Ensemble Interpretation

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The Ensemble Interpretation, or Statistical Interpretation of Quantum Mechanics, is an interpretation that can be viewed as a minimalist interpretation; it is a quantum mechanical interpretation that claims to make the fewest assumptions associated with the standard mathematical formalization. At its heart, it takes the statistical interpretation of Max Born to the fullest extent. The interpretation states that the wave function does not apply to an individual system – or for example, a single particle – but is an abstract mathematical, statistical quantity that only applies to an ensemble of similar prepared systems or particles. Probably the most notable supporter of such an interpretation was Albert Einstein:

“	The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems.	„
—Albert Einstein^[1]

To date, probably the most prominent advocate of the Ensemble Interpretation is Leslie E. Ballentine, Professor at Simon Fraser University, and writer of the graduate level text book "Quantum Mechanics, A Modern Development".

The ensemble interpretation, unlike other interpretations to the Copenhagen Interpretation, does not attempt to justify, or otherwise derive, or explain quantum mechanics from any deterministic process; it is simply a statement as to the manner of wave function interpretation. It is identical in all of its predictions as is the standard interpretations.

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

$| \psi \rangle = \frac {|1\rangle + |2\rangle + |3\rangle + |4\rangle + |5\rangle + |6\rangle} {\sqrt{6}}$

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 dice 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, in much the same way as classical statistical mechanics. It does not directly apply to a single experiment, only the statistical results of many. No single system is ever required to be postulated to exist in a physical mixed state so the state vector does not need to collapse. For example, it can be assumed that before the measurement, that the system was simply in the measured state, although this assumption is not strictly necessary. This notion is consistent with the standard interpretation in that, in the CI, statements about the exact system state prior to measurement can not be made. That is, if it were possible to absolutely, physically measure say, a particle in two positions at once, then QM would be falsified as QM explicitly postulates that the result of any measurement must be a single eigen value of a single eigen state.