Untenability of simple ensemble interpretations of quantum measurement probabilities
Abstract
Some interpretations of quantum mechanics try to describe the probabilistic nature of quantum measurements in a way that allows a system in a pure state to always have precise (if not simultaneously knowable) values for all its observable variables. In what might be called a simple ensemble interpretation, the quantum mechanical state vector is assumed to define a statistical ensemble of identically prepared systems, each of which has precise values for all its observable variables, and the act of measurement is equivalenced to a straightforward sampling of that ensemble. It is shown here, in a manner that should be suitable for a first course in quantum mechanics, that a simple ensemble interpretation is not possible for some quantum systems, and hence is untenable as a general premise. The analysis is essentially a repackaging of the Bell argument against hidden variables, although hidden variables are never invoked here.
 Publication:

American Journal of Physics
 Pub Date:
 October 1986
 DOI:
 10.1119/1.14784
 Bibcode:
 1986AmJPh..54..889G
 Keywords:

 03.65.Bz