Friday, March 13, 2015

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.)

8 comments:

Austin said...

I don't mind that the Copenhagen Interpretation is indeterministic; I just find it incoherent. And it's so strange how that same scientists who preach objectivity in their field have so easily accepted a subjectivist interpretation of the most successful physics theory yet.

As far as Everett's MWI, I find it metaphysically ad hoc, in addition to other issues.

Did you see this article about the de Broglie-Bohm theory?

http://www.wired.com/2014/06/the-new-quantum-reality/

Pretty interesting stuff. I don't think the experiment constitutes evidence in favor of the theory per se, but do think it provides good reason for researchers to try and find ways to test the theory.

Alexander R Pruss said...

I don't know about the historical Copenhagen interpretation, but there is nothing I can see incoherent in the von Neumann consciousness-causes-collapse interpretation. It might even be true. :-)

MWI isn't metaphysically ad hoc. We have good reason to think that the wavefunction (or something field-like that grounds it) is at least a part of physical reality. Simplicity then favors the theory that it's the whole of physical reality, and so a theory on which it's the whole of physical reality isn't ad hoc. But, nonetheless, it's false because of the problem of making sense of probabilities in the MWI setting.

Alexander R Pruss said...

Looks like there is a whole family of indeterministic Bohm-style theories. See section 6 here.

Austin said...

Does von Neumann's formulation bypass the incoherence of Schrodinger's Cat? It's one thing to have a superposition of the states of a fundamental particle, and another thing entirely to have a superposition of different states of a living being like a cat. If something like Eliminative Materialism or even Reductionism was true, then I might be able to accept that there is no problem (even then it would be hard), but if the actual cat in any straightforward non-reductive sense does exist, then the whole thing is bunk in my opinion. And since I lean towards Thomistic metaphysics, that's just where I stand.

As for MWI, it seems like the question is whether positing a single additional feature to the existing universe (one which can account for a non-local variable), or positing a potentially infinite number of additional universes is more metaphysically parsimonious.

Wouldn't (at least some of) your criticisms of Extreme Modal Realism in your defense of the PSR also apply to a MWI of QM?

Austin said...

Thanks for linking the paper, it looks interesting. I'll try to get through it when I have some time.

Alexander R Pruss said...

If the cat was awake, then it should collapse the wavefunction. (There is a tricky bit. A dead cat isn't conscious. But to handle cases where an observer is asleep and only wakes up if a measurement comes out a certain way, we have to count cases where one isn't conscious, but would have been conscious had things gone differently, as something like a blank observation.)

If the cat was asleep, then presumably not (as long as the death is painless). If presentism is true, this induces an objective indeterminacy whether the cat exists or not, while I do not think indeterminacy as to existence is possible. But that may just be a reason to reject presentism.

Given eternalism, we get objective indeterminacy as to which 4D region of spacetime is occupied by the cat. That indeterminacy doesn't bother me much.

We get a more serious problem, I think, if we consider the following version of Schrodinger's cat. The radioactive decay detector is tied to a machine that will join the sperm and egg of two cats if a decay is detected, all inside a sealed room empty of consciousness. Then in ten minutes everything in the room is destroyed unobserved.

Then whether presentism or eternalism is true, we seem to have an indeterminacy as to whether a new cat exists at all. (And you can do the experiment with a human, but it would be immoral.) That's a serious problem.

Michael Gonzalez said...

Or we could just go with Albert's "Many Minds" interpretation, and say that the wave function never collapses, and everything stays superposed, but we just experience some of the realities.

Personally, I think that any of the theories of quantum mechanics which even MENTION conscious observation are silly, since most of the world isn't being consciously observed. And even in the few cases where observations are happening, the thing that is doing the observing is itself composed of quantum particles, and so it makes no sense for the particular configuration of those particles to make a difference to the wave function.

I'm with Austin on this one, in thinking that it is much more parsimonious to add particle location (which isn't really an "addition", when you consider that we have ALWAYS taken it for granted up until now) to the ontology of QM and then the only big problem you're left with is the superluminal influences required to violate Bell's inequality. But then, I don't think of that as a big problem, because I think that a Neo-Lorentzian view of Relativity is almost certainly superior to an Einsteinean or Minkowskian view, and so superluminal velocities aren't a problem for me....

I would disagree with Pruss that recovering determinism is a primary motivation for Bohmians. As has been mentioned, there are indeterministic versions of Bohmian mechanics. I think Bell got the motivation right: You have to specify your local and non-local "beables" (the units of your ontology). The Copenhagen interpretation (in addition to being silly because of being predicated on an "observer"-style configuration of particles being in the vicinity) fails to do this. There are no local beables specified in the theory. Much worse in the MWI. At least GRW tries to do this, though I'd say that the most promising version of that is the so-called "flashy" GRW, and its ontological commitment is (in my opinion) even less palatable than MWI's.

Alexander R Pruss said...

We could go with Many Minds, but I suspect we're going to have probability problems, given that just about every possible situation is inhabited by infinitely many minds, and it's hard to say that some situations are more likely than others. (This is quick, but I think can be substantiated.)

It's not just particle location that we need to add to the fundamental ontology to get Bohm. We need to add the *particles* themselves. On Everett, our fundamental ontology is *just* the wavefunction. Either there are really no particles or the particles exist non-fundamentally. The Everett ontology is very attractive in terms of simplicity.

As for the observers being made of quantum particles, I deny that observers are entirely made of quantum particles. Every observer has a soul, or is a pure spirit.