At the beginning of the 20th century, Cohn was one of the most respectable experts in the area of theoretical electrodynamics. He was unsatisfied with the Lorentzian theory of electrodynamics for moving bodies and proposed an independent theory. His alternative theory, which was based on a modification of the Maxwell field-equations, was compatible to all relevant electrodynamic and optical experiments known at that time, including the Michelson-Morley experiment of 1887. Cohn's electrodynamics of moving bodies was based on the assumption that light travels within the Earth's atmosphere with a constant velocity - however, his theory suffered from internal failures. While the theory predicted the negative result of MMX within air, a positive result would be expected within vacuum. Another weak point stems from the fact, that his concept was formulated without the use of atoms and electrons. So after 1905 his theory was superseded by Hendrik Lorentz's and Albert Einstein's. Regarding his own theory, he used the Principle of Economy to eliminate the known concept of luminiferous aether and argued that one can simply call it vacuum. He also maintained that one can use a frame of reference in which the fixed stars are at rest. As a heuristic concept this can be described as a material "aether", but in Cohn's opinion this would be only "metaphorical" and would not affect the consequences of his theory. He also incorporated the transformation equations x'=x-vt and t'=t-vx/c² introduced by Lorentz in 1895 into his theory, calling them the "Lorentzian Transformation". In 1905 this name was altered by Henri Poincaré into the commonly used expression "Lorentz transformation". In 1904 he compared his theory with Lorentz's mature 1904 theory, employing physical interpretations of the Lorentz transformation that were similar to those later used in Albert Einstein's special relativity in 1905. For instance, local time was described by him as a consequence of the assumption that light propagates in spherical waves with constant velocity in all directions. He also illustrated the effects of length contraction and time dilation by using moving rods and clocks. He critically remarked that the distinction between "true time" and "local time" in Lorentz's theory is artificial, because it cannot be verified by experiment. However, Cohn himself believed that the validity of Lorentz's theory is limited to optical phenomena, whereas in his own theory it is possible that mechanical clocks might indicate the "true" time. Later in 1911, Cohn accepted the relativity principle of "Lorentz and Einstein" and wrote a summary on special relativity, which was applauded by Einstein.
Publications
; Second edition Berlin 1927:
"", Himmel und ErdeXIII, 117–136 ; auch als Broschüre veröffentlicht: Physikalisches über Raum und Zeit, Berlin/Leipzig 1920, 4. Auflage.
"Faraday und Maxwell", Deutsches Museum - Abhandlungen und Berichte4, Berlin 1932.