Ensemble Interpretation - Measurement and Collapse

Measurement and Collapse

The attraction of the ensemble interpretation is that it immediately dispenses with the metaphysical issues associated with reduction of the state vector, Schrödinger cat states, and other issues related to the concepts of multiple simultaneous states. As the ensemble interpretation postulates that the wave function only applies to an ensemble of systems, there is no requirement for any single system to exist in more than one state at a time, hence, the wave function is never physically required to be "reduced". This can be illustrated by an example:

Consider a classical die. If this is expressed in Dirac notation, the "state" of the die can be represented by a "wave" function describing the probability of an outcome given by:

It is clear that on each throw, only one of the states will be observed, but it is also clear that there is no requirement for any notion of collapse of the wave function/reduction of the state vector, or for the die to physically exist in the summed state. In the ensemble interpretation, wave function collapse would make as much sense as saying that the number of children a couple produced, collapsed to 3 from its average value of 2.4.

The state function is not taken to be physically real, or be a literal summation of states. The wave function, is taken to be an abstract statistical function, only applicable to the statistics of repeated preparation procedures, similar to classical statistical mechanics. It does not directly apply to a single experiment, only the statistical results of many.