# Does two people heading towards each other see each other's clock getting faster?

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?

• 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, 2018 at 14:37
• See my answer here: physics.stackexchange.com/a/307628/4993 Apr 28, 2018 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?
– user218113
Apr 28, 2018 at 15:46
• Yes. "Perfectly symmetric" means that the two worldlines have the same length. Then there is no differential aging.
– timm
Apr 29, 2018 at 8:10

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.

• 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?
– user218113
Apr 28, 2018 at 15:43
• 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. Apr 28, 2018 at 16:31
• But the symmetry is only because of the acceleration, and acceleration can be completely removed from the argument youtube.com/watch?v=GgvajuvSpF4, if we assume instant acceleration, then the space time diagram looks the same
– user218113
Apr 28, 2018 at 18:18
• 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, 2018 at 8:58