Quantum spin again.

[hammegk]

I vaguely recall that any "thingy with mass" (I want to say lepton, or at least, lepton like, IIRC) has attributes -- like orbital radius for a planet, or angular momentum for a spinning top -- actually restrained to assuming magnitudes each having a specific quantum number. For macro objects -- earth orbit say -- the computations would provide ?billions? of "allowed orbits" per inch. That is, the prediction of unmeasurably small changes.

 

[ppnl]

Ok, I think I'm getting this. You really can turn quantum spin into classical spin. That follows my intuition of how things should be.

But it still isn't very clear exactly how you do this. For example you can store angular momentum in a flywheel and extract it as needed. If you had a system of particles as large as a flywheel but with all the quantum spin alligned how much classical angular momentum would this translate into? How much energy?

 

[epepke]

But is classical spin quantized?

Yes. But in classical cases the masses are so great you wouldn't notice.

One of the elementary problems I fondly remember from high school was calculating the number of possible positions, using quantum theory, of a marble rolling around in a desk drawer. It's pretty easy to calculate, making the obvious assumptions, but the number is so ridiculously high that you might as well forget about it.

 

[epepke]

But you don't need to. Spin angular momentum is angular momentum. We call it spin, but there is not a classical counterpart (which seems to be your bigger problem).

We know it is angular momentum because it can be converted to other forms of angular momentum, such as orbital or even rotational. What you are doing is like saying that potential energy is _associated_ with a form of energy. That would be silly. Potential energy is a form of energy.

Similarly, spin is a form of angular momentum. I can apply the spin angular momentum operator to the wave function and calculate an expectation value, if I want. Spin behaves exactly as angular momentum, and can be converted to angular momentum. That's angular momentum.

Now, whether it is easily considered in terms of classical terms is a different issue, but that is irrelevent to what it is.

Like I said, it's a semantic argument. I could say from GR that energy/momentum is mass, and that time is the imaginary component of space, but that wouldn't mean much to someone who didn't already understand GR. I don't know a better phrase for spin and angular momentum for a popular audience other than "associated with," which I stole from Feynman.

 

[epepke]

Ok, I think I'm getting this. You really can turn quantum spin into classical spin. That follows my intuition of how things should be.

But it still isn't very clear exactly how you do this.

It isn't easy, which is why nobody did it until 1957.

[edited to add] OK, I'll probably be pilloried for details. It's been happening all the time, but 1957 was the first time someone actually showed clearly that's what was happening. And it was the other way around, turning a classically-modelable angular momentum into a quantum spin.