So I have read Feynman's QED, and it seemed to me from this that, if we are to build any sort of semi-intuitive picture of what particles might be doing, we have to account for particles going faster than light in order to get the right results in experiments. Indeed, in the book we had to account for paths in which particles went back in time and appeared as their antiparticles (although it was never clear to me if this is the only way we observe 'antiparticles'- if these are necessarily particles going back in time.
But anyway, with the mention of particles going faster than light I started to think about what this theory had to say about causality. But looking up 'quantum field theory and causality' just yielded many results referring to the commutator. Having read posts like this, I understand how the vanishing commutator translates to a statement about causality, but this is just the mathematics! Usually I am all about the math and don't bother too much about physical pictures, but in this case the commutator 'explanation' really settles nothing in my mind. I am still utterly confused as to how this theory, in which we integrate over paths involving particles travelling faster than light and back in time, in order to get results that agree with experiment, doesn't suggest that causality would be violated.
Despite Quantum field theories(the relativistic kind) incorporating special relativity, the picture we have of it involves particles going faster than light? Is causality perhaps not violated because this faster-than-light travel does not carry information (as in the case of quantum entanglement)? But surely it must do if it affects the experimental results! Perhaps does the commutator argument somehow translate to a physical interpretation in our picture that would settle what seems to me to be a discrepancy?