Abstract Absolute motion—motion relative to space itself—is detectable in the classical non-Euclidean geometries. Although this claim can be conveyed with a simple thought experiment, I argue that it was out of sight to the people who were best placed to take note of it in the nineteenth century, when non-Euclidean geometry was a central object of study. This is a perplexing state of affairs, and in the first part of this paper I offer an explanation for it. A central component of this explanation involves the shift from spatial to spatiotemporal thinking that had to wait for Einstein’s development of the theories of relativity in the early twentieth century. In the second part of this paper, I discuss how significant this lacuna was. If the possibility of detecting absolute motion had been recognized, it would have impacted all of the major positions in the philosophy of geometry. Indeed, some figures would have responded to it by claiming that space must be necessarily Euclidean after all.
Joshua Eisenthal (Tue,) studied this question.