Poincaré and Cosmic Space: Curved or not?

Abstract

By 1870, non-Euclidean geometry had been established as a mathematical research field but was yet to be considered relevant to the real space inhabited by stars and nebulae. It was of much less interest to physicists and astronomers than to mathematicians and philosophers. Although most astronomers took the age-old Euclidean geometry for granted, during the following decades a few of them such as K. F. Zöllner, S. Newcomb and K. Schwarzschild followed in the footsteps of the pioneer N. I. Lobachevsky by seriously considering the possibility that cosmic space might be curved. From the H. Poincaré’s conventionalist perspective the discussion was meaningless since there was no way in which observations or other empirical data could determine the geometry of space. Poincaré’s view was shared by a few astronomers, but its impact on astronomy was limited. The paper examines the question as it was discussed prior to the advent of the general theory of relativity.