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Department of Philosophy

Staff

Publication details for Prof Nancy Cartwright

Cartwright, N. & Jones, M. (1991). How to Hunt Quantum Causes. In Erkenntnis Orientated: A Centennial Volume for Rudolf Carnap and Hans Reichenbach. Spohn, W. Springer. 205-231.

Author(s) from Durham

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(a=±1/2&b=±1/2)=1/2sin2(θ/2)
P(a=±1/2&b=±1/2)=1/2sin2(θ/2)
P(a=±1/2&b=±1/2)=1/2−1/2sin2(θ/2)
P(a=±1/2&b=±1/2)=1/2−1/2sin2(θ/2)
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.