system
Given the following post, respond as if you're commenting on Reddit:
human
If electrons exist as a probability distribution then in what sense do they move around the atom?

Very likely some of my understanding here is wrong, so I'll try to clearly restate what I think I've heard physicists say.

1) Electrons exist as a probability distribution around the nucleus of an atom so that we cannot say where they are located but only give a likelihood of them existing in various places.  

2) Electrons move around the nucleus at some speed.

These two conceptions of electrons seem to contradict each other.
gpt
I can think of two ways to explain this: the easy way and the hard way.

**The easy way:** imagine a spherical probability distribution. Imagine that you have a huge number of electrons distributed according to that probability distribution. Each of the individual electrons rotates around in some circular orbit, but the overall distribution of the electrons doesn't really change. It stays a sphere. That's kind of how electrons can be moving without their probability distribution moving around in space.

This analogy kind of starts to fall apart once you consider non-spherical probability distributions, though.

**The hard way:** You're probably used to thinking that the only "fundamental" information about a particle is its position, and that velocity comes from the change in the position over time. But in quantum mechanics, that's not true. The "fundamental" properties of a particle include not only the position, but also the momentum.^1 Momentum is not something that you figure out by analyzing how the particle is moving; it's a separate and independent quantity in its own right.

A quantum particle exists as a probability distribution over _both_ position and momentum. So when physicists say that electrons move around the nucleus at some speed, they're not talking about how fast the likely location changes. They're talking about the electrons' "intrinsic" momentum divided by mass, which is completely unrelated to the position.

Actually, when you look at it this way, the fact that a classical (non-quantum) object's velocity equals the rate of change of its position in time, and also at the same time equals its momentum divided by its mass, is kind of a giant coincidence. Not literally a coincidence, of course; the theory was designed so that it would work out that way. But it's a really interesting consequence of the fundamental assumptions of QM - it's something that has to be derived, rather than a definition as in classical mechanics.

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 ^(1) Technically neither of these is fundamental; they both come from the wavefunction, but that doesn't matter for this explanation. The point is that velocity is not just something you get from looking at how the position changes over time.