If two events are simultaneous in one reference frame, are they simultaneous in all reference frames? Please provide thorough qualitative explanation
If blue light is going at speed $c$, with red light emitted in opposite direction, at speed $-c$, would't the speed of red light in the frame of someone moving along the blue light, be $2c$? Is this a violation of SR? Any help is appreciated.
(1) If 2 events have a space-like separation, then there is a reference frames where they are simultaneous (and also frames where A is before B and B is before A).
(2) If we work just on the collinear line of the photon's motion (or light pulses if you prefer)--then any observer confined to this line with any boost sees them moving away from each other at $2c$. Now if you boost orthogonal to that with $\gamma=10^9$--those photons are going to be nearly collinear, with a very low relative velocity.
BTW: this answer had no math in it--but @dmckee is right: you're going to need it.
Two events can be simultaneous in other frames. It depends the position of the events and the orientation of the movement between the frames. But no two events would be simultaneous in all possible frames.
Taken literally the answer to the question is no, simply because no massive object can travel alongside the blue light.
However, the wavefronts of light emitted in two diametrically opposite directions can be said to be moving at
2crelative to one another. It's not a violation of SR, because relativity deals with the speed of the interaction between two objects, not between two wavefronts of light.
In your example, any object which received any light from your source (whether it be the red or the blue light), will still have received it at
cfrom the source.