Pauli's Equation Solved!

Wolfgang:  "I heard some Russian guy solved my equation.  Really?"

Al:  "Yup.  He combined your equation for electrons with Maxwell's equations and solved the whole thing."

Wolfgang:  "Incredible.  How did he do it?  Since 1927 nobody, including me, was able to figure it out."

Al:  "Well, your original equation for the electron did not include the effect of electric charge."

Wolfgang: "Of course it did.  Look, the electron's charge is right there in the variable 'q' right in the middle. "

Al: "OK -- yeah, q is there. But that q represents only EXTERNAL forces on the electron.  You didn't include the force of  the electron's own field on itself. "

Wolfgang: "Of course not.  You can't do that.  If you include the self-field of the electric charge that would mean the electron would repel itself.   It would explode.   It doesn't work.  Just imagine if the left half of the electron repelled the right half.  Nonsense!  The only way out is to imagine the electron as a point charge, zero radius."

Al: "A point charge would have infinite density, infinite mass, infinite energy.  That's even more nonsensical.   Look at the example of gravity.  The gravitational self-field has no such problem.  The left half of the earth attracts the right half.  Every part of the earth feels the earth's gravity field.  Why can't an electron feel its own electric field?"

Wolfgang: "A lot of people tried that and it didn't work out.  Anyway, nobody actually believes the electron is a point particle with infinite density, but we are stuck with the point particle idea.  And thanks to Tomonaga, we can easily get rid of the infinite mass, infinite field, infinite density, infinite momentum by  'renormalization.'  Just ignore it."

Al: "So your point-charge electron still creates a field surrounding itself.  How does that electron know which part of the total electric field is due to external charge, from other electrons, and which part is due to its own charge?  Isn't there only one net electric field?"

Wolfgang: "In my equation I have to ignore the electron's self-field and self-forces."  

Al: "That would be like a person on earth ignoring the earth's gravity, yet still feeling the force of the moon's gravity.  Crazy.  Don't all the individual fields add up to one net gravity field?  We only feel the total field."

Wolfgang: "So how did this Russian guy stop the electron from immediately exploding?"

Al: "Well when he included the electron's self-field, he found that he also had to add in a new spin field."

Wolfgang: "My equation already had spin."

Al: "Yes, you have the intrinsic particle spin and the orbital spin due to particle motion, and the magnetic vector potential 'A,' but you missed the spin field 'G.'  That's the the classical vector field created by the spin (spin magnetic moment).  It's probably something like the curled magnetic field of a circularly polarized photon.

Wolfgang: "That's bullshit.  You can't just add a new field."

Al: "Well, you can't just subtract infinities either.  Anyway, the new combined equations and solutions look really nice and don't have all those quantum paradoxes, like entanglement and collapse."

Wolfgang: So the Russian equation doesn't collapse on measurement?  It's not interpreted as 'the probability of finding an electron?"

Al: "No.  This equation describes a REAL electron matter field, with distributed mass, distributed charge, and real electric and magnetic fields.  No probability.  No point particles. No wave-particle duality.  The matter field is just like the electromagnetic field.  It propagates, carries momentum, interacts with other fields.  And best of all, it gives the correct atomic spectra, and it works for atoms with many electrons.

Wolfgang:  "That's nuts!  Where can I find this guy?

Al: "Here.  Reference."

Wolfgang Pauli