A standard particle is not a point in 4D, it's a track, if it's locally static (compared to you for example) it's still churning happily along the t-dimension.

A standard particle is not a point in 4D, it's a track, if it's locally static (compared to you for example) it's still churning happily along the t-dimension. In GR, the 4D spacetime is curved, so when you burn along the t-dimension locally, you might be seen as moving along one of the spacial dimensions as seen from afar (like, when you observe another guy falling down a building or observing dust getting swooped up by a black hole).