Quote:
|
Originally Posted by scourge
Quote:
|
Originally Posted by Fortis
Quote:
|
Originally Posted by scourge
But here's where that seems like a dodge to me--we have precisely calculated and utilized the -precession- of the proton magnetic moment, the basis of MRI technology, so why can't we figure out the rate of the inherent spin? If we know the charge on the proton, and the magnitude of its magnetic field, why can't we determine the rate of rotation?
|
One way of looking at this is to say that experiments indicated that the electron behaved as if it had an intrinsic angular momentum (and an associated magnetic moment), with a z-component that could be +-hbar/2.
The problem occurs when you try to interpret this in terms of a classical spinning object, such as a sphere. As the electron looks pretty much point-like as far as anyone can determine, this would imply, to use a technical term, a humungous angular velocity. It is simpler to attribute spin angular momentum as being as much of a fundamental property of a particle as mass or charge. This may not be the answer that you were looking for, but hopefully it helps.  |
Thanks Fortis, but let's set aside the enigmatic electon for a moment, because MRI uses protons, and they have a reasonably well-established dimension. Given that, can't we at least approximate a rate of rotation for it, given its charge and magnetic field strength?
I'd like to know this, because it seems a little weird to me that the wavelength equivalent of a proton's rest energy appears to be quite close to a proton's radius. Does that seem even a little fishy to anyone else? |
I guess that it was inevitable that I would ramble on about the wrong particle.
In many ways the proton spin is more complicated than the spin of the electron. It is a composite particle consisting of three quarks, each of which possess their own intrinsic spin,contributing to the overall angular momentum of the proton. In addition they appear to contribute orbital angular momentum. The current experimental model has ~30% of the proton spin originating from the spin of the three valence quarks. The rest of the proton spin is thought to originate from orbital angular momentum contributions (which is counter-intuitive, as one might naively have expected the ground state of the particular three quark combination to have zero orbital angular momentum), or possibly from the gluons binding it all together. It looks like the jury's still out on this one.
As you can't consider the proton to be a simple spherical body (for these purposes), a classical analogy may help. Consider the solar system. Here we have a structure with a well defined angular momentum (don't ask me what it is, though, as I haven't a clue
). Like the proton it is also a composite structure consisting of objects with their own intrinsic angular momentum (i.e. rotating planets), as well as orbital angular momentum. Even though this is a well behaved classical system, you would still have great difficulty in assigning a single angular velocity to it.
This has all been a bit rambling (I'm fitting it in between sleeping and calming a baby) but I hope that it helps a bit more than my ramble on the proprties of the electron.