 Another way of expressing Einstein’s view is to say that, in Newtonian mechanics and special relativity, rotation is “absolute” because the transformations between inertial frames (Galilean or Lorentzian) preserve rotational states. Thus the “absoluteness” of rotation arises precisely from singling out one type of frame, by one type of transformation, instead of allowing arbitrary transformations and arbitrary frames. Einstein held that this epistemological insight had a natural mathematical representation in the principle of general covariance, or the principle that the laws of nature are to be invariant under arbitrary coordinate transformations. More precisely, what this means is that coordinate transformations are no longer required (as in the affine spaces of Newtonian mechanics and special relativity) to take straight lines to straight lines, and to preserve further metrical structures appropriate to each theory, but only to preserve the smoothness of curves (i.e. their differentiability). The general theory of relativity was intended to be a generally covariant theory of space-time, and its general covariance was intended to express the general relativity of motion (Cf. Einstein 1916, section 3). The extent to which the theory realized Einstein’s original aims remains a topic of philosophical debate. (Cf. Related Entries:  “space and time: the hole argument,” “Einstein’s philosophy of science”.) 