By 1912 Einstein was hot on the heels of a new theory of gravity that would incorporate his strong equivalence principle. By calling on this principle, he realized, he could avoid dealing with gravity as a force altogether. Move in the right way, by free-falling, and you don't feel gravity: in an inertial frame, you're weightless and gravity drops out of the picture. But Einstein also realized that the Lorentz transformation of special relativity wouldn't carry over to a more general setting because the way you have to move to cancel out gravity is different in different locations. What he needed was some mathematical way to stitch together local inertial frames in different places so that gravity canceled out everywhere. Although he wasn't yet sure what form his new theory of gravity would take, he did know this: If all accelerated systems are equivalent [with respect to the laws of physics], then Euclidean geometry cannot hold in all of them.