General Relativity’s Schwarzschild solution describes a spherically symmetric gravitational field as an utterly static thing. The Space Generation Model (SGM) describes it as an absolutely moving thing. The SGM nevertheless agrees equally well with observations made in the fields of the Earth and Sun, because it predicts almost exactly the same spacetime curvature. This success of the SGM motivates deepening the context—especially with regard to the fundamental concepts of motion. The roots of Einstein’s relativity theories thus receive critical examination. A particularly illuminating and widely applicable example is that of uniform rotation, which was used to build General Relativity (GR). Comparing Einstein’s logic to that of the SGM, the most significant difference concerns the interpretation of the readings of accelerometers and the rates of clocks. Where Einstein infers relativity of motion and spacetime symmetry, it is argued to be more logical to infer absoluteness of motion and spacetime asymmetry. This approach leads to reassessments of the essential nature of matter, time, and the dimensionality of space, which lead in turn to some novel cosmological consequences. Special emphasis is given to the model’s deviations from standard predictions inside matter, which have never been tested, but could be tested by conducting a simple experiment.