Editing Earnshaw's theorem (section)

==Effect on physics==
For quite some time, Earnshaw's theorem posed a startling question of why matter is stable and holds together, since much evidence was found that matter was held together electromagnetically despite the proven instability of static charge configurations. Since Earnshaw's theorem only applies to stationary charges, there were attempts to explain stability of atoms using planetary models, such as [[Hantaro_Nagaoka#Saturnian_model_of_the_atom|Nagaoka's Saturnian model]] (1904) and [[Rutherford model|Rutherford's planetary model]] (1911), where the point electrons are circling a positive point charge in the center. Yet, the stability of such planetary models was immediately questioned: electrons have nonzero acceleration when moving along a circle, and hence they would radiate the energy via a non-stationary electromagnetic field. [[Bohr model|Bohr's model of 1913]] formally prohibited this radiation without giving an explanation for its absence.

On the other hand, Earnshaw's theorem only applies to point charges, but not to distributed charges. This led [[J. J. Thomson]] in 1904 to his [[plum pudding model]], where the negative point charges (electrons, or "plums") are embedded into a distributed positive charge "[[Christmas pudding|pudding]]", where they could be either stationary or moving along circles; this is a configuration which is non-point positive charges (and also non-stationary negative charges), not covered by Earnshaw's theorem.  Eventually this led the way to [[Schrödinger_equation#Hydrogen_atom|Schrödinger's model of 1926]], where the existence of non-radiative states in which the electron is not a point but rather a distributed charge density resolves the above conundrum at a fundamental level: not only there was no contradiction to Earnshaw's theorem, but also the resulting [[charge density]] and the [[current density]] are stationary, and so is the corresponding electromagnetic field, no longer radiating the energy to infinity. This gave a [[quantum mechanics|quantum mechanical]] explanation of the stability of the atom.

At a more practical level, it can be said that the [[Pauli exclusion principle]] and the existence of discrete electron orbitals are responsible for making bulk matter rigid.