Albert Einstein, On the Electrodynamics of Moving Bodies, 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." http://www.fourmilab.ch/etexts/einstein/specrel/www/
This argument of Einstein is invalid: the conclusion ("peculiar consequence") is non sequitur - does not follow from the premises, Einstein's 1905 two postulates.
The two postulates of special relativity, true or false, entail that
the moving clock lags behind the stationary one as judged from the stationary system, and the stationary clock lags behind the moving one as judged from the moving system (SYMMETRIC time dilation).
Einstein abused logic in 1905 and "deduced" from the postulates that
the moving clock lags behind the stationary one as judged from both systems (ASYMMETRIC time dilation).
Why did Einstein abuse logic? Because SYMMETRIC time dilation, the valid deduction, is obviously absurd and entails no predictions. In contrast, ASYMMETRIC time dilation, the non sequitur, is false but not obviously absurd. It predicts TIME TRAVEL INTO THE FUTURE - the miracle that converted Einstein into a deity:
Thibault Damour: "The paradigm of the special relativistic upheaval of the usual concept of time is the twin paradox. Let us emphasize that this striking example of time dilation proves that time travel (towards the future) is possible. As a gedanken experiment (if we neglect practicalities such as the technology needed for reaching velocities comparable to the velocity of light, the cost of the fuel and the capacity of the traveller to sustain high accelerations), it shows that a sentient being can jump, "within a minute" (of his experienced time) arbitrarily far in the future, say sixty million years ahead, and see, and be part of, what (will) happen then on Earth. This is a clear way of realizing that the future "already exists" (as we can experience it "in a minute")." http://www.bourbaphy.fr/damourtemps.pdf
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