I have always been taught, that we can tell how fast a galaxy is moving away from us by it's amount of doppler shift. If the atoms in the stars of those galaxies are moving very fast (i.e. that galaxy is moving faster than our galaxy is moving), relativity would have a bigger effect on them. Time would run slower for them (i.e. their electrons have to slow down). Now, Wouldn't THAT also effect the wavelengths of the emitted light? That is to say, the electrons jiggle slower than they normally would if they were not moving so fast, so they emit lower frequency waves. Is THAT taken into account in the amount of doppler shift? Is my thinking off?