How can particles be in two simultaneous states until it is observed when the probability wave is collapsed?
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It’s not actually in 2 states at the same time, we just don’t know which state it’s in, and it’s acting like a wave. That wave just “looks” like the wave of both states added together. I put the “looks” in quilotes because we can’t actually see the wave function as any observation would collapse the wave function into one of the possible states.
Take for example, the double slit experiment with a single photon. We know that the normal double slit experiment produces an interference pattern, but with a single photon, we still get the interference pattern over a several runs of the experiment, despite there being no other photon to interfere with. That is because it is interfering with itself.
The photon goes through one of the two slots, but we don’t know which one. While it’s in the slit, we know that it’s wave function will be a 50% chance of being in the right slit, ans a 50% of it being in the left. Then as the photon moves out, those two halves of the wave function propagate out, and interfere with each other, but it’s still just the one wave function, the two states are just added together to make one. Once the photon hits the detector, the wave function collapses and we know exactly where it is.
If we put a detector over one of the slots so we can tell when the photon passes through the right slit, then we don’t get the interference pattern anymore. Instead we just get 2 fuzzy patches, basically an out of focus image of the two slits. That’s because when the photon goes through the right slit, we triggered the detector, so instead of that 50/50 split, we know the wave function is entirely in the right slit, so it will just travel out and hit the detector without interfering with anything. If the detector doesn’t go off, we know that the photon went through the left slit, and we still don’t get the 50/50 split, it just looks exactly the same as the right slit, just shifted over.
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