The prediction for what happens when you block the B to D path is wrong. We have three final configurations, not two as in the above.
From the configuration “A photon going from B to D”, with original amplitude (1 + 0i) o Amplitude of (1 + 0i) * 1 = (1 + 0i) flows to “Block with absorbed photon”.
From the configuration “A photon going from C to D”, with original amplitude (0 + -i) o Amplitude of (0 + -i) i = (1 + 0i) flows to “A photon going from D to F” o Amplitude of (0 + -i) 1 = (0 + -i) flows to “A photon going from D to E”.
Applying the magical detector, we get a 1⁄3 probability for each of these outcomes; detector 1 detects, detector 2 detects, neither detects (block absorbs photon).
Does this work?
The url for the listing of all of Eliezer’s posts is actually now at: http://www.cs.auckland.ac.nz/~andwhay/postlist.html