Einstein-Podolsky-Rosen Reasoning in Nonlocality Theorems

Abstract

Bell’s 1964 [1] argument that quantum theory is nonlocal consisted of three parts: (i) use of Einstein-Podolsky-Rosen (EPR) type reasoning to demonstrate that results of spin measurements on a singlet state must be predetermined if locality is assumed; (ii) derivation of a set of inequalities using the assumption of locality and the fact that the results of spin measurements are predetermined; and (iii) demonstration that the inequalities are violated by the predictions of quantum mechanics. In the Greenberger, Horne, Zeilinger (GHZ) argument [2] the structure is similar except that no inequalities are derived (in a sense parts (ii) and (iii) are rolled into one). The first part (i) in the GHZ argument is based on almost exactly the same reasoning as in Bell’s case. In another demonstration of nonlocality due to the present author [3], the corresponding part of the argument to (i) is a little more subtle. That the situation is different was pointed out to me by various people [4, 5, 6]. The purpose of this chapter is to clarify how the EPR type reasoning works in this case. Some of the ideas here were first presented in [7] (a reply to [6]). Also, a recent debate between Stapp [8] and Dickson and Clifton [9] covers some of the same ground as in this chapter, for the same nonlocality theorem, though at a deeper level. In particular, Dickson and Clifton emphasize the need for the outcome independence part of the locality assumption as will be emphasized below.