I've been looking into Feynman Diagram for quite some time, and the fact that anti-particles point backwards in time after an interaction has been puzzling me. I understand this to be some convention regarding charges and conservation, yet I wish to know what does this all mean. Does the fact that the pair of particles have lines at, say $t=0$, and an interaction occurs at $t=5$ mean that both particles existed at $t=0$ and we are just measuring the effects of a future interaction?
The arrows in Feynman Diagrams are convenctions. You use them when a particle has some kind of propagator like $\Delta(t-t')$, and the corresponding antiparticle has a propagator like $\Delta(t'-t)$ (this happens, for example, for fermions). Feynman diagrams are, at the end of the day, just compact ways to write terms of a perturbation series; I'm not sure if you can attribute some real physical meaning to them.