First-order Relativity: From Fresnel’s 1818 “drag” coefficient to Lorentz’s 1895 “local time” followed by Poincare’s 1900 interpretation, and finally up to Einstein’s 1911-1912 spatially flat metric

In his 1905 paper on relativity theory, Albert Einstein acknowledged the importance of what we call below “first-order relativity” (in V / c ). Our aim with this paper is first to revisit the origin of “first-order relativity” which began with Fresnel’s problem regarding Arago’s prism experiment. Then, we emphasize the historical importance of the 1895 Lorentz Transformations, based on the explanation they provide of the impossibility of detecting the Earth’s motion through the ether, as well as their acceptance by the scientific community, and their “relativistic” interpretation given in 1900 by Henri Poincare. Finally, we show that a better understanding of these transformations and of their physical consequences (especially length contraction) allows us to bring retrospectively a new look to Einstein’s 1911-1912 introduction of a spatially flat metric.