QED: Electron Spin & Magnetic Moment - Questions & Answers

[Urmi Roy]

Hi,
I've been doing Quantum Electrodynamics,and I've just finished the third chapter of QED-the strange theory of light and matter,by Richard Feynman.

I have just three questions in regard to this...

1. what does Feynman mean when he says that any electron or photon can be polarized relative to the dimensions of space and time, and so there are 4 possible states of polarization- X,Y,Z,T...(I'm specially confused as to what the T here is..if it's time,how can an electron be polarised in the time direction?)

Also,he says that electrons can exist in 4 conditions of polarization...but since polarization is basically the spin of an electron...and an electron can only have a spin of +/- 1/2 (only 2 possibilities),...this doesn't make sense.

(pg 120, QED-the strange theory of light and matter)

2. What does Feynman mean by the magnetic moment of an electron...he calculates it by adding up the probabilities of all the ways a photon from a magnetic field can interact with an electron...how can interpret this?

( Third chapter, QED-the strange theory of light and matter)

3. Unlike electrons,(which may change their polarization states while traveling from one point to another in space-time),why are photons not able to change their polarisation states after being emitted from their sources?

 

[Mentz114]

That's four questions. I think I can help with this one

electrons can exist in 4 conditions of polarization...but since polarization is basically the spin of an electron...and an electron can only have a spin of +/- 1/2 (only 2 possibilities),...this doesn't make sense.

Yes, but +/- 1/2 in in 2 directions makes 4.

2. What does Feynman mean by the magnetic moment of an electron...he calculates it by adding up the probabilities of all the ways a photon from a magnetic field can interact with an electron...how can interpret this?

Magnetic moment is defined to be how something reacts to a magnet field. Like a compass needle feeling a force in a magnetic field because it has a dipole magnet moment. So measuring the interaction between an electron and a magnetic field is exactly calculating its magnetic moment. Nothing to interpret.

I think the other questions are worth asking. Maybe someone else can explain.

 

[Urmi Roy]

That's four questions. I think I can help with this one

Yes, but +/- 1/2 in in 2 directions makes 4. .

I'm sorry,but I didn't exactly understand what you meant by two directions ( I must be sounding really dumb,but please forgive me)...I thought that the + and - represented the clockwise and counterclockwise directions...so we have already accounted for the two directions...also,does this not apply to photons(Richard Feynman says that for photons,the probability ampliudes for two of the possible conditions cancel out..I didn't understand why.)

P.S I'm sorry to be squeezing in more stuff into this thread...but I just recalled,(in relation to the interaction between an electron and a magnetic field),that there is a slight ambiguity as to if an electron performs photon exchanges only in a magnetic (or electric field)...if there is no external influence,does the electron still perform photon exchanges?

 

[Mentz114]

The +/- 1/2 is a magnitude. The spin axis is also aligned in a direction.

 

[Urmi Roy]

The spin axis is also aligned in a direction.

...any two mutually perpendicular directions, if I'm not wrong.

 

[Mentz114]

Yep, which makes the 4 states you're looking for.

that there is a slight ambiguity as to if an electron performs photon exchanges only in a magnetic (or electric field)...if there is no external influence,does the electron still perform photon exchanges?

Real photons can be spontaneously emitted but I'm not sure if that's relevant. The interaction with a field obviously needs a field to be there.

 

[Urmi Roy]

Real photons can be spontaneously emitted but I'm not sure if that's relevant. The interaction with a field obviously needs a field to be there.

Thanks Mentz114 for all your answers...actually I was pondering over the fact that Richard Feynaman calls an electron that moves from one place to another without emitting or absorbing photons as 'ideal' and adds up the probability amplitudes for the electron to emit or absorb photons only when calculating the 'magnetic moment'...so I thought that it might be that we add the probabilities for the photon exchanges only in a field.