Einstein's fundamental but invalid (the conclusion does not follow from the premises) argument:

http://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ECTRODYNAMICS OF MOVING BODIES, A. Einstein, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."

Herbert Dingle noticed the invalidity and asked a fatal question:

http://blog.hasslberger.com/Dingle_S...Crossroads.pdf
SCIENCE AT THE CROSSROADS, Herbert Dingle, p.27: "According to the special relativity theory, as expounded by Einstein in his original paper, two similar, regularly-running clocks, A and B, in uniform relative motion, must work at different rates. (...) How is the slower-working clock distinguished?"

Of course, Dingle's question is rhetorical - the slower-working clock cannot be distinguished on the basis of Einstein's 1905 postulates alone. The postulates entail that, as judged from the respective system, either clock runs slower than the other. That is, for an observer in the moving clock's system, the stationary clock at B lags behind the moving clock; for a stationary observer, the moving clock lags behind the stationary clock at B.

Einstein's famous conclusions that made him a superstar, "moving clocks run slow" and "travel into the future is possible", are based on two flaws. Initially Einstein advanced his false constant-speed-of-light postulate, which allowed him to validly deduce that:

moving clocks run slow, as judged from the stationary system.

Then he illegitimately dropped the second part of the above conclusion and informed the gullible world that:

moving clocks run slow, that is, travel into the future is possible.

Referring to the gullible world, Einstein once said: "I am sure that it is the mystery of non-understanding that appeals to them...it impresses them, it has the colour and the appeal of the mysterious":

http://plus.maths.org/issue37/featur...ein/index.html
John Barrow FRS: "Einstein restored faith in the unintelligibility of science. Everyone knew that Einstein had done something important in 1905 (and again in 1915) but almost nobody could tell you exactly what it was. When Einstein was interviewed for a Dutch newspaper in 1921, he attributed his mass appeal to the mystery of his work for the ordinary person: "Does it make a silly impression on me, here and yonder, about my theories of which they cannot understand a word? I think it is funny and also interesting to observe. I am sure that it is the mystery of non-understanding that appeals to them...it impresses them, it has the colour and the appeal of the mysterious." Relativity was a fashionable notion. It promised to sweep away old absolutist notions and refurbish science with modern ideas. In art and literature too, revolutionary changes were doing away with old conventions and standards. All things were being made new. Einstein's relativity suited the mood. Nobody got very excited about Einstein's brownian motion or his photoelectric effect but relativity promised to turn the world inside out."

Pentcho Valev