embracing Bohmian methods and declaring the universe deterministic isn’t the safe haven many think it is. Bohm theory does indeed match all of the predictions of standard quantum theory (and therefore matches decades of experimental results) including the stochastic nature of those predictions. Yes, Bohm theory declares that in addition to the wave function (regarded by standard theory as the full and complete specification of state), systems also possess a configuration (e.g., a set of particle positions) that evolves deterministically. But Bohm theory also assumes the configuration starts out with (and always retains) a random value, and rigorous analysis shows that we can never have knowledge of the configuration beyond that statistical description. So Bohm theory says that the configuration exists and has a precise value at all times, but we don’t get to know that value. For all practical purposes the uncertainty is still there, just like in all other quantum theories.
Furthermore, it turns out that Bohm theory makes no declaration about the nature of the configuration. A popular approach is to define the configuration as consisting of a set of classical, point-like particles, with positions that then change over time as specified by one of the theory’s equations. But this is not necessary – a perfectly valid Bohm theory can treat the configuration as a set of fields (this approach is often used in attempts to develop a relativistic Bohm theory). Bohm theory 1) denies us “greater than statistical knowledge” of the configuration, and 2) makes no statement whatsoever about the ontology of the configuration.
In other words, Bohm theory declares the existence of something (a deterministic configuration) while also declaring that said existence can never be confirmed. This is normally considered a weakness in a scientific theory, and that is the case here. Note that the theory doesn’t say that the existence of a deterministic configuration can’t be verified with current technology. It says that it can never be, in principle. No technology that we ever develop will allow us to measure the configuration more precisely than allowed by the Heisenberg Uncertainty Principle.
Really this is just restating the fact that Bohmian Mechanics matches all of the predictions of standard quantum theory. If it does, it must be subject to the same limitations. The theory’s determinism brings no tangible advantage when it comes to making scientific predictions. The configuration (or an ensemble of such configurations bearing the right statistical qualities) can be used as an intermediate value in calculations, but no precise details of it affect the final answer that corresponds to something we can actually observe.
So, if the determinism or non-determinism of quantum reality doesn’t affect what we can measure, do we need to care which camp wins the philosophy debate? I think we do. Standard quantum theory claims that uncertainty is real – that a precise, well-determined state simply does not exist, and that the quantities we measure don’t exist until we measure them. Bohmians, on the other hand, contend that precision does exist, at all times, and that uncertainty is just the uncertainty of our knowledge. This matters tremendously when one starts to consider the nature of consciousness.
I happen to believe that consciousness is real (and, actually, fundamental – see Hoffman’s theory of conscious realism) and that conscious entities have free will. A deterministic universe denies free will, fundamentally. If uncertainty is real, it offers a mechanism through which free will can act: conscious entities could, in an unknown way, “direct” quantum systems to specific outcomes, chosen from the suite of outcomes allowed by the theory. But if uncertainty is just a matter of our knowledge – if the configuration itself is fully determined by the equations of the theory – there is no such opportunity.
The nature of consciousness and mind is a subject of great controversy in contemporary physics (and other fields as well). Arguments can become heated indeed. To me that just means that the question is unanswered. I have prejudices on this front, but I have no reason to claim my own prejudices are better than someone else’s. What I can claim, though (and do) is that while debate still rages, we should avoid selecting a quantum interpretation that “settles” the question when there is and can never be experimental evidence directing us to do so.