Say I have 1 electron in some quantum state Defined by some wave function, and it's doing its thing fluctuating the probabilities of where it might be.
What if I put a measuring device in an area where there's consistently a 1% chance of the particle being and then quickly remove the measuring device 1 milisecond later vs what if I leave the measuring device there for 1 second
Each case wouldn't both have a 1% chance of finding the particle, right? I feel like the one left there for 1 second made 1thousand more measurements than the one there for 1 milisecond, so it should be 1thousand times more likely to be discovered by the 1 second detector? What are the details here?
Bonus part 2: If after our measurement we see absolutely nothing (my electron wasn't there). Does the fact we know it isn't there affect the wave function? (It can't still have a 1% chance of being there if it's not there, right?)
Actually I happen to know the answer to this is yes. Looking and seeing nothing does affect the particle's wave function, because in the double slit experiment if you measure slit A and find nothing, you'll find the particle behind slit B with its wave function collapsed as if you detected it at B. But, how exactly does this work mathematically? I've never heard anything about how the wave function gets modified by detecting nothing in some area. Only how it completely collapses when the particle is detected.