What happens if the clock is moving vertically, like in an elevator, instead of horizontally?
Going “up” fast enough would shorten the tock part because the bottom mirror would be closer to the position the top mirror was in when the light beam left it on the return journey.
Hey, mabye I’ve discovered how to “warp” time by taking the clock with me and moving fast enough in the vertical direction!
Nahhh.
As the elevator's upward speed approached the speed of light, it would take longer and longer for the upward traveling light pulse to reach the upper reflector. But on the way down, the light pulse could only approach the midway point. (i.e., if the elevator could theoretically travel at light speed, it would meet exactly at the mid-point) And so the longer duration of the upward pulse would increasingly win out over the limited duration of the lower directed light pulse and time dilation would still grow to infinity for the complete round trip (full tick-tock).