Some difficulties for Clifton, Redhead, and Butterfield's recent proof of nonlocality

Robert K. Clifton, Michael L. G. Redhead, Jeremy Butterfield

G. C. Ghirardi

Jean Paul VAN BENDEGEM

Henry Pierce Stapp

Clifton, Butterfield, and Redhead [1989] have constructed two separate arguments that bear some resemblances to a proof of mine pertaining to the nonlocal character of quantum theory. Their arguments have flaws, which they point out. I explicate my proof by explaining in detail both how it differs logically from the two arguments they have constructed, and how it avoids the pitfalls of both.

Robert K. Clifton, Jeremy Butterfield, Michael L. G. Redhead

Stapp ([1971], [1977], [1985a], henceforth Stapp 1) claims to give a proof of the existence of nonlocal influences acting on correlated spin-1/2 particles in the singlet state which does not require any particular interpretation of quantum mechanics (QM). (Except Stapp holds that the proof fails under a many-worlds interpretation of QM—a claim we analyse in 1.2.) Recently, in responding to Redhead's ([1987], pp. 90-6) criticism that the Stapp 1 proof fails under an indeterministic interpretation of QM, Stapp [1989] (henceforth Stapp 2), has revised the logical structure of his proof including its crucial locality assumption. Our main aim is to show that this revision is a step in the wrong direction because it faces two difficulties which undermine the resulting proof's significance (3.1) and validity (3. 2). We also clarify and extend the Stapp 1 proof (1. 1) with the aid of Lewis' analysis of counterfactuals (1. 2) and causal dependence (2. 2 and 2. 3). In so doing, we are able to identify two new defects in the Stapp 1 proof (1. 3 and 2. 1) in addition to corroborating Redhead's criticism (2. 2). Also, the additional assumptions which save the Stapp 1 proof's validity are detailed (2. 3) and some new difficulties for the determinist are pointed out by exploiting a slightly extended version of the proof (2. 4). In providing this full analysis of the Stapp 1 proof, we also construct the necessary framework within which to provide a critique of Stapp 2's proof (3).

Nick Huggett

The principle of the identity of indiscernibles (PII) states that if two systems are qualitatively identical then they are logically identical. French and Redhead (1988) and Butterfield (1993) have shown the sense in which bosons and fermions violate the PII, but did not investigate the issue for particles of other kinds of statistics: i.e., for the (p,q) particles -- or `quarticles' -- of Hartle, Stolt and Taylor (1970). This paper shows that for any type of indistinguishable quarticle the PII is violated but that for distinguishable quarticles there are states in which it is violated by any pair of particles, states in which it is violated only by some pairs of particles and states in which it is violated by no pairs of particles. The updated version corrects a minor statement of mathematical fact, and provides a short proof for a conjecture made in the original.