Phenomenally accessible hidden variables

Consider Jeffrey Barrett's traveling minds interpretation of Quantum Mechanics (see also here). On this interpretation, minds traverse a branching Everett-style multiverse in accordance with the probabilities given by the Born rule. But unlike on the Albert-Loewer many-minds interpretation, the minds are constrained to travel together: they are always found in the same branch of the universe.

Here is something interesting about the position in logical space of this interpretation. It is a hidden-variables interpretation in the sense that it supposes that there are realities that cannot be reduced to the wavefunction. The hidden variables on this story correspond to facts about brain states. For instance, the wavefunction may place my brain in a superposition of a brain state in which I feel I am sitting with a state in which I feel I am standing, but the minds (jointly) pick out a branch of the wavefunction--the one in which I feel I am sitting (and writing a post on quantum mechanics). Notice, however, that the hidden variables in this story are hidden from the wavefunction but not hidden from us: they are phenomenally accessible to us.

Interestingly, the Bohm interpretation can be seen also to be a hidden-variables interpretation where the variables are not entirely hidden from us. For presumably it is the "hidden" positions of the particles that determine the brain state that gives rise to my phenomenal state. So from my phenomenal state, I can tell something about the hidden variables--for instance, that they comprise a brain. Bohm is a paradigmatic hidden variable interpretation, and yet it does not actually hide the variables from us. So we need to be cautious about the phrase "hidden variables".

I think the Albert-Loewer many-minds interpretation is also a hidden variable theory. The variables are the states of the many minds. But there is a difference between the Barrett and Albert-Lower interpretations, on the one hand, and the Bohm interpretation, on the other. In the Bohm interpretation, the hidden variables are a part of physical reality. On the mind-based interpretations, the hidden variables are a part of mental reality. In all cases, we have at least partial access to the hidden variables.

Two motivations for Bohmian quantum mechanics

There are two different motivations for the Bohm interpretation of quantum mechanics. One comes from a philosophical affinity for determinism. The other comes from the desire to have the Schroedinger equation, with all its mathematical elegance, hold without the exceptions that collapse leads to, while avoiding the multiverse excesses of Everettian quantum mechanics.

Now, deterministic hidden variable theories like Bohm's match up with the stochastic predictions of indeterministic quantum mechanics by supposing that the initial state is chosen according to a "special" probability distribution. But there are serious philosophical problems with justifying the assumption of that special probability distribution.

Interestingly, if all one is after is avoiding the Scylla of collapse and the Charybdis of an Everettian multiverse, one can find indeterministic hidden variable theories that avoid the initial distribution problem that deterministic hidden variable theories suffer from. A dualist example is what I call the "Traveling Minds" interpretation. But one should also be able to cook up physicalist hidden-variable theories that mimic something like the dynamics of the Traveling Minds interpretation.

It may seem silly to have indeterministic hidden variable theories, given the history of positing hidden variables in order to regain determinism. But I see no good reason to try to regain determinism, while I do see good reason to try to keep unitarity, i.e., to avoid collapse. And there is good reason to avoid the Everett multiverse, because of the serious probabilistic problems facing it. And so there is actually good reason to consider indeterministic theories. (I understand that there already is a Bohmian field theory with stochastic particle creation/destruction.)