3 ms·

I had the same reaction. If you make it to the end he concludes with: > The wave function’s pattern can travel across regions of possibility space that are ass

by bryan0 2y ago

I had the same reaction. If you make it to the end he concludes with: > The wave function’s pattern can travel across regions of possibility space that are associated with the slits. Which to me conflicts with his emphatic “no” at the beginning of the article because this implies you can define some mapping between the physical and probability space. And of course you can because if you couldn’t the theory would not be physically predictive.

tsimionescu 2y ago
His point from the beginning is this: the particle described by the wavefunction can't be said to move through both slits at once, because ψ(t, x, y) has a single value for a particular x and y at a particular time. The particle has non-0 probability for both x, y1, t and for x, y2, t, of course - but that just means the particle has non-0 probability to pass through either slit. And as for saying that the wave moves through both slits, that also doesn't make sense, by the very definition of the wave function - it's a wave in probability space, not in space, so it just doesn't move through space.
- bryan0 2y ago
  I’m with you on point 1, (I think this is also obvious from experiment because you will never measure a particle at both slits). for point 2 it seems you can define a mapping from the physical space to probability space. Saying that the wave doesn’t “move through” space might be technically correct but also seems like semantics on the definition of the phrase “move through” ?
  - tsimionescu 2y ago
    Of course it is to some extent semantics. But the important point is that the wavefunction is not something like a sound wave, or even something like a classical EM wave. Those are all waves defined over 3-dimensional physical space. In the original QM model, light is not a wave in the classical electrical theory sense. Light is made up entirely of photons, which are particles just like electrons or billiard balls, and they are described by a wavefunction. That wavefunction gives them various probabilities of being in various states at a certain time, and those probabilities can increase or decrease when more particles come into the mix. The states can represent position, momentum, charge, spin, energy levels, etc.
  - GoblinSlayer 2y ago
    Interference pattern is a measurement of a particle at both slits.
- lmm 2y ago
  > And as for saying that the wave moves through both slits, that also doesn't make sense, by the very definition of the wave function - it's a wave in probability space, not in space, so it just doesn't move through space. I don't think that's a valid argument. Imagine a regular water wave, i.e. a wavefunction h = h(x, y, t) describing the height of the water at position (x, y) at time t. You could say "this is a wave in height space, not in space, so it just doesn't move through space" and in a certain sense that's true. But obviously there is something that does "move" through "space" to the extent that anything can ever be said to do so.

by bryan0 2y ago

tsimionescu 2y ago

His point from the beginning is this: the particle described by the wavefunction can't be said to move through both slits at once, because ψ(t, x, y) has a single value for a particular x and y at a particular time. The particle has non-0 probability for both x, y1, t and for x, y2, t, of course - but that just means the particle has non-0 probability to pass through either slit. And as for saying that the wave moves through both slits, that also doesn't make sense, by the very definition of the wave function - it's a wave in probability space, not in space, so it just doesn't move through space.

bryan0 2y ago
I’m with you on point 1, (I think this is also obvious from experiment because you will never measure a particle at both slits). for point 2 it seems you can define a mapping from the physical space to probability space. Saying that the wave doesn’t “move through” space might be technically correct but also seems like semantics on the definition of the phrase “move through” ?
- tsimionescu 2y ago
  Of course it is to some extent semantics. But the important point is that the wavefunction is not something like a sound wave, or even something like a classical EM wave. Those are all waves defined over 3-dimensional physical space. In the original QM model, light is not a wave in the classical electrical theory sense. Light is made up entirely of photons, which are particles just like electrons or billiard balls, and they are described by a wavefunction. That wavefunction gives them various probabilities of being in various states at a certain time, and those probabilities can increase or decrease when more particles come into the mix. The states can represent position, momentum, charge, spin, energy levels, etc.
- GoblinSlayer 2y ago
  Interference pattern is a measurement of a particle at both slits.
lmm 2y ago
> And as for saying that the wave moves through both slits, that also doesn't make sense, by the very definition of the wave function - it's a wave in probability space, not in space, so it just doesn't move through space. I don't think that's a valid argument. Imagine a regular water wave, i.e. a wavefunction h = h(x, y, t) describing the height of the water at position (x, y) at time t. You could say "this is a wave in height space, not in space, so it just doesn't move through space" and in a certain sense that's true. But obviously there is something that does "move" through "space" to the extent that anything can ever be said to do so.