Richard Feynman's 'sum of all possibilities' means that a single photon of light takes all possible paths, to arrive at the detector at exactly the same time, but in fact averages out having chosen the shortest route. It's a graph with time running vertically and distance horizontally. Simplified, the photon travels in all possible curves to reach the fixed detector in a straight line, so the vertical destination is the same regardless of the horizontal movement. So light speed is the average of all the speeds at which the photon of light that we detect has actually traveled. It's Schrodinger's cat. It's everywhere, until you look at it.
A positron, or anti-electron, is an electron with the sign reversed, including the time sign, so anti matter can be expressed in the mathematics (I believe) one way as matter moving backwards in time. At electron level, time is a very malleable thing.
Also, light-speed is measured in vacuo.
It travels slower through air or water or glass, and not at all through a brick wall. But neutrinos aren't slowed by anything.
Perhaps some very small percentage of neutrinos are refracted somehow to travel ex vacuo through these extra dimensions proposed by string theory, and an even smaller percentage re-emerge?
We'll see ...