I was trying to say three things: 1) it still somehow works like other fundamental forces since it derives from asking invariance under a local symmetry group

I was trying to say three things: 1) it still somehow works like other fundamental forces since it derives from asking invariance under a local symmetry group 2) it is different from other forces since the symmetry group associated to it is directly symmetries of space-time (rather than some internal U(1) vector bundle like maxwell or SU(3) nuclear strong force) 3) in weak fields like on earth it mostly reduces to a conservative force driven by a gravitation potential (what you experience while climbing a mountain) 3 bis) like (mostly) anything in physics there is a duality i.e. there are regimes where you can consider it as a force, and there are regimes where you cant. read the textbook, i know it's a 1000 pages but it's a great introduction :)