So Inversion was a scientific development that helped reverse objects. Eventually they get all the pieces to build a machine that allows you to invert people. But it's a closed loop meaning that what happens, always happens. If you invert, and try to go back and change something, it always happens how it did when you weren't inverted and everything you do was already factored in the original timeline.
From how I understood it, every time a person enters inversion, there can be multiple versions of self at the same event.