Consider the two animated gifs. The one on the left is a Newtonian prediction of the trajectory of a test particle around a massive star. The one on the right is the GR prediction of the trajectory with the striking difference that it predicts the precession of the perihelion.
https://en.wikipedia.org/wiki/File:Newton_versus_Schwarzschild_trajectories.gif Whether or not GR is the better theory is not the issue. What is noteworthy is that in order to compare the Newtonian and GR predictions the different trajectories are both displayed in Euclidean space. I call this the geometrical space of observation in order to differentiate it from a geometrical space of explanation. In Newtonian gravity the geometry of explanation happens to correspond with the geometry of observation but in GR the two spaces are different. My contention is that the geomety of observation is logically necessary for making sense of data regardless of the geometrical explanation expounded. Harry Harry
