Do photons change velocity instantaneously? Any object traveling at c is observed as traveling at c in all reference frames. When a photon travels through a vacuum at c, all reference frames observe it traveling at c.
When a photon passes through a medium, it's speed is less than c. The moment that it begins to slow down, there is a reference frame in which the photon is stationary, as all reference frames at a speed of less than c (perceived in another reference frame) are equally possible and valid. 
This would imply that if a photon were to change speed at all, in some reference frame, the photon is traveling at c, and then its velocity immediately goes to zero. Is this the case?
 A: The "slowing" of light in a medium can be entirely explained using a classical wave-based approach.  An incoming EM wave wiggles the electron clouds around the atoms in the material.  These electrons clouds re-emit a much weaker EM wave having a very small amplitude.  This re-emitted wave is 90-degree phase shifted from the original wave but superposes with the original wave.  This results in a tiny backward phase shift in the net field of the wave at each atom.  After traversing many atoms, the original wave plus the superposed re-emitted waves yield a net wave that appears to be travelling slower in the medium.  Nothing is slowing down.
Another classical example:  Consider a long lightweight rope tied on one end to a heavy metal chain.  If you send a wave pulse down the rope, the speed of the pulse changes at the interface with the chain to a much slower (and narrower) wave pulse, but there is no deceleration taking place.
This is not to say that actual photons are waves in the classical sense, but they should NOT be thought of little bullets having mass which can be accelerated.  The interaction of photons with actual particles having mass does appear to take place locally, giving them the appearance of having a definitive position when detected, as if they were particles.
