How to Hunt Quantum Causes

Abstract

In Bohm’s version of the Einstein-Podolsky-Rosen (E.P.R.) paradox, a source prepares paired spin-1/2 particles in the singlet state. This is a state in which the total spin must be zero. Yet, when a measurement is made along any given direction, each of the particles must yield a value of + 1/2 or — 1/2. Hence when measurements are made along the same direction on both members of a singlet pair, even though the two measurements can be carried out at quite distant places, the outcomes must be strictly anti-correlated. For measurements along two different directions, quantum mechanics also predicts a correlation, though it is not total:

$$P\left( {a = \pm 1/2\& b = \pm 1/2} \right) = 1/2{\sin ^2}\left( {\theta /2} \right)$$

$$P\left( {a = \pm 1/2\& b = \pm 1/2} \right) = 1/2 - 1/2{\sin ^2}\left( {\theta /2} \right)$$

where a represents outcomes of spin measurements on the left-hand particle along a given direction, b are outcomes on the right-hand particle along some possibly different direction, and θ is the angle between the two directions. The famous inequalities of J. S. Bell are commonly taken to rule out the one obvious account of these distant correlations — that they are due to the action of a common cause. The justification for this claim involves Reichenbach’s conjunctive fork condition.

We would like to thank Michael Redhead, Jeremy Buttrfield, and J. B. Kennedy for several conversations about robustness, and David Papineau for the use of his manuscript.