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(1) If you measure the velocity, you're absolutely guaranteed to find that it is positive (i.e., moving to the right); and (2) nonetheless, the probability the particle is to the right of the origin actually _decreases_ over time.
That sounds just straight up impossible - if something is guaranteed to be moving to the right, it can't be less likely that it's to the right of the origin over time!
Well, there's a description of quantum particles based on what's called a quasiprobability function that actually makes it work. It provides a kind of "probability" p(x, v) that the particle has position x and velocity v.
Turns out - I wish I had a movie to show you, it makes it much easier to understand (hi @3blue1brown ) - that what's going on is that small amounts of _negative_ quasiprobability are flowing to the right, & that's why the probability of being to the right of the origin decreases
Now, how to think about the negative probabilities themselves? Well, quantum mechanics tells you that you can't ever observe position and velocity simultaneously. So there's no need to find a direct interpretation.
Still, that feels like a copout to me - I think there probably is a really good, clear interpretation of what it means. I'm not sure what that is, unfortunately!
My physics is rusty, but if it's "guaranteed to be moving to the right" (ie you've measured its velocity with certainty) surely you therefore don't know anything about its position at all?
It doesn't tell you what the magnitude of the velocity is, just the sign. There can actually be quite a lot of positional information without violating things like the uncertainty principle.
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