Once, I read that Einstein founded the special relativity theory by imagining how an observer moves at the speed of light.
How does this thought experiment work? How to reach from this imagination to the relativity of time?
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John Norton at Pitt relates the story quite nicely.
In Einstein's own words:
After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with a 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. . . on the basis of experience. . . . From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how, otherwise, should the first observer know, that is, be able to determine, that he is in a state of fast uniform motion?
In other words, assuming both
(1) that all motion is relative and
(2) that it's possible for an observer to travel at $C$
leads to an impossibility:
(3) that there is a reference frame in which a beam of light is just a "spatially oscillatory electromagnetic field at rest" i.e, a motionless electromagnetic wave.
Since he judged (3) to be impossible, then either (1) or (2) or both must be wrong. His insight was that (2) is wrong, that the speed of light is not attainable.
http://www.ivorcatt.co.uk/x41w.pdf This idea is undermined by the pulse, or step, travelling unchanged down a transmission line (a circular loop of coaxial cable) at the speed of light. It happens in a USB cable, which Einstein did not know about. Ivor Catt