IF BERTLMANN HAD THREE FEET

Abstract

It is argued that perfect quantum correlations cannot be due to additive conservation. Dr. Bertlmann likes to wear two socks of different colours. Which colour he will have on a given foot on a given day is quite unpredictable. But when you see that the first sock is pink you can already be sure that the second sock will not be pink. Observation of the first, and experience of Bertlmann, gives immediate information about the second. Bell (1981) Most interesting features of quantum mechanics have at least something to do with interference, which will not, however, be at issue here at all. Interference is brought out by an appeal to different bases, but here the same (product) basis is adhered to throughout. It is often claimed, and even more often suspected, that conservation accounts for quantum correlations (by which perfect quantum correlations will be meant). The underlying intuition is well expressed by Bertlmann’s socks, or by the fact that the distribution of wine over two glasses can be worked out, provided one knows the total amount in both, by a measurement on one of them. Or consider a conservative classical Hamiltonian where T is kinetic energy and the potential energy V depends only on position. Conservation here means that exchanges of kinetic and potential energy along a trajectory have to satisfy where is the total energy of that motion. Kinetic energy will then be a function only of position, so that at any stage of the motion can be deduced from the potential; they are perfectly correlated. Or take two free classical particles, each one subject only to the influence of the other, with initial momenta and Irrespective of whether they collide their total momentum will remain the momentum of the primed particle can always be derived from the momentum p of the other. These cases are paradigmatic for additive conservation. ( ), H T V q = +