[cgbg]

each of the six ions is spinning both clockwise and counterclockwise simultaneously

I wouldn't believe that even if I saw it--but if I saw it it couldn't be happening anyway. :-)

This stuff reminds me of the square root of -1--it shouldn't exist but it is a useful tool in the real world.

[snarks_when_bored]

each of the six ions is spinning both clockwise and counterclockwise simultaneously

I wouldn't believe that even if I saw it--but if I saw it it couldn't be happening anyway. :-)

You're in good company: as (I think) Feynman said, nobody understands quantum mechanics...you just get used to it.

This stuff reminds me of the square root of -1--it shouldn't exist but it is a useful tool in the real world.

Imaginary numbers—which aren't imaginary at all, of course—play a crucial role in quantum mechanics. Here's a GIF image of the time-dependent one-dimensional Schrödinger equation, which describes how the wave function of a non-relativistic (i.e., slow-moving), undisturbed elementary particle such as an electron evolves over time:

Note the multiplication by i, the square root of -1.

[Doctor Stochastic]

This stuff reminds me of the square root of -1--it shouldn't exist but it is a useful tool in the real world.

Why shouldn't it exist? I would imagine that it's as real as any other number. (Note the complex sentence.)

The real question (IMNSHO) is: "Why does the Sqrt(-1) suffice?" In other words, why do we not need CubeRoot(-1), etc.?