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Comment by tsimionescu | Hacker News Reader

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.

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> 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.

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” ?

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.

Interference pattern is a measurement of a particle at both slits.

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