It appears that there are two different concepts of time dilation (in my amateur point of view):
- Time delation due to relative velocity. Let‘s say a second is measured by the time it takes for light to travel from my left ear to my right ear and vice versa. If you, now, think of yourself as being stationary and I am moving relative to your position, light must travel a longer distance to get from my left ear to my right ear (because I am moving). As the speed of light is constant, it takes more time for light to get from my left ear to my right ear and so does my time appear to be ticking more slowly from your point of view.
- With gravitational time dilation. Let‘s say I am standing on a massive object and you are watching from a great distance. The light that travels from me to you is at the constant speed of light but due to gravitation, it appears red-shifted to you. So from what I have read, the explanation for time dilation in this case is that while it takes let‘s say one second for a light wave to go from crest to crest at my position on the massive object, it takes the wave two seconds to go from crest to crest when it reaches your position. So what I can achieve in one second of my time actually takes two seconds of your time an thus my clock appears to be ticking more slowly from your point of view.
Now my question: in both examples, time is defined differently. In the first example, a second is defined as the time it takes for light to get from one position (my left ear) to another (my right ear). In the second example, a second is defined as the time it takes to get from one crest to the other. So what actually is a clock measuring?
Also, I hope I‘m not asking a duplicate question. I just started with physics (not studying but in my free time) and I am not really in the position to tell if two question are equivalent in their essence.