This Quantum World

Contextuality

Discussion, first conclusions, interpretational strategy

Try to fill in the following table in such a way that each cell contains either a +1 or a –1, that the product of the three X components equals –1, and that the product of every pair of Y components equals the remaining X component.

	A	B	C
X
Y

You will of course find that it can't be done. Suppose you get to this point:

	A	B	C
X	+1	+1	–1
Y	–1	+1	?

X_A = Y_B Y_C requires Y_C to be +1, whereas X_B = Y_A Y_C requires Y_C to be –1.

Now remember the experiment of Greenberger, Horne, and Zeilinger. The possible measurement outcomes are +1 and –1. Whereas the product of the three x components always comes out equal to –1, the product of the y components of two spins always comes out equal to the x component of the third spin. You have no choice but to conclude that these spin components are in possession of values only if and when they are measured.

Or is it? Well, if for some strange reason you insist that these spin components have either of their possible values (+1 or –1) even if they are not measured, then you have to accept that their values are contextual.

This is a strange concept. (But then what isn't strange in the quantum world?) It means

that the values of these spin components exist not as individuals but as groups,
that the same spin component belongs to more than one group,
and that the value possessed by one and the same spin component can differ from one group to another.

In this particular instance the group X_A, Y_B, Y_C has the respective values 1, 1, 1, whereas the group Y_A, X_B, Y_C has the respective values –1, 1, –1.

If this notion gives you a headache, join the club. The alternative conclusion — that to be is to be measured — is perhaps no less strange, but it takes us somewhere, as we will see, whereas contextuality is just a dead end.

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