I've been reading on the construct of considering antimatter as matter traveling backward in time, which seems like an useful tool. There seems to be some discussion around this concept, if antimatter is "really" traveling back in time, but from what I can tell it becomes mostly semantic/philosophical. To avoid that, for purposes of this question, I would like to dispose of the concepts of "moving" and "time." So, instead of considering an electron to be a particle moving in space, lets consider it a string existing in four dimensions of spacetime. i.e. matter/anti-matter annihilation/creation are just places this string changes orientation ala Feynman's explanation of bombardiers viewing switchbacks in a road.
With that preface, then, my question is about the interaction of antimatter and gravity. The effect of gravity on antimatter appears to still be an unknown? If we model gravity as a curvature in spacetime which affects the path of the string. Then wouldn't that argue that matter and antimatter portions of the electron/positron string would be affected the same? And, as we evaluate each 3D slice of spacetime, that electrons and positrons would both appear to "move" in the same direction due to gravity?
Am I thinking about things the wrong way or missing an argument?