Jones Beene wrote:
----- Original Message ----- From: George Holz & Stephen Lawrence > If my mental picture is right, then a free electron's dipole must > be aligned with the external field (parallel or antiparallel). This is experimentally observed but is something that I find extremely strange. Although one of the orientations is a true stable equilibrium the other should be an unstable equilibrium and the dipole should flip with any perturbation. Spin must come in here somehow but I don't see quite how. Eight? Aha ... maybe the answer is "eight" in the sense of QM (excuse this comment from the peanut gallery, as this is an interesting thread) - aren't you assuming in that 'mental picture' that the electron dipole is a result of classical spin - when it could just as well be the "figure eight" type looping from the QM model ?
<g> I was assuming no such thing -- my mental picture is not nearly that sophisticated in this case!
All I was assuming was that the electron has just 2 so-called spin states, spin-up and spin-down, and that its dipole is connected to its so-called spin states, and I was assuming that because ... the textbooks say so. I've actually read some sufficiently confusing things about so-called "spin" states that I would not even hazard a guess as to what its so-called "spin" "really" is! :-)
But, moving along, if it's got just two states, and those states are referenced to a vector field in 3-space, then they've got to be parallel and antiparallel to the vector field. If it's got a crosswise state versus the field, then, in 3-dimensional space, it could have an infinite number of possible "spin states" -- all rotations of its "spin axis" with the direction of the B field. It doesn't, so its dipole axis must be aligned to the B field. Deep reasoning here, huh... not!
As to those "confusing things" I've read about spin -- my understanding is that the "spin" terminology is actually related to how far around you have to "spin" the particle before it gets back to its original state. In other words, it's an expression of the particle's symmetry rather than a statement of what the particle is doing. In this case it happens to be tied to a magnetic dipole moment, and since it's a charged particle that makes it _seem_ like it must also refer to some internal rotation of the particle -- but since electrons are apparently point particles, there's no way any physical "spin" of the electron could produce a finite B field anyway, AFAICS...
Spin 1/2 particles act like little tops, but it's not clear they really are. Spin 1 particles don't act like tops. And spin 2 particles are just plain weird.
And going much further afield ... 'field' being the operative word, does the honeybee routinely use QM principles in the insect's characteristic "figure eight" type looping (performed to communicate a food source to other bees)? http://www.physics.helsinki.fi/~matpitka/honey.html
When bees do the dance outside the hive, the other bees watch them and then act on what they just saw.
But ... when bees do the dance _inside_ the hive, how do the other bees know what they're doing? It's _dark_ inside the hive, after all.
Just one of those questions...
One of those synchronicity things - I happened to be reading the honeybee thing when this post came in... Jones
