Are Photons Capable of Traveling Faster Than Light?

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In Feynman's famous book QED, he repeatedly reminds us that we must include the possibilities of photons traveling faster than light and slower than light to get the right answers. At least for short distances, short times. For longer distances, longer times, those possibilities cancel and the average speed, c, is adequate.

Is this because of uncertainty, or a fluke in the math, or some other physics?
 
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Where does he say that?
 
Feynman said:
In other words, there is an amplitude for particles to travel faster than the speed of light and no arrangement of super-position (with only positive energies) can get around that.

Feynman said:
It may surprise you that there is an amplitude for a photon to go faster or slower than the conventional speed c. The amplitudes for those possibilities are very small compared to to the contribution from speed c;in fact they cancel out when light travels long distances.

He mentions the same thing several times in QED: The Strange Theory of Light and Matter .

I found my question in another PF thread here but the answers seemed contradictory and unclear.