4 ms·

> But that's no more valid than saying that a regular water wave is "just a function that assigns a height to the water at every (x, y, t) co-ordinate, it doesn

• lmm 2y ago
  > when a water wave gets pushed through two slits, it breaks into two separate water waves, one coming from each slit, and those two waves push the water up and down at the same time at different locations. What physically observable distinction are you drawing? The points of water on the far sides of the slits will have a certain height at each point at each time, forming the interference pattern you'd expect. You can decompose that function into a sum of two separate waves, if you want, but you don't have to. And exactly the same thing is true of the quantum mechanical wavefunction for a particle passing through a pair of slits. > A wavefunction amplitude does not represent a displacement in any kind of medium. They represent a measure of the probability that the system being described is in a particular state at a moment in time. That state need not even be a position, it might be a charge, or a spin, or a speed, or any combination of these. Basically quantum systems oscillate between their possible states, they don't oscillate in space-time like matter affected by a wave does. I don't think that's a real distinction. Water height is a different dimension from (x,y) position and it behaves very differently; that the wave is moving across the surface and that the surface is moving up and down are orthogonal facts, the reason the former is movement isn't that the latter is movement. A classical electromagnetic wave moves even though it isn't in a medium that's moving (and so does e.g. a fir wave). > You can decompose the system's wavefunction as a sum of multiple wavefunctions corresponding to certain measurables, but this is an arbitrary choice: any such decomposition is exactly as valid. In matter waves, if I drop two stones in water at different locations, the water surface's movements can be described as a single wave, but there is a natural decomposition into two interfering waves each caused by one of the stones. There is no similar natural decomposition that quantum mechanics would suggest for a similar quantum mechanical system. Again I don't think this is a real distinction. You have exactly that natural decomposition in the QM system - it's not the only valid decomposition, but it is a valid one and it has some properties that make it nice to work with. And similarly for dropping stones in the water, infinitely many other decompositions are possible and equally valid (e.g. decomposing as two copies of a wave where you dropped two half-sized stones into the water).
  • tsimionescu 2y ago
    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.