Ritz ballistic theory

Ritz ballistic theory is an emission theory in physics, first published in 1908 by Swiss physicist Walther Ritz. In 1908, Ritz published Recherches critiques sur l'Électrodynamique générale, a lengthy criticism of Maxwell-Lorentz electromagnetic theory, in which he contended that the theory's connection with the luminiferous aether (see Lorentz ether theory) made it "essentially inappropriate to express the comprehensive laws for the propagation of electrodynamic actions." He argued that, among its difficulties, is that there are too many solutions. Problems admit both advanced and retarded solutions, but advanced solutions are unphysical, since they allow the future to influence the past.

Ritz also rejected special relativity. He proposed to preserve classical mechanics, and modify the equations of electromagnetism instead. He argued that the advanced solution is unacceptable, but cannot be excluded based on the mere Maxwell equations. Therefore, he proposed to add another assumption, that only the retarded solution is physically allowed. He proposed a new equation, derived from the principles of the ballistic theory of electromagnetic waves, a theory competing with the special theory of relativity. The equation relates the force between two charged particles with a radial separation r relative velocity v and relative acceleration a, where k is an undetermined parameter from the general form of Ampere's force law as proposed by Maxwell. The equation obeys Newton's third law and forms the basis of Ritz's electrodynamics.

${\displaystyle \mathbf {F} ={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}r^{2}}}\left[\left[1+{\frac {3-k}{4}}\left({\frac {v}{c}}\right)^{2}-{\frac {3(1-k)}{4}}\left({\frac {\mathbf {v\cdot r} }{c^{2}}}\right)^{2}-{\frac {r}{2c^{2}}}(\mathbf {a\cdot r} )\right]{\frac {\mathbf {r} }{r}}-{\frac {k+1}{2c^{2}}}(\mathbf {v\cdot r} )\mathbf {v} -{\frac {r}{c^{2}}}(\mathbf {a} )\right]}$