The apparatus below represents an apparatus for the typical delayed erasure experiment. My question is, why is there no interference pattern observed at D0 in this experiment (interference is only observed in hindsight looking at photons that coincided with photons striking D2 and D3)? I would have thought the top part of the apparatus, looking like the typical double slit experiment, should show an interference pattern. I would like an answer that does not make reference to the rest of the apparatus, since according to Lubos Motl, the results at D0 should not depend on the set up or measurements in rest of the apparatus, although results may be correlated with the rest of the apparatus.
Below is the quote from Lubos Motl in his answer to this question,
If you're only observing what's measured in the upper part of the picture, e.g. the photographic plate D0, then everything that happens in the lower part of the picture is completely inconsequential for the measurements done in the upper part of the picture. So whether you replace the system of mirrors and detectors by another photographic plate E0 is totally irrelevant for the results in D0 only.
I have read the entirety of Lubos' post yet this fundumental question remains unanswered.