From EP we have that gravity is not a force but a pseudo force, i.e an inertial force due to a gravitational field an accelerating a body independantly of its mass, in other words, the trajectory of any body only depends on its initial position and velocity, but not on its composition/mass.
- Pseudo forces are well described by newtonian mechanics in the accelerated (non-inertial) frames formalism, so why not gravity? Pseudo forces are taken into account by a change of coordinates, as for example fictitious forces on earth are just the acceleration terms coming from the curvature of spherical coordinates. Therefore these pseudo forces could also be described by a metric and a connection and everything in a manifold...
But then why do we need to describe spacetime as a curved manifold and geometrizing (curvature,metric...) gravity? Can't we stick with the (old newtonian gravity+SR) approach, what makes it false?
- Is it that this old approach does not fulfill SR? But then SR describes dynamics, so can't we describe gravity as a force in SR (it doesn't work?)? Is it because a newtonian grav. field acts instantaneously (faster than speed of light)? In the end, my question is:
How much of GR formalism is derived/constrained from the EP alone? What's different from (newtonian gravity(contains EP)+SR), why is it better? Or are curvature+metric+connection vs Newton gravity (fictitious force)+SR two ways to describe the same physics?