It is possible to write down Maxwell's equations in any coordinate system, and predict the future in the same way. But in order to formulate electromagnetism in an arbitrary coordinate system, one must introduce a description of the space-time geometry which is not tied down to a special coordinate system. This description is a metric tensor at every point, or a connection which defines which nearby vectors are parallel. The mathematical object introduced, the Minkowski metric, changes form from one coordinate system to another, but it isn't part of the dynamics, it doesn't obey equations of motion. No matter what happens to the electromagnetic field, it is always the same. It acts without being acted upon. In General Relativity, every separate local quantity which is used to describe the geometry is itself a local dynamical field, with its own equation of motion. This produces severe restrictions, because the equation of motion has to be a sensible one. It must determine the future from initial conditions, it must not have runaway instabilities for small perturbations, it must define a positive definite energy for small deviations. If one takes the point of view that coordinate invariance is trivially true, the principle of coordinate invariance simply states that the metric itself is dynamical and its equation of motion does not involve a fixed background geometry. Einstein's resolution In 1915, Einstein realized that the hole argument makes an assumption about the nature of spacetime: it presumes that there is meaning to talking about the value of the gravitational field (up to mere coordinate transformations) at a spacetime point defined by a spacetime coordinate — more precisely, it presumes that there is meaning to talking about physical properties of the gravitational field, for example if it is either flat or curved (this is a coordinate independent property of the gravitational field), at a spacetime point. By dropping this assumption, general covariance became compatible with determinism. While two gravitational fields that differ by an active diffeomorphism look different geometrically, after the trajectories of all the particles are recalculated, their interactions manifestly define 'physical' locations with respect to which the gravitational field takes the same value under all active diffeomorphisms. (Note that if the two metrics were related to each other by a mere coordinate transformation the world lines of the particles would not get transposed; this is because both these metrics impose the same spacetime geometry