> Double slit experiment with one detector has a seemingly impossible phenomenon when the interference pattern disappears without measurement in our branch
Then you don't understand quantum mechanics at all. You should read this:
The TL;DR is that measurement and entanglement are the same phenomenon. A particle can become entangled with a detector even if the detector doesn't register anything.
But that is neither here nor there. Why do you get interference with no detectors? Your theory is that a detector at one slit is somehow paired with a "virtual detector" in a parallel branch at the other slit. But why would that "virtual detector" go away when the real detector is removed? Why is it never the case that there is a "virtual detector" at either slit unless there is a real detector at one of them?
Before measurement it's one detector, then it interacts with half photon, which is superposition |photon>+|no photon>, and the detector's state splits, the first state interacts with the |photon> state and measures it, nothing happens to the second state, because there's nothing to measure in the |no photon> state, but the first state splits away from the second state and leaves it alone, that's how the second state ends up alone with pure |no photon> state, but this really was done to it by the first state, the second state can't do it by itself. For this to happen in the second branch you need measurement to happen in the first branch, so when you are in the second branch, the first branch still needs to exist even though you don't see it, otherwise your branch won't be able to be as it is.
When you remove detector and start next measurement, you start with your one branch, branches from previous measurements don't affect it, the phenomenon happens during decoherence, nothing happens after it.
Your article explains this with branching without saying the word.
It's a part of photon's state at the slit with detector, the other part is at another slit. It's superposition of photon near detector and no photon near detector.
Then you don't understand quantum mechanics at all. You should read this:
https://flownet.com/ron/QM.pdf
The TL;DR is that measurement and entanglement are the same phenomenon. A particle can become entangled with a detector even if the detector doesn't register anything.
But that is neither here nor there. Why do you get interference with no detectors? Your theory is that a detector at one slit is somehow paired with a "virtual detector" in a parallel branch at the other slit. But why would that "virtual detector" go away when the real detector is removed? Why is it never the case that there is a "virtual detector" at either slit unless there is a real detector at one of them?