Brian Greene: "Time travel is absolutely possible. And this is not some sort of weird sci-fi thing that I'm talking about here. Albert Einstein taught us more than 100 years ago that time travel is possible if you're focusing upon time travel to the future. And I'm not referring to the silly thing that we all age, right. We're all going into the future. Sure, I'm talking about if you wanted to leapfrog into the future, if you wanted to see what the Earth will be like a million years from now, Albert Einstein told us how to do that. In fact he told us two ways of how to do it. You can build a spaceship, go out into space near the speed of light, turn around and come back. Imagine you go out for six months and you turn around and you come back for six months. You will be one year older. But he taught us that your time is elapsing much slower than time back on Earth. So when you step out of your ship you're one year older but Earth has gone through many, many years. It can have gone through 10,000, 100,000 or a million years depending on how close to the speed of light you traveled." https://www.youtube.com/watch?v=6yMiUq7W_xI

Time travel to the future is only possible if Einstein's 1905 conclusion

"the clock moved from A to B lags behind the other which has remained at B" http://www.fourmilab.ch/etexts/einstein/specrel/www/

is true. The conclusion is non sequitur - it doesn't follow VALIDLY from Einstein's 1905 postulates. This means that, even if the postulates were true (actually the second one is false), the conclusion remains unjustified.

The following two conclusions 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.

In contrast, Einstein's INVALIDLY deduced conclusion

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

provides a straightforward prediction: The moving clock is slow and accordingly its (moving) owner can remain virtually unchanged while sixty million years are passing for the stationary system (travel into the future par excellence):

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