The common justification for time dilation in the special theory of relativity goes like this:
(Sacamol, CC BY-SA 4.0)
From Wikipedia: In the frame in which the clock is at rest (see left part of the diagram), the light pulse traces out a path of length 2L and the period of the clock is 2L divided by the speed of light:
From the frame of reference of a moving observer traveling at the speed v relative to the resting frame of the clock (right part of diagram), the light pulse is seen as tracing out a longer, angled path. Keeping the speed of light constant for all inertial observers requires a lengthening of the period of this clock from the moving observer’s perspective. That is to say, as measured in a frame moving relative to the local clock, this clock will be running more slowly. Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity:
The total time for the light pulse to trace its path is given by:
And so on. Because the distance between the mirrors is given, distance is the independent variable and duration is the dependent variable.
The left diagram shows the observation in the rest frame of light and its nominal speed, and the right diagram shows the observation in the moving frame of light and its nominal speed. The distance traversed on the left equals the height of the triangle on the right, which is given as L. The Pythagorean theorem enables one to calculate the hypotenuse D of each right triangle as the square root of (vt/2)² + L². The distance traversed in the moving frame is greater than the distance traversed in the rest frame. Distance dilates.
Since the speed of light is nominally the same for both observers, the amount of time is longer for the moving observer relative to the observer at rest. Time dilates.
Which one dilates? Time or distance? Or both? Or neither?
If the pace of light for the first or the second leg (but not both) equals zero, then for that leg the distance for both observers would be the same.