http://www.aip.org/history/einstein/essay-einstein-relativity.htm John Stachel: "How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair."
If a light source emits a series of pulses the distance between which is d = 300000 km, then an observer moving with speed v = 100000 km/s towards the source measures the frequency of the pulses to be (relativistic corrections are ignored, for the sake of simplicity):
Relativity: f' = (c + v)/d = (300000 + 100000)/300000
The speed of the pulses relative to the observer is:
Rational science: c' = (f')d = 400000 = (4/3)c
Relativity: c' = (f')d' = 300000 = c
where d' is the procrusteanized distance between the pulses guaranteeing the equality c'=c, Divine Einstein, yes we all believe in relativity, relativity, relativity. In this particular case the distance is contracted:
d' = cd/(c + v) = (3/4)d
but it could be stretched as well - e.g. if the observer were moving with speed v AWAY from the source:
d' = cd/(c - v) = (3/2)d
Clearly relativity is invincible - starting from 1889 (FitzGerald performs the first length contraction), lengths always contract or stretch so that the constancy of the speed of light, c'=c, simply cannot be wrong. And once the irrational takes over and becomes official science, rational opposition disappears very quickly - nowadays there can be nothing more reasonable than shrinking or stretching lengths as long as the speed of light remains constant, Divine Einstein, yes we all believe in relativity, relativity, relativity.