Imagine a particle in a very large box which takes years to travel from one end to the other. Alice and Bob are outside the box, on opposing ends. Each can remove their side of the box to check if the particle is on their side of the box.
Around the middle of the box, but outside the box, a star explodes. Alice and Bob agree to both check if the particle is on their side of the box when they see the star explode.
If Alice sees the particle on her side, we would expect Bob to not see it on his side, but the problem with this is that wave function would have to collapse instantly over all space in the box. In other words, it's non-local.
If the wave function were to collapse locally over time, it would start where Alice observed it, and information about the collapse would propagate at the speed of light to the other side of the box. But since it takes years to span the box, the probability distribution would still be non-zero probability on Bob's side.
Since it would break conserved quantities, a particle would not be able to be detected on both sides of the box, so it seems like the wave function collapses non-locally.
I think a non-local collapse looks something like the following.
I say it's non-local because the part of the probability distribution closer to Bob's side is changing by Alice's discovery of where the particle is or is not. A positive or negative observation by Alice affects Bob's chances of detecting the particle on his side. This is a non-local cause and effect.
Is this correct? This seems like an experiment that could be done. For example, a long tube has only an electron inside. The detectors Alice and Bob are photon detectors on each end of the tube. Turning on a very strong magnet on each end of the tube is equivalent to Alice and Bob opening the tube and looking inside. If the electron's spin flips in response to the magnetic field, then a photon is detected and may be detected. The time between turning on the magnet and detection of photon tells us where the electron was. If we run the experiment many times (throw away results where no photon is detected because electron spin did not flip or photon did not hit photon detector), will it produce a distribution of detections which is "uniform" (ignoring interference patterns), or will it produce a distribution which is more concentrated as you get further away from the magnetic field source (magnetic field is only on when we want to detect).
Further clarification: I understand the particle is everywhere in the box as some state before measurement. I understand that the particle IS the state. Measurement just forces the particle to be in a pure state. And, it seems like this transition from superposition to pure state happens instantly. No time passes. But my question is about what happens in the time between when Alice looks into the box and when she measures the position. As she sees that the space in front of her does not contain the particle, does this altar the particle's state? Does measurement of where the particle is NOT affect its state?
I have found this answer: https://physics.stackexchange.com/a/476738/159153 But just like the commenter on that answer, I am left unsatisfied with this story. The reason being, if negative measurement affects state, then I am still wondering how Bob's side of the box seems to be affected instantaneously.
Also, could this resolve the paradox seen in the delayed choice quantum eraser experiment? Since simultaneity can be broken by changing reference frames, it can also be fixed by changing reference frames. We can find a reference frame where the 2 events, detecting the particle on the main detected, and detecting the entangled particle in one of the other detectors, happens simultaneously. And if the wave function collapses instantly, then there's no paradox in this frame of reference.