Brian Greene teaches ASYMMETRIC time dilation: The moving clock is slow, the stationary one is fast:
Asymmetric time dilation is non sequitur - doesn't follow from Einstein's 1905 postulates. The postulates, true or false, entail SYMMETRIC time dilation: Either clock is slow as judged from the other clock's system.
Why does Brian Greene abuse logic? Because SYMMETRIC time dilation, the valid deduction, is an obvious absurdity. It says that, if two clocks are initially stationary and synchronized, then move towards one another and finally meet, either clock lags behind the other as judged from the other clock's system. Einstein knew that SYMMETRIC time dilation is absurd and fraudulently "deduced" ASYMMETRIC time dilation in 1905:
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/
It is easy to see that the valid deduction (SYMMETRIC time dilation) doesn't, but the non sequitur (ASYMMETRIC time dilation) does predict TIME TRAVEL INTO THE FUTURE - the miracle (more precisely, idiocy) that converted Einstein into a deity:
"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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