I have come to realize something that never seems to get discussed in popularized presentations of Einstein’s theory of relativity: It implies at least a fifth dimension to the make-up of the universe we experience.
In the case of a single dimension, a linear universe, the only possible difference in location and/or movement has to be on a straight line, ahead or back. Deflection from that straight line, to one side or the other, results only from the existence of a second dimension to form a planar universe. Euclidian geometry is based on the two dimensions of the plane and, of course, it breaks down at the larger scale of our whole earth, a sphere that curves into a third spacial dimension. In space differences in location and/or movement can occur ahead or back, to one side or the other, and above or below. Yet in reality, movement also requires time and existence may be separated by duration. Time gives our universe a fourth dimension to permit possible differences in location and/or movement ahead/back, side to side, above/below, and in time. Thus, we sense our most familiar experience of our universe.
Yet Einstein tells us that the entirety of space/time curves at mass. Gravity is curved space/time. If space and time curve, they must curve into ... an aspect of existence other than space and time themselves. Only the existence of yet a fifth dimension to our universe could accept curvature of space and time together. Without such a fifth dimension space/time could not curve. Thus, we must live in a universe defined by a minimum of five dimensions.