Removing classical singularities by use of quantum mechanical sources

TL;DR

This paper demonstrates that quantum mechanical effects can eliminate classical singularities in electromagnetic and gravitational fields around a bound electron, leading to bounded fields and finite densities at small scales.

Contribution

It shows how quantum sources modify classical fields, removing singularities in electromagnetism and gravity at sub-electron Compton wavelengths.

Findings

Maxwell and Einstein tensors become bounded at small scales.

Quantum effects produce a finite magnetic field of several Tesla.

Apparent mass density near the singularity is approximately 2 kg/m^3.

Abstract

For distances large relative to the electron Compton wavelength, the Maxwell and gravitational fields from a bound electron in its groundstate are essentially those from a rotating, charged, massive point particle. For distances small relative to the electron Compton wavelength, the corresponding Maxwell fields and General Relativity metric, Riemann and Einstein tensors become bounded, showing that, for this example, quantum effects remove the corresponding classical singularities in electromagnetism and General Relativity. The asymptotic magnetic dipole field from the bound electron produces a constant magnetic field of several Tesla, aligned along the spin axis of the electron, at the singularity position. The corresponding apparent mass density from the gravitational field from the bound electron is about 2kgm$^{-3}$, at the singularity position.