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Luke_A_Somers comments on Configurations and Amplitude - Less Wrong
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You are. If you were to put a detector 3 there instead of an absorber, it would go off half the time, and detectors 1 and 2 would each go off a quarter of the time.
Are you implying that the presence of a detector instead of an obstacle changes what the other detectors detect, or not?
The text is unclear here:
Does "half the time" mean "half the time that any detector goes off", or "half the time you shoot a photon"? I would expect that, with the obstacle in place, half the time you shoot a photon no detector would go off, because the first mirror would deflect it into an obstacle. Seeing no detector go off is distinct and observable, so I don't see any way it could be eliminated as a possibility like the other case described here where two possible timelines that lead to the same world interfere and cancel out. So I would assume Eliezer means "half the time that any detector goes off". If so, I'd like to see the text updated to be more clear about this.