Theory of relativity/Equivalence principle

Einstein has been quoted as saying that the happiest thought of his life was the realization that someone in free fall from a height would not feel his own weight. At the weakest level of equivalence this infers an equivalence of inertial and gravitational mass. More generally, he realized then that the free falling observer's local physics would be equivalent to that of an inertial frame and likewise a rocket firing in deep space would experience the same physics as that local to an observer standing on a planet of the same surface g force.

He realized then that gravitation needed be mathematically described the same way as a fictitious force, an effect of noninertial or curvilinear coordinates. Gravitational sources then must impart an intrinsic curvature to the spacetime so that there is no globally rectilinear coordinate system.

In the strongest assertion of equivalence or the general principle of relativity, the general laws of physics do not depend on frame. Tensor equations valid for one frame remain valid for all frames. As such this principle of relativity told him what kind of equations he would need to model the physics of gravitation, tensor equations.

Einstein was able to satisfy these thoughts in modeling gravitation with the tensor equations known as Einstein's field equations, General relativity/Einstein equations, where the properties of matter in the spacetime described by the stress-energy tensor act as a source term in nonlinear second order differential equations for the metric tensor, and motion due to gravitation is described by the geodesic equation, a statement that the acceleration 4-vector is zero, which is also a tensor equation.