In 1905 Einstein deduced, from his two postulates, the conclusion

"the clock moved from A to B lags behind the other which has remained at B"

That is, he concluded that the moving clock was slow and the stationary one was fast:

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/

The conclusion, asymmetrical time dilation, was non sequitur - it didn't follow from Einstein's 1905 postulates. In other words, the argument extracting the conclusion from the postulates was INVALID.

The following two conclusions (symmetrical time dilation) validly follow from the postulates:

Conclusion 1: The clock moved from A to B lags behind the other which has remained at B, as judged from the stationary system.

Conclusion 2: The clock which has remained at B lags behind the clock moved from A to B, as judged from the moving system.

Conclusions 1 and 2, in their combination, give no prediction for the readings of the two clocks as they meet at B. That is, although conclusions 1 and 2 are logically correct (do follow from the postulates), their combination amounts to nonsense. We have reductio ad absurdum par excellence: the postulates entail absurdity which means that at least one of them is false. If Einstein had been honest, he would have identified the false postulate ("the speed of light is constant") and abandoned his theory immediately.

The INVALIDLY deduced conclusion

"the clock moved from A to B lags behind the other which has remained at B"

provides falsifiable (in principle) predictions. That is, if the invalidity is unnoticed or ignored, there is no apparent reason to abandon the theory - the author is justified to present it to the scientific community and wait for experimental verifications. So in 1905 Einstein's sleight of hand (invalid deduction) saved a theory whose conclusions were absurd.

The famous "travel into the future" is a direct implication of the INVALIDLY deduced conclusion - the slowness of the moving clock means that its (moving) owner can remain virtually unchanged while sixty million years are passing in the stationary system:

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

Pentcho Valev