It follows logically from Einstein's 1905 postulates that, if two clocks are in relative motion, either clock is slow as judged from the other clock's system (SYMMETRIC time dilation). Here is an obvious implication:

Time SPEEDS UP for any traveler.

That is, any traveler who checks stationary clocks against his spaceship's clocks will find stationary clocks slow and his spaceship's clocks FAST. This also means that the traveler sees himself aging FASTER than stationary people.

Some (very few) Einsteinians obey logic and teach the correct deduction:

David Morin, Introduction to Classical Mechanics With Problems and Solutions, Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [...] For the entire outward and return parts of the trip, B does observe A's clock running slow..." http://www.people.fas.harvard.edu/~djmorin/chap11.pdf

"The situation is that a man sets off in a rocket travelling at high speed away from Earth, whilst his twin brother stays on Earth. [...] ...the twin in the spaceship considers himself to be the stationary twin, and therefore as he looks back towards Earth he sees his brother ageing more slowly than himself." http://topquark.hubpages.com/hub/Twin-Paradox

High priests in the Einstein cult (including Einstein himself) almost universally abuse logic and teach 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. Here is an obvious implication:

Time SLOWS DOWN for the traveler.

High priests teaching the asymmetric-time-dilation hoax:

Brian Greene: https://youtu.be/Q1y3YnPgaY4?t=1157

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..." http://www.fourmilab.ch/etexts/einstein/specrel/www/

Albert Einstein 1911: "The clock runs slower if it is in uniform motion..." http://einsteinpapers.press.princeton.edu/vol3-trans/368

Richard Feynman: "Now if all moving clocks run slower, if no way of measuring time gives anything but a slower rate, we shall just have to say, in a certain sense, that time itself appears to be slower in a space ship." http://www.feynmanlectures.caltech.edu/I_15.html

Brian Greene: "If you're moving relative to somebody else, time for you slows down." https://m.youtube.com/watch?v=QnmnLmwBmfE

Neil deGrasse Tyson: "...Einstein's special theory of relativity, which gives the precise prescription for how time would slow down for you if you are set into motion." http://abcnews.go.com/Entertainment/back-future-30th-anniversary-neil-degrasse-tyson-talks/story?id=32191481

Jim Al-Khalili: "Einstein showed that for anything (or anyone) travelling at speeds approaching that of light...time literally runs more slowly." https://scienceinschool.org/2009/issue11/timetravel

Why do high priests abuse logic and teach asymmetric time dilation, knowing that it does not follow from Einstein's 1905 postulates? Because symmetric time dilation doesn't, but asymmetric time dilation does imply TIME TRAVEL INTO THE FUTURE - the miracle (idiocy) 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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