Phi 272 F06, reading guide

Mermin and Redhead both address an aspect of quantum theory that is often labeled “nonlocality.” The issue is roughly as follows: quantum theory predicts certain correlations between spatially separated events that are each undetermined. It was argued (by Einstein among others) that this indicated a gap in the theory and that it should be supplemented with some sort of “hidden variables” that were responsible for the correlation. It was shown that adding such hidden variables would have implications for the specific correlations that were predicted in some cases (these implications of the use of hidden variables are known as “Bell inequalities”). Standard quantum theory predicts somewhat different correlations in these cases (i.e., it violates the Bell inequalities), and its predictions were confirmed by experiments.

Mermin and Redhead tell this story with different emphases. Mermin, who I suggest you read first, focuses on the kind of phenomena in question, and his argument is closer to the sort of argument originally offered by Bell. Redhead describes an analogous but different situation that is modeled after a sort that was actually subjected to test, and he has more to say about the issues raised by these phenomena.

• Mermin published his paper around the time that a particularly notable set of confirming experiments were performed, and he describes himself as a physicist presenting an issue for philosophers to reflect on. (At about the same time, he published a similar piece designed for a general physics audience.) Although he avoids a philosophical discussion of his own, he says things that suggest the direction he thinks one might take, and you should watch for these comments.

• The middle portion of Redhead’s talk (pp. 431-437) is also devoted to explaining the sort of phenomena in question with the bulk of his philosophical discussion appearing the last few pages of the talk.

It would be OK simply to substitute Mermin’s example for the one Redhead describes and imagine that he is speaking of that example in his discussion at the end of the paper (pp. 437-441)—I’ve asked you to read Mermin mainly to give you that option—but I’ll offer a few suggestions that may help in following Redhead’s example and comparing it to Mermin’s.

• First note that Mermin and Redhead use colors and numbers in more or less opposite ways. The property-labeling colors in Redhead correspond more or less to the numbered device settings in Mermin (since different settings measure different properties) and the +1 and -1 measurements in Redhead correspond to the red and green lights that flash on Mermin’s device.

• It may not be clear from Redhead’s presentation, but the argument for the inequalities (2) and (3) is algebraic. It’s not very obvious algebra, however, and his imagined experiment and the table on p. 435 are designed to suggest what’s going on (i.e., that a couple of the terms always end up canceling each other).

• It also might not be clear where the Heisenberg uncertainty principle, which Redhead mentions on p. 436, comes into this. It figures into the prediction made by quantum theory. That is, if the properties represented by two sides of a disc were a pair that could have determinate values simultaneously, the prediction made by quantum theory would be different.

• Finally, Redhead doesn’t sketch the actual physical set up in the way Mermin does at the end, but it’s not far different from the one Mermin describes. As in Mermin’s case, the experiment measures the direction of particle spin using magnets with different orientations. The two magnets available for each particle are perpendicular to each other, but they are not oriented in the same way as the pair for the other particle (which is why Redhead has four colors). (The specific prediction by quantum theory that Redhead notes is associated with a 45° difference between the orientations.)

Most of Redhead’s philosophical discussion is devoted to finding ways of describing the sort of reality this sort of correlation points to. Part of this is his effort to show that it is not the sort of “action-at-a-distance” that would come into conflict with the special role assigned to the speed of light in relativity theory. But part of this is a simple effort to find vocabulary and metaphors that capture the special features of this phenomenon. Which of his suggestions seem to work best?

Nonlocality can be seen to challenge common views about explanation and causality in ways that go beyond the challenges posed by simple indeterminism. (It has implications for those, too, because one motivation for hidden variable theories was to work around the indeterminism of standard quantum theory.) In particular, even people who embrace statistical explanations may be committed to what has been called the “common cause principle.” This holds that any correlation between events neither of which could be a cause of the other must be explained by a correlation of each with some third event. Now the lack of such a common cause in standard quantum theory for correlations between spatially separated measurements can be seen as one motivation for hidden variable theories. And experimental confirmation of violations of Bell inequalities might then be seen as indications that the common cause principle cannot be applied. If this analysis is right, what you do you make of the situation? Is the common cause principle too much to ask of statistical explanations? Or have we found aspects of nature that cannot be explained—even statistically—and where we must be content with description?