"Steve Harris " wrote in
message m...
| (Gregory L. Hansen) wrote in message
...
| In the usual textbook representations, the Dirac spinor has the particle
| spin and magnitude in the top two components and antiparticle spin and
| magnitude in the bottom two components. But I've never really
understood
| (nor needed to understand in class) what that means. A stationary
| particle is all upper. Boost it and you put some magnitude in the lower
| components. Does that mean a likelihood of detecting an antiparticle?
| Suppose we shot electrons into a magnetic field that's as weak as we
like
| but will sufficiently separate charge, do we expect most of them to turn
| left but some to turn right? I'm sure that can't be quite right.
|
| COMMENT:
|
| I'm a out of my league on the math, but can give you some language and
| handwaving. You shouldn't be wary of the lower spinor components
| showing up when you give some KE to an electron (or drop it into some
| E or B potential, also). That's just the Dirac equation's "way" of
| accounting for the change in the "relativistic mass" of the electron.
| Or the increase in total energy of the thing, as we say today. The
| extra KE has no charge (obviously), so what kind of "stuff" is it made
| of, particle-wise? According to the Dirac theory the extra stuff over
| the rest mass (rest energy) of the electron is composed of half
| virtual electron and half virtual positron. These travel along with
| the original electron, and appear and disappear in a ghostly was as
| you view the electron from frames other than the rest frame. So if you
| boost an electron to total energy 2mc^2 it's composed of 1.5 electrons
| and 0.5 positron. But the positron component is virtual since it's off
| mass shell and hasn't got enough energy to be real.

I think it is more than 1.5 electrons and .5 positrons. It is a mix of all
the charged fermion pairs. But the mix is for sure dominated by virtual
electrons and positrons at lower energies.

| So long as you haven't boosted the electron to a total energy higher
| then 3mc^2, however, the virtual positron traveling along with it
| never has enough energy to be real, so there's no danger of detecting
| it directly as a free particle. It does, as a virtual field, has some
| mild effects on the interaction of the whole ensemble on stationary
| potentials, however. Over energies of 3mc^2 or kinetic energies of
| 2mc^2, of course, you can have pair production of the virtual
| components if you can figure out a way to offload the momentum through
| another interaction.

I think this is what happens in accelerated e+e- scattering. When the
energies are high enough, the heavier charged fermion pairs in the mix can
become more dominate.

| If you think the Dirac solutions for freely propagating particles are
| strange, consider what happens when you drop an electron into a
| positive potential well, as with a nucleus, and the well is really
| deep. Say a 1s orbital for a nucleus of a couple of hundred Z (if
| there was such a thing). At classical Z=137, the negative potential
| energy of binding is equal to mc^2, so the total energy of the
| electron is zero! It doesn't exist! Make the positive binding
| potential even stronger and now the energy of the electron starts to
| go negative, which means that you start to get more positronic
| components than not. At some point, you have enough energy that this
| positron will have enough energy to be real and pop out of the
| potential, leaving only the electron's negative charge behind like the
| smile of the Cheshire cat, to neutralize some of the positive nuclear
| charge. This is a lot like polarization of a black hole's horizon by
| the strong G field there (except this is a strong electric field). You
| get pair production with one component of the pair being eaten and the
| other popping free. So that counts as detection. In the black hole
| when that happens, the mass of the hole decreases. For the Dirac case,
| the charge of the potential decreases. So you can't have + charge
| greater than Z= 180 or so in the Dirac theory, since vacuum breaks
| down, and positrons are emitted until you get back down to critical
| field (of course the same is true for - fields, where electrons are
| emitted). The difference between Z=137 and 180 is due to corrections
| resulting from the 2 center Dirac equatiion, and the one you usually
| see, which is for only one particle (the electron).

This looks like Gribov's vacuum scenario.

FrediFizzx