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What is going on there to make it appear that light is slower than $c$ ?

Here is the popular science news article:

Speed of light not so constant after all; Pulse structure can slow photons, even in a vacuum

and here is an arXiv article that motivated it:

Photons that travel in free space slower than the speed of light

Does this mean that photons may not be massless?

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    No. The effect is not attributable to a photon mass. – JEB Dec 04 '18 at 02:15
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    The article is confusing but the paper is much more detailed and complex. The photons interact with materials before traveling in the vacuum, this may explain the time difference. – PhysicsDave Dec 04 '18 at 02:44
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    photons build up by superposition of their wavefunctions the classical EM wave .. The slowness of light in materials is interpreted in different paths that the individual photons take within the lattices , longer distances because of interactions meaning slower overall average,. The structuring of the beam described has happened with some interactions, and although interesting as an effect, it is similar. – anna v Dec 15 '18 at 19:39

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