I recommend that you read the first part of this series first.
The ensemble interpretation goes back to Albert Einstein, who assumed that W does not describe an individual system, but instead an ensemble of equivalent systems or experiments. (Notice that Chad Orzel emphasizes that we need to use many photons to see an interference effect in the Mach-Zehnder interferometer.)
This resolves the mismatch between W and R, without assuming that anything is wrong with either W or R (*).
It seems to me that this minimalist interpretation is actually quite popular with many physicists and especially experimentalists.
Further, I think it is the philosophical basis of the "shut up and calculate" approach and suspect that some physicists use it who are otherwise convinced that Einstein never understood quantum theory.
In stark contrast, the Copenhagen interpretation assumes that W very well describes individual quantum systems, but emphasizes that we necessarily have to use classical concepts to describe the outcome of experiments. Therefore, one needs to change the 'description' during a measurement and the wave function
'collapses' at some point; Nowadays one could refer to decoherence to better determine that point.
In this interview Werner Heisenberg emphasized that W does not describe (fundamental) reality itself...
"That is just the point; I do not know what the words fundamental reality mean.
They are taken from our daily life situation where they have a good meaning,
but when we use such terms we are usually extrapolating from our daily lives
into an area very remote from it, where we cannot expect the words to have a meaning.
This is perhaps one of the fundamental difficulties of philosophy: that our thinking hangs in the language."
... instead he assumed that W does describe what he called 'potentiality'.
'What does a wave function actually describe?' In old physics, the mathematical scheme
described a system as it was, there in space and time.
One could call this an objective description of the system.
But in quantum theory the wave function cannot be called a description of an objective system,
but rather a description of observational situations.
The explanations of Niels Bohr were usually even more profound, with complementarity playing
a prominent role in his philosophy; But it seems that they were indeed so profound that nobody actually read them (x).
Let me finally mention some results which emphasize that
the problem to understand the measurement process results from the impossibility of self-measurement.
The observer of an experiment can therefore not use W to describe herself and her own experience.
In my opinion one could either use these results as further argument in support of the 'collapse' of the
Copenhagen interpretation or as the starting point for a new 'relational interpretation'.
(*) Notice that in many cases a Wick rotation translates between quantum and statistical mechanics.
(x) "In a widely used compendium of papers on quantum theory [...], the pages of Bohr's reprinted article are out of order.
This paper (Bohr's response to the famous 1935 Einstein-Podolsky-Rosen critique of the standard Copenhagen interpretation)
is widely cited in contemporary literature by physicists and philosophers of science.
Yet I have never heard anybody complain that something is wrong with Bohr's text in this volume."
Mara Beller about the philosophical pronouncements of Bohr, Born, Heisenberg and Pauli.
continue to part 4.