Leibnizian resonances
pp. 99-118
in: J.C. Smith (ed), Historical foundations of cognitive science, Berlin, Springer, 1991Abstract
This is the gist of the principle of equivalence: In order to account for the equality of inert and gravitational mass within the theory, it is necessary to admit non-linear transformations of the four coordinates. That is, the group of Lorentz transformations and hence the set of the “permissible” coordinate systems has to be extended. What group of coordinate transformations can then be substituted for the group of Lorentz transformations? Mathematics suggests an answer which is based on the fundamental investigations of Gauss and Riemann: namely, that the appropriate substitute is the group of all continuous (analytical) transformations of the coordinates. Under these transformations the only thing that remains invariant is the fact that neighboring points have nearly the same coordinates; the coordinate system expresses only the topological order of the points in space including its four-dimensional character. The equations expressing the laws of nature must be covariant with respect to all continuous transformations of the coordinates. This is the principle of general relativity.
