Again, this if fine for an orbit for example, it does not explain how a particle will accelerate, it also does not explain momentum, because when that particle accelerate it exchanges momentum with another particle - it does not give momentum to the "geodesic".
And explain please what information is not captured by saying "Gravity is a force that acts on energy". What nuance is lost by saying that?
> it also does not explain momentum, because when that particle accelerate it exchanges momentum with another particle - it does not give momentum to the "geodesic".
No one has said that it should. The geodesic is merely the straight path that the particle must follow when it _isn’t_ exchanging momentum with other particles.
> And explain please what information is not captured by saying "Gravity is a force that acts on energy". What nuance is lost by saying that?
You can’t explain time dilation that way, or length contraction.
Quoting from the abstract of The Motion of Point Particles in Curved Spacetime <https://web.archive.org/web/20151203142700/http://relativity...>
> This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle.
Note especially that the charged particle won’t actually follow the geodesic. Because the synchrotron radiation carries away some energy, the particle will be continually pushed off of the geodesic; it will spiral inwards instead of orbiting forever.
Then there would be a fundamental difference between curved and straight geodesics which would be a contradiction to the Einstein Equivalence Principle. How do physicists explain that contradiction?
It seems like the point is that the particle is actually not accelerating when it follows the one path through spacetime. It only accelerates when it's stopped by something (e.g. the surface of the earth).