In the famous double slit experiment, setting up a measurement device that watches which slit an electron passes through changes the eventual outcome on the screen, causing the wave function to collapse.
If the measurement device were a light year away and were precise enough to “zoom in” and see which slit the electrons went through, what would happen on the final screen?
Surely, if the measurement device were off, then the electrons would behave like waves and not particles. An interference pattern would appear on the final screen as there is no observer. On the other hand, if someone a light year away turned on the measurement device, this far-away person (and the measurement device) wouldn’t know which slit the electrons went through until a year later. And, the electrons going through the slits wouldn’t “know” they are being observed because no information (ie the measurement device turning on) can travel faster than the speed of light.
The links to the older articles are dead in that link. Here’s an archive of the 3rd essay (and it links to the second and first). The 3rd essay presents a thought experiment very close to what OP is asking. If we delay the choice of inserting a detector then would we still get an interference pattern when we’re not supposed to? It seems that the question is still unanswered but theoretically, no, because the universe is not locally real and quantum effects seem to happen faster than light in plenty of other experiments.