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It implies that all experiments within the two frames will have identical results, provided the acceleration of the moving frame equals the acceleration of falling bodies in the rest frame. Einstein used the principle of equivalence to investigate path light the path of light in a gravitational field. Imagine light entering an accelerating rocket ship in free space.

By 1916, Einstein had developed a complete mathematical theory of gravitation, the general theory of relativity, in which the effect of a mass is to deform the geometrical properties of the space surrounding it. Using the ideas of the non-Euclidian geometers, he suggested that the path of a light ray is a geodesic—that is, light always travels the shortest time path between two points. However, while that shortest path is usually a straight line in Euclidean flat space, it is curved in non-Euclidean curved space.

A passenger measures its path as a curved line because between the time it enters one side of the ship and leaves on the other, the ship has moved forward and changed its velocity. But by the principle of equivalence, the same curved path must be measured by a physicist located in a gravitational field at rest. Therefore light falls in a gravitational field. More sophisticated arguments are needed to calculate light deflection over extended regions.