Dear Cecil,
I was reading about Scully and Druhl’s delayedchoice quantum eraser in Brian Greene’s Fabric of the Cosmos today and I had a couple of questions that maybe you can help me with.
As I understand the idea, in one type of this of experiment a photon is fired(?) to a beam splitter the photon then has a 50% probability of going to one two downconverters which then separates the photon into two different photons. The signal photon continues on to a reflective surface and then to a screen while the idler photon then goes to a detector. Since we know which way the original photon went at the beam splitter there is no interference pattern shown at the screen.
In another version of the experiment instead of the idler photon going directly to the detector another beam splitter is added which gives the idler photon a 50% chance of going to a detector (d1) or to another beam splitter which gives the photon a 50% chance of going two different detectors (d2, d3). If the idler photon is detected at d1 (or d4 if went the other way at the first beam splitter) there is no interference pattern at the screen for the signal that corresponds to the idler photon detected at d1 (or d4). However, if the idler photon is detected at d2 or d3 there will be an interference pattern since it cannot be determined where the original photon went at the first beam splitter.
Now for my questions.

If there are no idler photon detectors will there only be an interference pattern?

What if idler photon detectors are there but are not setup to detect idler photons (there are turned off) will there only be an interference pattern?

What if the idler photon detectors are far enough away from the beam splitter that the signal photon will hit the screen before the idler photon reaches any detector, will there be an interference pattern? What if the detectors are tuned off after the signal photon has hit the screen but before the idler photon reaches the detector, will there be an interference pattern?

What if more beam splitters are added so that no idler photon detector will show which way the original photon went at the first beam splitter, will there only be an interference pattern? If detectors are added that will determine the which way the original photon went at the beam splitter will there be an interference pattern? What if the new detectors are are left turned “off”? What if they are set turned “off” but will turn on after the signal photon hits the screen but before the idler photon will reaches the new detectors, will there be an interference pattern?
I hope this makes sense and thank you.