I'm a layperson learning about quantum mechanics and probability waves. My understanding is that the probability wave for the position of a particle disperses throughout all of the universe.
I have two questions about probability waves:
1) Does the probability wave for a particle take time to disperse throughout space?
For example, if a particle is formed at $t=0$ and I have a detector one light year away, will it be impossible for the detector to detect the particle until the probability wave reaches the detector and at least establishes probability where the detector is located? If so, is there a given speed for the wave (e.g., speed of light)?
2) In the double split experiment where single electrons are fired and detected on the other side of the slits, why do the physical barriers cause the waves to interfere with each other? I was thinking that if the particles were photons, then would the double slits cause the same interference? What if the slits were cut into perfectly clear glass? I assume that the probability waves would not be disrupted by the glass, but is that true?