Your original post was wrong in saying "acceleration is not handled by SR for the simple reason that acceleration is mitigated by curved space-time" because an object's path is not only determined by the curvature of spacetime (and your later posts seemed to argue that it was). Anyway, in practice it's standard to treat a negligibly-curved spacetime as equivalent to a flat one--otherwise the only flat spacetime would be one devoid of all particles (even without force fields, their masses would curve it slightly), and the equivalence principle couldn't be used in any finite-sized region.Ok, so we go from I am wrong to it's neglible.
I'm not sure about the technical details of how spacetime curvature is quantified or whether it is proportional to "the amount of energy applied to accelerate an object" even in pure GR without other forces. (Since everything moves on geodesics in pure GR, does it even make sense to talk about an object 'accelerating' if its path is always locally inertial?) But put it this way: if an object is accelerated by non-gravitational forces it takes far less energy than it would to alter its path in a similar way using only gravity. You can use the muscles in your legs to jump upwards, but you'd need a vast density of energy over your head to pull you away from the Earth at the same speed based only on the gravitational force. Also, consider the fact that a force fields will curve spacetime the same way for everyone, so why is it that two particles with identical masses and initial positions and velocities but different charges will move in different directions in an electromagnetic field? Why is it that a neutrino can travel straight through the entire planet as if it were empty space, while a proton or electron cannot? If objects' paths were determined only by spacetime curvature, then even if particles still generated fields with the same energy densities as real fields in our universe (but with the fields having no other effects besides curving spacetime), then every particle would be even more "ghostly" than the neutrino, since the neutrino does at least interact with matter via the weak nuclear force (but the electromagnetic and strong forces have no effect on it, apart from how they curve spacetime of course).MeJennifer said:So let me get this right; are you claiming that the total amount of energy applied to accelerate an object is not equal to the amount of space-time curvature induced?