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