Photon and matter

>Electromagnetism tells us that electromagnetic waves changes its velocity of propagation according to the medium it is propagating into.
Correct.

>Special relativity tells us that massless particles must propagate at c
Wrong. special relativity tells us that all observers agree on the velocity of things traveling at c. Classical field theory tells us that only massless things can do this, and what the value of c is. Electromagnetism is a classical field theory that predicts the value of c can vary from place to place with the presence of matter.

Jesus Veeky Forums why the fuck are you struggling with this

>1. Electromagnetism tells us that electromagnetic waves changes its velocity of propagation according to the medium it is propagating into.

The wave is always travelling at c. As was mentioned earlier in the thread the reason that it is effectively slowed is because its absorbed by the particles in the material and then remitted. This has a time dependence.

2. Special relativity tells us that massless particles must propagate at c

They do

Its not wrong faggot, massless particles MUST travel at c, a rapid Google search will tell

You have shitty reading comprehension.
When I said this was wrong:
>Special relativity tells us that massless things must propagate at c
I wasn't referring to the fact that massless things move at the speed of light. I said you were wrong about what special relativity has to say on the matter. Special relativity is a theory of coordinates. It predicts that all inertial coordinate systems, regardless of momentum with respect to one another, will measure the speed of light to be the same. The existence of massless things and their motion is understood without the use of special relativity (Maxwell).

Special relativity is not properly equipped the talk about massless things by themselves. This is illustrated by the fact that a transformation which boosts the velocity of one coordinate system to be moving at the speed of light relative to another does not exist in the theory. The purpose of special relativity is to investigate the dynamics of massive and massless things with respect to different observers.