The detector clicks 50% of the time because “detector makes a clicking noise” is so complex that it doesn’t ever end up in the same state as “detector doesn’t make a clicking noise” to interfere with it. There are multiple paths this photon can take to end up in the same configuration, because the photon moving around is simple enough that we can design an experiment to make some of the amplitude that’s flowed to different configurations flow back to the same configurations – but the detector is complex enough that it separates the amplitude flows far enough that next to none of the amplitude from “detector 1 goes off” and “detector 2 goes off” will flow to the same configuration; hence they won’t (noticeably) interfere with each other. And then the human either hears or doesn’t hear the detector; the human is also complex enough that “human hears a clicking noise from detector 1” and “human hears a clicking noise from detector 2″ aren’t going to interfere; there’s no way they’re ending up in the same configuration afterwards.
Anything that remembers where the photon went will not observe interference from the photon going the other way, because it needs to be able to reach the same configuration from both of those configurations for any amplitude flow to interfere.
The detector clicks 50% of the time because “detector makes a clicking noise” is so complex that it doesn’t ever end up in the same state as “detector doesn’t make a clicking noise” to interfere with it. There are multiple paths this photon can take to end up in the same configuration, because the photon moving around is simple enough that we can design an experiment to make some of the amplitude that’s flowed to different configurations flow back to the same configurations – but the detector is complex enough that it separates the amplitude flows far enough that next to none of the amplitude from “detector 1 goes off” and “detector 2 goes off” will flow to the same configuration; hence they won’t (noticeably) interfere with each other. And then the human either hears or doesn’t hear the detector; the human is also complex enough that “human hears a clicking noise from detector 1” and “human hears a clicking noise from detector 2″ aren’t going to interfere; there’s no way they’re ending up in the same configuration afterwards.
Anything that remembers where the photon went will not observe interference from the photon going the other way, because it needs to be able to reach the same configuration from both of those configurations for any amplitude flow to interfere.