Humean Supervenience and Quantum Physics
When sometime between 1986 and 2001, Lewis accepted (a certain version of) standard quantum physics, did he thereby accept that Humean Supervenience is false? I'm not sure. My knowledge of quantum physics ("knowledge" in the sense of "probably false, unjustified guesses" rather than "true, justified beliefs") doesn't suffice to see through this with any confidence. Anyway, here's some thoughts.
Humean Supervenience is the hypothesis that in worlds like ours, all
truths supervene on the spatiotemporal distribution of fundamental
properties at spacetime points. This appears to contradict what quantum physics says about entangled states: if two electrons are suitably entangled, their combined state is a superposition of X-spin(electron 1)=up & X-spin(electron 2)=down and X-spin(electron 1)=down & X-spin(electron 2)=up (![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5Csqrt%7B1%2F2%7D%7C%5Cmbox%7BX-up%7D%5Crangle_1%7C%5Cmbox%7BX-down%7D%5Crangle_2+-+%5Csqrt%7B1%2F2%7D%7C%5Cmbox%7BX-down%7D%5Crangle_1%7C%5Cmbox%7BX-up%7D%5Crangle_2)
Bell's Theorem is not directly relevant here, I think. What it shows is that one gets into trouble if one assumes that standard quantum physics is fundamentally incomplete and that there really are local qualities ('hidden variables') underlying the entangled state. The trouble, if I understand it correctly, is that any possible distribution of these local qualities contradicts the empirically verified predictions of standard quantum physics about what local measurements will deliver. This is serious trouble, but it does not refute Humean Supervenience. There could, for instance, be a fundamental law of nature linking the local qualities to one another so that measuring one particle instantaneouly alters the other one. If all else fails, there is always the Cambridge solution: apply Prior's egocentric logic to translate all claims of standard quantum mechanics into claims about, say, the center of the universe, and state that the properties thereby attributed to that point are extrinsically specified intrinsic properties. No matter what the world looks like, all truths will then supervene upon the 'distribution' of local intrinsic qualities at the center of the universe.
All this is important if we ask whether the available empirical evidence rules out Humean Supervenience. (Answer: no, but squaring the evidence with Human Supervenience might result in an otherwise inacceptable theory.) But what I'm interested in is something else: can one accept that standard quantum physics gives a more or less complete and correct account of physical reality and still endorse Humean Supervenience? Here the answer appears to be more straightforwardly that one cannot.
In 1986, it seems that Lewis agreed, but he didn't have much confidence in quantum physics as an account of physical reality:
I am not ready to take lessons in ontology from quantum physics as it is now. First I must see how it looks when it is purified of instrumentalist frivolity and dares to say something not just about pointer readings but about the constitution of the world; and when it is purified of doublethinking deviant logic -- and, most of all, when it is purified of supernatural tales about the power of the observant mind to make things jump. If, after all that, it still teaches nonlocality, I shall submit willingly to the best of authority. (Introduction to Phil. Papers II, p.xi)
In 2001, when he wrote "How many lives has Schrödinger's cat?", he apparently accepted (though not wholeheartedly) the GRW interpretation of quantum mechanics, which is neither instrumentalist nor at odds with logic and does not assign any special role to the power of the observant mind: "it is a comfortable and plausible way for nature to work", Lewis says (p.10).
So did he came to accept by 2001 that Humean Supervenience is empirically false? As Ralf Busse pointed out to me yesterday, this isn't clear.
Apart from the measurement problem (to which GRW provides an answer), quantum physics also raises the question of what superposition actually means: what does it mean to say that a cat is in a superposition of dead and alive? This is not a question about the mathematical representation: vector addition is easy enough to understand. The question is what the representation represents about the external, unobserved world. Here is Lewis's answer, illustrated by benzene molecules in a superposition of two different chemical structures:
[...] each molecule is in a superposition: a state objectively indeterminate between the two structures. Objective indeterminacy is multiplicity: a cload of indeterminate extent, for instance, is really many clouds, almost but not quite identical to one another [...]. Likewise a molecule with an objectively indeterminate structure is really two coexisting molecules, one with one structure and one with the other. (Or at any rate, two things that are molecule-like except for from their coexistence with one another.) Picture the molecule as a double image, as if we drew the two structures on two transparencies and laid one over the other.
Some terminology. We call the resolutions of the indeterminacy -- the superimposed images -- branches of the superposition. And we call a state which is not a superposition [...] a sharp state. (4f.)
[...] When a superposition collapses, it is instantaneouly replaced by a sharp state corresponding to a single one of its branches. Instead of the multiple coexisting actualities of superposition, we end with one of several alternative possibilities. Which one is a matter of chance. (6f.)
So return to the entangled electrons mentioned above. On Lewis's interpretation, there are literally two colocated pairs of objects here: one where the first electron (or electron-like thingy) has X-up and the second one X-down, and another where the first has X-down and the second X-up. When a collapse occurs, one of these pairs disappears. (In fact, I suppose there are continuum many superimposed pairs, and a collapse doesn't reduce them to one but replaces them by still continuum many superimposed pairs with different local qualities.)
Doesn't this vindicate Humean Supervenience? It appears that the properties of the entangled system are after all determined by the local properties of the superimposed branches. (This is what Ralf Busse pointed out to me.)
One problem is that something must link together the parts of a branch: what distinguishes the up1-down2/down1-up2 system from an up1-up2/down1-down2 system? The local qualities appear to be distributed the same way in either case. It seems that we need a new fundamental relation here. Or perhaps we could say it is just another spatiotemporal relation: the branches are real spatiotemporal branches along a fifth dimension.
Another, somewhat related problem is that branches have a novel fundemental property: intensity. Where is that located? The only reasonable answer compatible with Humean Supervenience appears to be: at every spacetime point in the branch. Even that sounds rather ad hoc, though. We'd need a fundamental law of nature saying that the intensity distribution within a branch is always constant.
So for all I can tell, the interpretation of quantum physics Lewis endorses in "How many lives" does not strictly rule out Humean Supervenience, but it is also not easily reconciled with it. (Lame conclusion, I know.)
Dear Wo,
I enjoy your disucussions particularly of Lewis.
Here are a few comments concerning your remarks about HS and QM.
From your remarks one could get the impression (it is unfortunately a widespread impression) that Bell showed that the price of adding local ?hidden variables? to QM is non-locality. That is not quite right since as Einstein much earlier argued and as Bell reiterates QM is already non-local. Bell?s argument shows that adding hidden variables doesn?t avoid non-locality (as Einstein may have thought it would) and more generally that any scientific account of the empirically obtained result must be non-local.
You are right that there could be a fundamental law linking the local qualities so that measuring one particle instantaneously alters the other. But the law would have to specify which particles are "entagled" it is not easy to see how that can be done without violating HS since which particles are "entangled" is not dependent on a spatial/temporal relations that the particles bear to each other (they may be light years apart). In QM entanglements are specified by the wave function. If HS is taken to mean that the fundamental ontology of the world consists of local qualities instantiated at points of 3-space then any theory that is realist about the wave function violates HS since the wave function is not in 3-space but in a high dimensional space (configuration space). If HS allows configuration space to be the fundamental space then the values of the wave function in config space can be construed as instantiated at points. A different approach would be to adopt Bohm?s account and say that the ontology consists of particles (instantiated at points) and construe the wave function as a fundamental law specifying how the particles move. There problems about this idea but the relevant one here is that such a law will need to be a primitive and so it doesn?t supervene on the distribution of particle positions. So HS is violated.
**As to whether GRW violates HS. There are basically three ways of understanding GRW 1) the wave function is the entire ontology and particle talk etc. supervenes on the wave function; 2) there is a mass distribution and the wave function characterizes how it evolves 3) the wave function is the entire ontology and particle talk supervenes on the collapses. 1 is the way David Albert and I understand GRW, 2 is Ghirardi?s way and 3 is a suggestion of Bell?s. All of these end up violating HS basically because they take the wave function seriously as part of the ontology or as a primitive law.
I think the right thing to say is that quantum mechanics is incompatible with the part of HS that says that space is 3-d and that the only fundamental relations are spatial temporal relations. But one can give this up and still hold onto Lewis? accounts of laws, chance, counterfactuals etc. (although they all need a bit of fixing up but that is another matter).