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It appears that there are two different concepts of time dilation (in my amateur point of view):

  1. 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.
  2. 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.

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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.

In both examples, time is defined as what any clock measures, whether it's a light beam counting back and forth, the oscillation of a wave, the baking of cookies in an oven, or the aging of a child into adulthood. These all have to be affected in the same way by the principle of relativity -- if they were affected differently, you could use this to tell who was "really" moving, for instance.

Since you can consider any clock, we typically choose the clock that's the simplest for illustrating the point. Those are different between the two examples, but the principle isn't.

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  • $\begingroup$ Thanks for your answer! Getting back to being able to use any clock: let‘s say in the second example I define a second as the time it takes for light to travel from me (standing on the massive object) to you (floating in space). Now this time would not be affected by the object I am standing on being massive or not, right? How does this work together with the times still being different from your point of view? $\endgroup$ – frederik May 5 at 19:51
  • $\begingroup$ @frederik The equivalence principle also tells us that the clocks have to be local -- they can't be so large that they "feel" the different in gravity from one place to another. $\endgroup$ – knzhou May 5 at 19:57
  • $\begingroup$ I‘m sorry I still don‘t get it. What if I take the 2. example but define a second as the time it takes to get from my left ear to my right ear. The speed of light is constant and since both you and me are at fixed position (relative to each other), there would be no difference in time.. also the clock is not large enough to feel the difference in gravity (it is simply not affected by it). What am I getting wrong here? $\endgroup$ – frederik May 5 at 20:16

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