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In classical mechanical waves like water waves or sound waves, the wave equations are just an approximation of the "real" movement happening. You can theoretica

In classical mechanical waves like water waves or sound waves, the wave equations are just an approximation of the "real" movement happening. You can theoretically get the precise results of the movement of every part of the medium by just applying Newton's laws of motion to all of the particles of the medium (assuming they're coarse grained enough that you can ignore quantum effects, of course). That is, you can model the surface of the water and the rocks as little balls of mass connected by ideal springs and such, and you'll see that the movement of the water is directly caused by the two rocks, whose contact with the water pushes it here and there. And so, the "real" picture is two separate waves, and any other way to model the system, even if mathematically equivalent, is artificial in some sense. Even for EM waves, the classical theory explains them somewhat mechanistically, as an interaction between electrical and magnetic forces that originate from the charged sources and self-propagate. There is no similar picture you can draw for the quantum mechanical wavefunction. It's the base reality of the system, and it turns out in fact that Newton's laws can be derived as an approximatiom of the wavefunction. But there isn't any kind of "reason" for which the wavefunction does what it does, like there is for the water waves. And so all models for separating the wavefunction into different components is just as "natural" as any other.

lmm 2y ago
> you can model the surface of the water and the rocks as little balls of mass connected by ideal springs and such, and you'll see that the movement of the water is directly caused by the two rocks, whose contact with the water pushes it here and there. And so, the "real" picture is two separate waves I don't see that that follows? Both wave pictures are a mathematical approximation to the "real" system of particles moving. Both are ways of calculating the same result. Neither is objectively more valid than the other. You can say that picturing it as "the wave from the first rock overlaid on the wave from the second rock" is an interpretation that makes more physical sense or is nicer to think about, but that's just as true in the QM case.
- tsimionescu 2y ago
  > Both wave pictures are a mathematical approximation to the "real" system of particles moving. Yes, exactly. > You can say that picturing it as "the wave from the first rock overlaid on the wave from the second rock" is an interpretation that makes more physical sense or is nicer to think about, but that's just as true in the QM case. No, because in QM, the wavefunction is the real, final picture. Any split is arbitrary, the two rocks didn't "cause" the waves, the the wavefunction of all the molecules that make up the rocks and the water has higher amplitudes for states in which the water molecules look like the wavey surface, and lower amplitudes for states in which the rocks touch the water but the water doesn't move at all, etc. That's all the physics can say.
  - lmm 2y ago
    > No, because in QM, the wavefunction is the real, final picture. Any split is arbitrary, the two rocks didn't "cause" the waves But at the wave picture level that's always true. You can break down a water wave into a bunch of particles moving according to forces, sure. But that doesn't actually help you answer the question of whether a wave that's gone through a pair of slits is now one wave or two waves, because when you're looking at the particles and forces you can't see the waves any more (except as patterns in the particles and forces - but then you're back in the wave picture).

lmm 2y ago

> you can model the surface of the water and the rocks as little balls of mass connected by ideal springs and such, and you'll see that the movement of the water is directly caused by the two rocks, whose contact with the water pushes it here and there. And so, the "real" picture is two separate waves I don't see that that follows? Both wave pictures are a mathematical approximation to the "real" system of particles moving. Both are ways of calculating the same result. Neither is objectively more valid than the other. You can say that picturing it as "the wave from the first rock overlaid on the wave from the second rock" is an interpretation that makes more physical sense or is nicer to think about, but that's just as true in the QM case.

tsimionescu 2y ago
> Both wave pictures are a mathematical approximation to the "real" system of particles moving. Yes, exactly. > You can say that picturing it as "the wave from the first rock overlaid on the wave from the second rock" is an interpretation that makes more physical sense or is nicer to think about, but that's just as true in the QM case. No, because in QM, the wavefunction is the real, final picture. Any split is arbitrary, the two rocks didn't "cause" the waves, the the wavefunction of all the molecules that make up the rocks and the water has higher amplitudes for states in which the water molecules look like the wavey surface, and lower amplitudes for states in which the rocks touch the water but the water doesn't move at all, etc. That's all the physics can say.
- lmm 2y ago
  > No, because in QM, the wavefunction is the real, final picture. Any split is arbitrary, the two rocks didn't "cause" the waves But at the wave picture level that's always true. You can break down a water wave into a bunch of particles moving according to forces, sure. But that doesn't actually help you answer the question of whether a wave that's gone through a pair of slits is now one wave or two waves, because when you're looking at the particles and forces you can't see the waves any more (except as patterns in the particles and forces - but then you're back in the wave picture).