After working as a Gymnasium (school) teacher, he became Privatdozent for theoretical physics at the University of Königsberg in 1920, where he eventually became professor extraordinarius in 1926.
Historians Don Howard and John D. Norton suggest that Einstein may have failed to adequately acknowledge Kretschmann's contribution.
Einstein wrote concerning Kretschmann's objection: "Although it is true that every empirical law can be put in a generally covariant form, yet the principle of relativity possesses a great heuristic power....Of two theoretical systems, both of which agree with experience, the one is to be preferred which, from the point of view of the absolute differential calculus is the simpler and more transparent.
Let one express Newtonian mechanics four-dimensionally in the form of generally covariant equations and one will surely be convinced that the principle of relativity excludes this theory from the practical, though not the theoretical, viewpoint."
In a letter of 1927 to Karl Försterling Arnold Sommerfeld wrote favorably of Kretschmann's work in relativity and the statistics of electrons, but said that he needed to get a different teaching position (get away from Königsberg) in order to be able to do more research.
This argument initially had led Einstein in 1913 for a time to reject generally covariant theories, because a region of space/time without forces would undermine determinism or unique extension of trajectories.
It has been claimed also that Kretschmann discovered that the conformal geometry of General Relativity corresponds to the light cone structure, a point rediscovered by and extensively exploited by Hermann Weyl, and since then developed by Jürgen Ehlers and collaborators.
He had a number of objections which were mostly not very well conceived, but he claimed, in particular, that in the usual derivation of the Boltzmann equation one had made unjustified use of perturbation theory.