If antiparticles are particles moving back in time, would messages from the future be possible? So, here's the idea: if Feynman's interpretation of antiparticles is true and antiparticles are particles moving back in time, then they are carrying with them information from the future, no? If that's the case, then we could build two terminals, that communicate using antiparticles, maybe positrons? Then someone could write a message on one terminal, send that message using these positrons, and the other terminal would then receive a message from the future.
I know the interpretation isn't really believed in by most physicists, but if we assume it is true, isn't future-to-past/present messaging possible?
 A: No.
The Feynman-Wheeler interpretation of antiparticles as particles going backwards in time is a heuristic description of how antiparticles propagate.  It is not possible, in actuality, to disentangle the interactions of electrons and positrons entirely, in much that same way that it is not possible to distinguish the effects of one electron from another; electrons are identical, and both the electrons and positrons are manifestations of the same underlying quantum field.  (Schwinger, who was one of the people, along with Feynman, who independently worked out quantum electrodynamics, was very critical of people taking the particle and antiparticle lines in Feynman diagrams to literally and interpreting them as actual trajectories, when they were actually shorthand for manifestations of a single local field.)
One upshot of this is that, if you try to measure particles going backwards in time—that is, by arranging the state of a virtual positron today and seeing if it could transmit backwards the information you observed yesterday—is never possible.  There is always interference between the electrons moving forward in time and positrons moving backwards in time.  The upshot is that if you construct a physically observable quantity, it always depends on the combination of electron and positron behavior in such a way that the influence of any preparations you make today are limited to your own future light cone.  That is, the preparations you make cannot affect what happens in your own past, nor can information about them in the future propagate faster than the speed of light (since that would indicate backwards-in-time signaling in some other potential observers' rest frames).
