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I apologize for my naivete

If two people are moving away from each other at a constant speed then both see the other to have been slowed, basically because the travel time of light is continuously increasing linearly.

But isn't this argument valid the other way around when two people are approaching each other at a constant velocity, as the travel time of light is decreasing linearly, don't they see each other's clock tick faster?

why? why not?

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    Look for relativistic Dopper Effect in Feynnan Lectures. Yes, approaching clock appears ticking faster. Howewer, this "faster" includes time dilation of moving clock i.e. it will be still $\gamma$ times slower than it "should be". Time dilation reduces very, very, very high frequency (or clock rate) to just "very high". –  Apr 28 '18 at 14:37
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    See my answer here: https://physics.stackexchange.com/a/307628/4993 – WillO Apr 28 '18 at 15:00
  • Thank you so much, please do answer this, what if two twins flew off in opposite directions and were reunited in a perfectly symmetric way, would they have aged same? –  Apr 28 '18 at 15:46
  • Yes. "Perfectly symmetric" means that the two worldlines have the same length. Then there is no differential aging. – timm Apr 29 '18 at 08:10

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Do not confuse the time dilation with the relativistic Doppler effect.
A stationary observer measures a time dilation against the proper time of a moving observer whether the moving frame is approaching or going away. Of course it is reciprocal, as SR (special relativity) states that every inertial reference frame is equivalent.
The well known relation is $dt = \gamma d\tau$, where $t$ is the stationary observer time, $\tau$ the proper time of the moving frame and $\gamma = 1 / \sqrt{1 - v^2/c^2}$ the Lorentz factor.
Technically the squared velocity in the formula means that the sign of the velocity is not affecting the measure.

Michele Grosso
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  • Thank you so much, please do answer this, what if two twins flew off in opposite directions and were reunited in a perfectly symmetric way, would they have aged same? –  Apr 28 '18 at 15:43
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    In that case yes, as the thought experiment is symmetric, contrary to the famous twins paradox, where only one of the twins moves forth and back to earth. – Michele Grosso Apr 28 '18 at 16:31
  • But the symmetry is only because of the acceleration, and acceleration can be completely removed from the argument https://www.youtube.com/watch?v=GgvajuvSpF4, if we assume instant acceleration, then the space time diagram looks the same –  Apr 28 '18 at 18:18
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    Accelerating can be avoided assuming three inertial clocks. Twin clock and earth clock are set to zero when the former is passing the earth clock. At some distance another clock passing by is set to the time the twin clock shows while traveling to the earth. Passing by the earth clock the differential aging is recorded. – timm Apr 29 '18 at 08:58