Like Henri Poincaré, Bucherer believed in the validity of the Principle of relativity, i.e. that all descriptions of electrodynamic effects should only contain the relative motion of bodies, not of the aether. However, he went a step further and even assumed the physical non-existence of the aether. Based on those ideas he developed a theory in 1906, which also included the assumption that the geometry of space is riemannian. But the theory was vaguely formulated and in 1908 Walther Ritz showed that Bucherer's theory leads to wrong conclusions with respect to electrodynamics. And contrary to Albert Einstein, he didn't connect his rejection of the aether with the relativity of space and time. In 1904 he developed a theory of electrons in which the electrons contract in the line of motion and expand perpendicular to it. Independently of him Paul Langevin developed a very similar model in 1905. The Bucherer-Langevin model was an alternative to the electron models of:
Hendrik Lorentz, Henri Poincaré and Albert Einstein. in which the electrons are subjected to length contraction without expansion in the other direction
and the model of Max Abraham, in which the electron is rigid.
All three models predicted an increase of the electron mass if their velocities are approaching the speed of light. The Bucherer-Langevin model was quickly abandoned, so some experimentalists tried to distinguish between Abraham's theory and the Lorentz-Einstein theory by experiment. This was done by Walter Kaufmann who believed that his experiments confirmed Abraham's theory, and disproved the Lorentz-Einstein theory. But in 1908 Bucherer conducted some experiments as well, and obtained results which seem to confirm the Lorentz-Einstein theory and the principle of relativity. With exceptions like Adolf Bestelmeyer with whom Bucherer had a polemical dispute, Bucherer's experiments were regarded as decisive. But it was shown in 1938 that all those experiments of Kaufmann, Bucherer, Neumann etc. showed only a qualitative increase in mass, but were too imprecise to distinguish between the different models. This lasted until 1940, when similar experimental equipments were sufficiently accurate to confirm the Lorentz-Einstein formula, see Kaufmann–Bucherer–Neumann experiments and Tests of relativistic energy and momentum. Bucherer was the first who used — during some critical remarks on Einstein's theory — the expression "Einsteinian relativity theory / theory of relativity". This was based on Max Planck's term "relative theory" for the Lorentz-Einstein theory. And in 1908 Bucherer himself rejected his own version of the relativity principle, and accepted the "Lorentz-Einstein theory". Later, Bucherer criticized general relativity in some papers. However, this criticism was rejected because Bucherer misinterpreted Einstein's equivalence hypothesis.
