[epluribus_2]

Yes, you see a red or blue shift, but the light still appears to be going at 3X108 m/s, no matter how fast you are going. Since light always appears to go at this speed, traveling at high velocity causes distances and time to distort.

unless what is happening is the "appearance" of distances and time distort, not the reality. Light will always "look" like it's going 3*10^8 but may actually change speed in a reality we cannot measure. (by observation that requires light)

[Redcloak]

The heart of Einstein's theory is that light is always observed moving at 3x10⁸ m/s no matter the observer's location. Our perception of time and distance changes to compensate for this. Thus c apears constant whether you're moving or stationary.