Is the speed of light measurement dependent on local clocks?

Hello I want to ask the following questions:

If Clock A is undergoing only a natural gravitational time dilation, and possesses 0 rate of change in time dilation, and if it is measuring seconds at a different rate than Clock B, which for our purposes is a clock at higher gravitational potential where the seconds are different - what if:

Clock A was used in a measurement of the speed of light, and the value for this clock reads 1 second within which light travelled 299,792,458 meters. However, Clock B, which we will assume to have 0 relative velocity with Clock A, being in a higher gravitational potential, reads 1.000001 seconds passed.

If you take the "distance traveled by light / the time passed for Clock A", you will get a different value than "distance traveled by light / the time passed for Clock B".

Of course, you could take the reverse, where you have, say, 1 second passing for Clock B and .99999 seconds for Clock A

Am I getting this right?
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 Recognitions: Gold Member Science Advisor Staff Emeritus Light only travels at c locally. The only speed of light you can directly measure is the speed of light moving through an apparatus moving with you, and that speed will always be c. On the other hand, if an observer at high altitude watches some experiment operate at lower altitude, she might conclude that the speed of light "down there" is slower than the speed of light "up here." However, to an observer "down there," the speed of light is still c, and that's really the only meaningful measurement. - Warren

 Quote by chroot Light only travels at c locally. The only speed of light you can directly measure is the speed of light moving through an apparatus moving with you, and that speed will always be c. On the other hand, if an observer at high altitude watches some experiment operate at lower altitude, she might conclude that the speed of light "down there" is slower than the speed of light "up here." However, to an observer "down there," the speed of light is still c, and that's really the only meaningful measurement. - Warren
So the measurement by Clock B (the clock outside) wouldn't be meaningful then? It is only meaningful to measure the speed of light with respect to proper time? When (if at any time) is it meaningful to measure the speed of light with respect to coordinate time?

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Is the speed of light measurement dependent on local clocks?

Well, I guess I shouldn't say such measurements are not meaningful -- I just mean that no apparatus will ever measure the speed of light as anything but c.

You can't really measure the speed of light "down there" without putting an apparatus "down there." In doing so, that apparatus will always measure c. You could claim that the speed of light is slower "down there," because the apparatus's entire operation appears time-dilated to you, but someone comoving with the apparatus would disagree. So, we simply say the speed of light is always locally c.