I apologise for the very non-technical nature of this question. I am new to QED and perhaps am interpreting things in the wrong way, but I'll ask anyway, and hopefully someone can provide a non-technical response.
There are lots of questions on here about virtual particles travelling faster than the standard speed of light such as this one. However, in Feynman's book QED, The Srange Theory of Light and Matter, it seems that Feynman is not saying that virtual photons can travel faster than light (which is what these questions are asking about), but that there is a probabilty that (real) photons will travel faster (or slower) than $c$ but that these probabilities cancel out over longer distances. (I have added quotes at the bottom to support this).
Is this, like the virtual photons, just a mathematical construction and not to be taken as reality? From reading the rest of the book I would guess not since Feynman uses words like appear frequently when describing what light appears to do.
As a secondary question, Feynman also seems to suggest that photons do not only travel in a straight line. Instead, they can take all paths, but the probabilities of these are very low and once again cancel out.
Is Feynman describing this in a different way from usual? Or am I misinterpreting what he is trying to say? Or is it really true that over short distances photons can travel faster than light (and seemingly violate relativity)?
Here is a quote from Feynman's book (p89):
"...there is also an amplitude for light to go fsster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn't only go in straight lines; now, you find out that it doesn't only go at the speed of light!"
Later he goes on to say:
"The amplitudes for these possibilities are very small compared to the contribution from speed c; in fact, they cancel out when light travels over long distances."