Quantum Mechanics and Antimatter

Special relativity has some protection built in for that, right? It says this can only happen for things that are really, really far apart. We call these space-like events instead of time-like events. You can't reorder those events just by going faster or slower. So then how does that figure into antimatter? Well, you might think that this makes the universe nonsense because if different people can see events ordered different ways, does not just break causality? Does that mean you can eat an apple before it's grown? And so on.