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?
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.
