Friday, June 27, 2014

The Quantum Spin Explained

Dear Diary,

I had these grand plans to figure out what exactly the hell a spin in quantum mechanics came from.  It's this little physical fact that only has a finite number of configurations (like 2: can be up or down...weird!) and every electron has one that interacts with magnetic fields.  But it isn't clear in physics texts that there's a better physical description other than it is measured.

I swear I had this idea that you could get a spin from the path integral semiclassically and evaluate motions with electrodynamics involved.  I even went so far as to ask Raphael a few months ago if you could get thermodynamic properties of solids from the path integral to coyly ask if you could do it with a charged particle and a spin.  Wasn't I clever to have outsmarted really, dangerously smart people from hundreds of years of staring at math on pieces of paper?

But blast!  I've been scooped by several decades!  Those old physicists are crafty foxes, they are!

It turns out that the American Journal of Physics ran an article by Ohanian (author of a widely used book on physics) in 1986 that explains exactly how a spin comes about from the electromagnetic field which summarizes previous efforts to do so by Belinfante.  It's actually pretty simple!  Using a few conservation laws and Dirac's equation, it comes out that photons have spin 1 because of the way electromagnetism works.  Meanwhile, if you quantize things, electrons get the half spin, just like I wanted to show!  Basically, it's a consequence of the electric field from the point charge.

Oh man, I had all these plans to derive something super cool and be "that guy" that made future generations of physicists have to learn all about that damn spin (*eye roll*).  I'd be cursed by successive generations of everyone for making their lives harder for learning more! Glorious! But now I see I would have just been Belinfante!

Previously, I had only read that two guys:  Uhlenbeck and Goudsmit tried to actually say the electron itself is spinning! (The story goes that their advisor, Ehrenfest, poor guy who wound up committing suicide because physics was becoming too mathy and he had a major life crisis, submitted it saying that since the pair was young, they could afford a wrong caused quite a stir nonetheless).  But making the charged particle actually spin implied it was spinning too fast to make sense with the rest of physics (about 10 times faster than the fastest thing there is, light).  That article I linked to you above presents a solution without those problems; it works with lots of other things like quantum field theory.

Well, this is surely a taste of bitter physicist's medicine where you realize that nothing that you do will ever be important.  Ever.  I guess the only thing left to do is get physical exercise, talk to people, and find an inner purpose in life.  I also ought to get back to whatever Kieron wanted me to do...something involving spin, actually.  This is somehow proving karma exists, no doubt.

But I should avoid getting too into my work!  There's more lessons to be learned from old physicists than just the physics.  Good thing I skipped out on work yesterday to watch the USA win against Germany 0-1 and advance in the cup!

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