Just for the record, here is what Einstein wrote.
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Wenn ich einem Lichtstrahl nacheile mit der Geschwindigkeit c (Lichtgeschwindigkeit I am Vacuum), so sollte ich einen solchen Lichtstrahl als ruhendes, raümlich oszillatorisches elektromagnetisches Feld wahrnehmen. So etwas scheint es aber nicht zu geben, weder auf Grund der Erfahrung noch gemäss den Maxwell'schen Gleichungen.
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Here is an English translation.
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If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations.
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If he were traveling at c behind the beam of light, then he would not be catching up to it. He said "nacheile", which means "lag". So it should be "If I lag a beam of light...". He didn't say "gehe mit" (go with) or "reise mit" (travel with) that beam of light. So he hasn't explained just how he thought he could experience those (for him) stationary oscillations, and he hasn't explained just how he might have transformed those Maxwell equations to that moving frame of reference. But this is just a remembrance of something from his early thoughts, before his theory of relativity. It would have been about 1895 and (he says) he was sixteen.
I think he agrees with the topic originator. It would be just like standing still (relativity principle), so the light beam can't be at rest even in this frame of reference. Relativity theory won't permit this (traveling at lightspeed)to be a frame of reference at all.
*autobiography from Schilpp Library of Living Philosophers
