Self-Interacting Electron: QED Horror

Audio Feed Back Can Ruin Your Loud Speakers

Schrödinger's equation (S) describes the Hydrogen atom as a negative electron charge density $\phi (x)$ in the Coulomb potential field $\frac{1}{\vert x\vert}$ generated by a positively charged point kernel at $x=0$, with electron potential energy (combined with "kinetic energy" measured by $\vert\nabla\phi\vert^2$)

• $\int\frac{\phi^2(x)}{\vert x\vert}dx$     

of finite size. This is a prefect model of an electron bound in a Hydrogen atom, as basic building block of the Universe. 

In classical electrostatics the electrical field $E$ generated by a point charge (scaling like $\vert x\vert^{-2}$) appears to have infinite total energy in the sense that the integral 

• $\int \vert E\vert^2 dx$

diverges. This is viewed with suspicion because it suggests that an electron as a point charge has infinite energy. The troubling question without answer is to what extent the electron interacts with the electric filed it has generated, so called self-interaction or feedback. 

Even worse, infinite electron energy is a feature of both Dirac's equation (D) and Feynman's Quantum ElectroDynamics QED both supposed to describe the electron as the ultimate achievement of modern physics. Both Dirac and Feynman viewed this to be a deeply troubling aspect, but to save modern physics from collapse Feynman invented a technique of "renormalisation" getting rid of the infinities captured in Feynman diagrams. 

We know the phenomenon of audio feedback and its dangers, as with feedback in general. The system my go berserk. Electrons do not go berserk.

Real Quantum Mechanics RealQM extends (S) to atoms with more than one electron as a system of non-overlapping electron charge densities interacting by Coulomb potentials without self-interaction. Each electron has an individuality by occupying a specific domain in space, and as such is interacting with the kernel and the other electrons through Coulomb potentials. 

There is no self-interaction. This is like a group of people interacting with each other without anyone interacting with her/himself.

So we have two theories for the electron. (S) extended to RealQM for electrons bounded in atoms without infinities. QED for "free electrons" with self-interaction and infinities. 

The electrons in an atom can by shifting configuration back and forth interact with electromagnetics of light outside the atom through the Abraham-Lorentz recoil force and so generate an absorption/emission radiation spectrum as described here. There is no feedback in this system, only balance like in a good audio system. 

QED seems to say nothing about atoms and atomic radiation and so may be overrated as the jewel of modern physics. 

• With quantum physics, who needs drugs? (Richard P. Feynman in QED: The Strange Theory of Light and Matter)

Also listen to Wolfgang Pauli in his Nobel Prize Lecture in 1946 about his Exclusion Principle: 

• At the end of this lecture I may express my critical opinion, that a correct theory should neither lead to infinite zero-point energies nor to infinite zero charges, that it should not use mathematical tricks to subtract infinities or singularities, nor should it invent a 'hypothetical world' which is only a mathematical fiction before it is able to formulate the correct interpretation of the actual world of physics.
• From the point of view of logic, my report on Exclusion Principle and Quantum Mechanics has no conclusion. I believe that it will only be possible to write the conclusion if a theory will be established which will determine the value of the fine structure constant and will thus explain the atomistic structure of electricity, which is such an essential quality of all atomic sources of electric fields actually occurring in nature.

Pauli died in 1958 and did not live to experience QED with its infinite zero-point energies and mathematical tricks.

Connecting to the previous post on the concept of self-energy of an electron as particle, recall that in Newton mechanics there is no self-gravitation, only gravitational between different masses as in RealQM.