I recommend that you read the first part of this series first.
"If the facts don't fit the theory, change the facts." Albert Einstein
If you assume that nothing is wrong with the wave function W and you dislike
the interpretations of the previous part 3, then you have to conclude that
something is wrong with (your perception of) the reality R.
So, one way out of the interpretation problem, as posed in the first part of this series, is to simply assume that actually both detectors clicked; You are just somehow confused about it.
The many-worlds interpretation and its variants (consistent histories, many minds, etc.) are increasingly popular and solve the interpretation problem by pointing out that the wave function W = |1> + |2> continues to evolve into |1>|D1> + |2>|D2> and finally |1>|D1>|Y1> + |2>|D2>|Y2> , where Y1 indicates you, puzzled why click 1 has been observed but not click 2.
But, as I have argued previously, the full meaning of a many-worlds interpretation can only
be appreciated if one goes 'backwards in time', trying to find the origin of W (which
cannot evolve from a 'collapsed' wave function). In the words of Matthew J. Donald:
"Each time we pass back (through the appearance of a collapse) we get a better approximation to W.
Eventually, we arrive back at the big bang. ...
The quantum state of the universe coming out of the big bang looks - at least in its non-gravitational
aspects - very like a thermal equilibrium state. In the Hamiltonian time propagation of that state,
the stars and planets which we see now do not exist as definite objects, and certainly neither does any particular
measuring device now being used by us on one of those planets. W seems to be a complete mess.
However, it does have a great deal of hidden structure, and it is the job of a no collapse interpretation to explain
how that hidden structure comes to be seen." (*)
You may think that we have only replaced the original interpretation problem with a much more complicated one.
But the beauty of it is that this allows us to continue to think about the meaning of life, the universe and everything... (x)
(*) While I agree with the overall conclusion, I disagree with the details.
i) Nowadays the multiverse landscape seems very popular (especially among string theorists) and it is not clear at all that we arrive back at one big bang.
ii) In general, I doubt that one could really reconstruct W as suggested or otherwise determine the wave function of the universe, unless
there is a new general principle which limits the possibilities (notice that we only know about one branch out of an infinity of possible branches.)
iii) If one assumes that W may contain an infinite number of branches and since those branches (assuming decoherence) are only almost-orthogonal to each other this poses a real problem, If one wants to use W to calculate anything.
(x) As far as I know, Frank Tipler was the first who realized that the many-worlds interpretation opens the door to theological interpretations of quantum theory. If one wants to follow this path (and don't we all want to believe?), then I would use a previous result to conclude that the wave function of the universe is not only invisible but necessarily pink.