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How Einstein believed that gravity bends space at the beginning of general theory of relativity?

Einstein got this idea from equivalence principle. He assumed an elevator moving in space at an acceleration equal to gravity of earth, and observed that there will be no difference between the elevator moving in outer space (where there is no gravity) with an acceleration equal to gravity of earth, and another elevator standing on earth as the persons in both elevators will feel same weight.
Now, in the elevator moving in space, if a light beam is thrown from one wall of the elevator in a horizontal direction towards another wall, the beam will not reach exactly opposite point on the other wall because the elevator would have moved up in the time the light beam would travel the width of elevator. Light beam will hit on the opposite wall at a slightly lower height than the height from which the light beam was emitted. Thus the path of light will be curved.
Situation in the elevator on earth being exactly equivalent, light path should bend in the stationary elevator also. Thus gravity should be bending the path of light. As we know light travels straight in space, so the space itself should be bending. This way Einstein reached a conclusion that space is curved in the vicinity of gravity.

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