lew@ihuxr.UUCP (06/06/83)
Bell's theorem is actually quite prosaic in itself. The only subtlety is in its application to QM phenomena. Bell's theorem is described in the Scientific American article, "Quantum Mechanics and Reality" by Bernard d'Espagnat ( I was involved in a net discussion of this about a year ago.) I think it was in the November '79 issue. Here is a description of Bell's theorem: Suppose you have a set of events, each of which can be described by three binary valued properties. This gives eight possible categorizations of each event. d'Espagnat represents this situation with a square divided into quarters with a smaller circle in the center. The three binary properties are (top,bottom), (left,right), (in,out). I find it easier to think of a cube divided into octants since the symmetry among the properties is more evident. Thinking of the cube then, any pair of edge cubelets forms a subset with the values of two of the three properties specified. There are three pairs of properties each with four possible values. A face of the cube is a subset with one property specified. Bell's theorem corresponds to a Soma cube piece, namely either of the twisty ones that go "over, up, [left or right]". This piece contains three overlapping edges. Bell's theorem says that the center edge is less than the sum of the two end edges. Each of the end edges overlaps the center edge and the end edges together comprise all four cubelets of the piece. The complement of the piece has the same (not the opposite) symmetry, so you'd need two of the same pieces to make the 2 by 2 cube. (I'm running on here to give a mental picture.) This makes for 24 versions of Bell's theorem which are symmetrically equivalent under relabelling of the properties and polarity reversals of the values. For example: N(A+,B+) <= N(B+,C-) + N(A+,C+) I think I'll post another article later about how this theorem shows QM to be inconsistent with local realistic theories. Lew Mammel, Jr. ihuxr!lew