What is spin at the quantum level (redux)

In this thread, ultrafilter asks what exactly is “spin”, as referenced in quantum mechanics.

The consensus seems to be, spin should be considered a quantum number (property) of a particle, and we should read too much into the analogy with everyday macroscopic spin of large objects. I was OK with this, but then I read the following in Hawking’s “A Brief History Of Time”, where he’s discussing symmetries:

He seems to be considering quantum spin as if it’s exactly like our everyday notion of spin! I realize he’s “dumbing down” for the general public, but why would he try to make us think the spin of a sub-atomic particle is just like the spin of a top?

(Netiquette: I wasn’t sure whether to bump a very old thread or open a new one. Sorry if I chose wrongly.)

Spin is called spin because it shares some of the characteristics of the spin of a top. Sometimes, the analogy holds, and you can use it for illustration and heuristic–as Hawking does. Other times, it doesn’t, which is why the other posters warned about taking the analogy too far.

What RM Mentock said.

This is rather an old thread, but in case someone is searching the archives, I thought I’d provide an explanation I found that I like. From p171, “The Elegant Universe” by Brian Greene:


That really cleared it up for me. I can sleep soundly :smiley:

Let’s try it this way:

What observed behavior of subatomic particles leads quantum physicists to infer an intrinsic property that has been dubbed “spin”?

Lumpy - something to do with angular momentum? I know angular momentum is a “big deal” in particle physics (because it’s always conserved? Not sure why, but it seems to come up in all the books I read.)

Hawking is talking about parity transformation which is a very mathematical thing and quite important in quantum mechanics and particle physics. The “mirror image” of an electron will give you an electron with an opposite spin. This is basically due to the fact that the world has “right-handed” and “left-handed” things. Basically what angular momentum does is define a “plane” and a direction. The direction can either be “up” or “down” so that whenever something has an angular momentum, you ascribe to it a direction. This is something you think about every day without noticing. Whenever you make a turn to the right or to the left you have basically been interacting with a fundamental property of the universe that associates one of two directions with your travel. While you and some visitor may not agree one which is the “right” and “left” side of the world, you will always agree that the right and the left sides are distinct and opposite. A similar thing is true of spin-angular momentum of the electron.

In fact, parity (the number of different kinds of “hands”) is always equal to n-1 of the dimensions of the space you are living in. That’s SPATIAL dimensions and not time-dimensions, so don’t get all yippy and think that we live in a 4D universe. The parity of our universe is therefore 3-1 or distinctly 2 (right and left, or positive and negative as physicists put it).

However, if we consider extra-spatial dimensions (as in Kaluza-Klein theory or string theory) we have to begin to consider the question of what parity means in those universes. In effect, one’s mirror image of a mirror image might not be the same thing as oneself. Crazy!