# What is the difference between relative time dilation and absolute time dilation

I know special relativity says that traveling at high speeds (or really any speed) causes time dilation; and General relativity says that gravity also causes time dilation. I was wondering if relative time dilation (where two observers each measure the other's time to be slow) was caused not by time dilation, but instead because with the relative velocity difference between them, if they became increasingly far from each other, light would take longer and longer to reach them from the other. This would result in them both observing each other to have a slower time, though neither would necessarily experience the time dilation.

It's a sensible thought but no. "A sees B's clock running slow." , which you meet in introductory relativity explanations, is shorthand for "A sees the ticks of B's clock arrive at a certain rate. A knows that with every tick, the clock is getting further away (or, in some cases, nearer) so each light signal has further (or less far) to travel, and A compensates for that in working out the rate at which B's clock had to be ticking in order to arrive at the rate they perceive. This calculated rate is slow."

Time dilation in special relativity does not depend on the distance of the two observers. It depends on their relative velocity $v$ only, according to $\Delta t'=1/\sqrt(1-v^2/c^2)\Delta t$. This shows that $\Delta t'$ is in fact delayed compared to $\Delta t$.

In SR (special relativity) two inertial reference frames in relative motion experience the time dilation each vs. the other. The well known relation states
$\Delta t = \gamma \Delta \tau$
where:
$t$ stationary observer time
$\tau$ moving observer proper time
$\gamma = 1 / \sqrt{1 - v^2/c^2}$ Lorentz factor
$v$ relative velocity of the moving frame vs. stationary

The time dilation in SR is symmetrical between the two frames in relative motion and depends on the norm of the relative velocity. It does not depend on the sign of the relative velocity and not on the spatial distance between the observers either.

The time dilation in GR (general relativity) is caused by gravity (curvature of spacetime) and it is not symmetrical between two stationary observers at different radial distances from a massive object.