The theory of General Relativity was born in 1915 and its father is Albert Einstein. The basic postulate is that there is no preferable frame of reference what so ever. So basically the concept of an inertial observer is banned and every observer needs to be treated equally.
For example when an inertial observer looks at a spring that is making a circular orbit around him. He will write down the law of Hooke in order to describe the spring. But a non-inertial observer, moving along with the spring, will have extra terms in this equation that have nothing to do with the spring but with the fact that he is NOT inertial.
These extra terms can come from the fact that this frame of reference itself, is making a circular motion, for example, so there is a constant centripetal force that works onto this reference frame. Though the non-inertial observer moving along with the spring, and being submitted to the spring force; will write ma' = -kx. This means that the non-inertial observer is basically hanging like a block on the spring so the spring works on the observer.
But this is incorrect because there is also the centripetal force mv²/R. this force is a socalled pseudo-force for the non-inertial observer and he must write : ma' = -kx –mv²/R. This is correct because the inertial observer would have written ma = mv²/R = -kx. This is the second law of Newton for a spring in circular motion. Basically what we see here is a manifestation relativity, meaning that equations of motions are different when we change our point of view. It really depends on how we look at things. Basically a' =a -a_0 where a_0 is the acceleration of the non-inertial frame with respect to the inertial frame.
This equation states that the non-inertial force or acceleration (a') is equal to the inertial force or acceleration (a) without this influence of the motion of the non-inertial frame (-a_0). The inertial force is here -kx and it denotes the correct physical laws...
read my journal (page 8, 'the string theory part 1' entry) for more indept info
regards
marlon