Some remarks about general relativity principle

Abstract

In most textbooks that introduce the General Relativity (GR), it is often written that this theory is a generalization of Special Relativity (SR) in which Einstein extends the principle of relativity to all motions. Students who specialize in another branch of physics or mathematics, even after degree did not understand that general covariance is profoundly different from the special relativity principle. This short note reviews this fundamental difference that is, in our opinion, all too often not analyzed in depth. We emphasize that it can be didactically very useful for students to realize how the request of covariance does not necessarily imply a principle of relativity.