Quick question: Suppose I hold two initially synchronized clocks on earth and throw one up and catch it when it comes back down. Now my (small amount of) knowledge of GR tells me that the proper time on the thrown clock should be maximized since it was on a geodesic. However, this seems like the twin paradox, and in the twin paradox, the thrown clock shows less time than the stationary clock. What am I wrong about? Thanks in advance!