Posted: Jun 22, 2010 3:39 pm
Spin is classical
I don't know if you appreciate the significance of this, but it means spin is isn't "intrinsic" after all. It's classical. See the wiki Stern-Gerlach article which says:
If the particles are classical, "spinning" particles, then the distribution of their spin angular momentum vectors is taken to be truly random and each particle would be deflected up or down by a different amount...
The experiment shows that this doesn't happen, so we know the particles aren't spinning spheres. However the article, which is in line with the current consensus, goes on to say:
Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values, called spin-up and spin-down. The exact value in the z direction is +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast. The speed of rotation would be in excess of the speed of light, 2.998×108 m/s, and is thus impossible.
There's actually nothing wrong with that, but here comes the non-sequitur:
Thus, the spin angular momentum has nothing to do with rotation and is a purely quantum mechanical phenomenon. That is why it is sometimes known as the "intrinsic angular momentum."
Whoa! We've established that the particle isn't rotating like a planet, but why can't it be rotating in some other fashion? There is no justification here for asserting that spin angular momentum has nothing to do with rotation, particularly since the electron exhibits magnetic dipole moment. And particularly since the Einstein-de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". It's easy to see what's happening in the Stern-Gerlach experiment, especially if you've played football and practised your free kicks. Imagine a whole bunch of spheres, like this:
Now give them an earth-style spin to give yourself a set of "classical particles". Next, jumble them around so that the spin axes point in a variety of directions, then throw them through the inhomogeneous magnetic field. You'd see a line on the screen as per the classical prediction:
Now collect all your still-spinning particles together again, and set them down on the table like a bunch of spinning globes. Now give them another spin in another orientation. Spin the spin axis. You have two choices as regards this new spin direction, this way: ↓O↑, or that way: ↑O↓. Now throw them through the inhomogeneous magnetic field and ask yourself what you'd see. Two spots, because there are two chiralities to the two compound spins. Apart from that, you can't say which way they're spinning. Spin a glass clock like a coin, and the rotation of the hands is clockwise when its face-on, anticlockwise when its rear-on, clockwise when its face-on, and so on. It's spinning both clockwise and anticlockwise. Spin the glass clock with your other hand and the compound rotation is different, but you can only describe the difference by using terms like spin-up and spin-down.
I don't know if you appreciate the significance of this, but it means spin is isn't "intrinsic" after all. It's classical. See the wiki Stern-Gerlach article which says:
If the particles are classical, "spinning" particles, then the distribution of their spin angular momentum vectors is taken to be truly random and each particle would be deflected up or down by a different amount...
The experiment shows that this doesn't happen, so we know the particles aren't spinning spheres. However the article, which is in line with the current consensus, goes on to say:
Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values, called spin-up and spin-down. The exact value in the z direction is +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast. The speed of rotation would be in excess of the speed of light, 2.998×108 m/s, and is thus impossible.
There's actually nothing wrong with that, but here comes the non-sequitur:
Thus, the spin angular momentum has nothing to do with rotation and is a purely quantum mechanical phenomenon. That is why it is sometimes known as the "intrinsic angular momentum."
Whoa! We've established that the particle isn't rotating like a planet, but why can't it be rotating in some other fashion? There is no justification here for asserting that spin angular momentum has nothing to do with rotation, particularly since the electron exhibits magnetic dipole moment. And particularly since the Einstein-de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". It's easy to see what's happening in the Stern-Gerlach experiment, especially if you've played football and practised your free kicks. Imagine a whole bunch of spheres, like this:
Now give them an earth-style spin to give yourself a set of "classical particles". Next, jumble them around so that the spin axes point in a variety of directions, then throw them through the inhomogeneous magnetic field. You'd see a line on the screen as per the classical prediction:
Now collect all your still-spinning particles together again, and set them down on the table like a bunch of spinning globes. Now give them another spin in another orientation. Spin the spin axis. You have two choices as regards this new spin direction, this way: ↓O↑, or that way: ↑O↓. Now throw them through the inhomogeneous magnetic field and ask yourself what you'd see. Two spots, because there are two chiralities to the two compound spins. Apart from that, you can't say which way they're spinning. Spin a glass clock like a coin, and the rotation of the hands is clockwise when its face-on, anticlockwise when its rear-on, clockwise when its face-on, and so on. It's spinning both clockwise and anticlockwise. Spin the glass clock with your other hand and the compound rotation is different, but you can only describe the difference by using terms like spin-up and spin-down.