Quantum Theory Paralysed by Self-Interaction

A basic idea/postulate of quantum mechanics is that electrons as particles lack identity/individuality, and so cannot be distinguished and surveyed, as if in face-recognition all faces are the same (or everybody wears a mask) which prevents survey. 

This  menas that the interaction between fields created by electrons/particles, and electrons/particles gets muddled and so opens to self-interaction with a particle interacting with the field it itself creates, which is (very) problematic.  

The same confusion would arise if you cannot distinguish yourself as a person from other persons. 

The previous post made the remark that there is no self-interaction in Newtonian mechanics since material particles, even of the same kind, can be distinguished by having different positions and can be surveyed under continuous motion. 

To see the interplay between particles and fields in Newtonian mechanics, recall that the gravitational potential field  $\phi_y (x)$ created by a point mass at $x=y$ is given by (modulo gravitational constant) for $x\ne y$:

•  $\phi_y(x)=-\frac{1}{\vert x-y\vert}$   

with  

• $-\nabla \phi (x) = -\frac{x-y}{\vert x-y\vert^3}$ 

the gravitational force between a point mass at $x\ne y$ and the point mass at $y$ (scaling with $\vert x-y\vert^{-2}$ as Newton's familiar law of gravitation.)

For a continuous distribution $\rho (y)$ of mass the gravitational potential is given by the integral 

• $\phi_y (x)=-\int\frac{\rho (y)}{\vert x-y\vert}dy$ 

where thus the point value $\rho (y)$ gives no contribution under the integration, which signals no self-interaction; we can safely assume that $x\ne y$ thus avoiding infinities arising if $x=y$.  

In Newtonian mechanics mass particles occupy distinct positions and interact by Newton's law of gravitation without self-interaction. Particles and fields are separated in the sense that the potential field/force created by a particle does not act upon itself, only at particles with distinct positions. 

In quantum mechanics this is not so because particles lack individuality and so can occupy the same position (if spins are opposite). This means that the a particle and its field are intertwined and open to self-interaction with infinities causing severe problems. 

In RealQM electron densities do not overlap and there are no infinities.