How can particles be in two simultaneous states until it is observed when the probability wave is collapsed?

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What you describe is just one interpretation of what we can observe and its called the copenhagen interpretation. There is others like pilot wave theory that picture a small particle riding on the wave.

Its just that there are experiments(like the famous dubble slit experiment) that show that light is a wave and acts like one untill you try to measure its position, then suddenly it has a distinct position but is not a wave anymore.

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.

Broadly – they aren’t, and we don’t know.

Wavefunction are mathematical objects that exist over all space and evolve over time per mathematical equations (Schrodinger etc). Among other things, these wavefunction each describe what (or the odds of) the particle is doing at any point in space and time. The queer part is that a particle can have _multiple_ wavefunction that are associated with it.

When we want to physically experimentally measure where the particle is, we generally get a point (or small region) in space. Mathematically, _each wavefunction_ assigns a complex number to that point in space and time, and the odds that we see the particle in _wavefunction_ at that point in space and time is the magnitude of the square of the value of the wavefunction there.

If wavefunction A says ‘always here’ and wavefunction B says ‘always there’, the particle exists in a bona fide superposition of both wavefunctions at once – not because it is (or isn’t), but because we need two abstract mathematical objects to describe the entire system. Then, when we measure it, it’s either _here_ or _there_ – in effect, the system has resolved its quantum weirdness and decided ‘yes I’m there/here’.

Now, is that all just a mathematical contrivance to describe ordinary classical ‘marble-like’ particles? Turns out no! QM makes predictions that CM can’t – e.g., electrons have a small chance of being discovered outside their atom. By shoving a metal needle near a surface, we can encourage this ‘chance appearance’ (quantum tunnelling), in a way CM forbids. Not only do we see this slight flow of electrons (verification of QM!), but it gives us a measure of the distance to the surface.

Hence, we can exploit this wholly quantum effect to make technology: scanning tunnelling microscopy, and atomic force microscopy.

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Tldr: its a mathematical abstraction to describe the system that yields accurate predictions. We don’t know what the wavefunction actually ‘is’, if it ‘is’ anything physical. Its like a velocity vector in CM – velocity vectors aren’t real and the particle isn’t the vector, but the latter is associated with the former in a useful way.

I think the answer to this is that it is wrong to think of it bring “in” two simultaneous states. It is not in either it just has the potential to be in them. It is not a particle like a little snooker ball bouncing around but is rather a probability wave.