General Theory of Relativity

1. Accelerated frame of reference is described by a transformation to a curvilinear co-ordinate system.
2. Physical laws in a uniform gravitational field is identical to those same laws expressed in an accelerated frame of reference (or a curvilinear co-ordinate system).
3. Tidal force is the obstruction to replacing a non-uniform gravitational field with an accelerated frame of reference. Curvature is the obstruction to describing a non-flat surface with the rectilinear co-ordinates. There is a connection: tidal force originates from the curvature of space-time!
4. Einstein's Law of Gravitation has two parts in it: (part: 1) how the geometry of space-time changes when matter is present - namely, that the curvature expressed in terms of the excess radius is proportional to the mass inside a sphere and this law should be true in any moving system (Einstein's Field Equation) and (part: 2) how objects move if there are only gravitational forces - namely, that objects move so that their proper time between two end conditions is a maximum (Einstein's Equation of Motion). The three discrepancies from Newton's Law of Gravitation, first derived by Einstein have been experimentally confirmed: The orbit of Mercury is not a fixed ellipse; starlight passing near the sun is deflected twice as much as you would think; and the rates of clocks depend on their location in a gravitational field. Whenever the predictions of Einstein have been found to differ from the ideas of Newtonian mechanics, Nature has chosen Einstein's.