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I have read these questions:

Is there any paper analyzing the validity of Relativity in expanding space?

The Great Atomic Clock of Kansas

photons in expanding space: how is energy conserved?

Is an atomic clock itself affected by gravity?

https://en.wikipedia.org/wiki/Speed_of_light

https://en.wikipedia.org/wiki/Second

And it made me curious.

The definition of c depends on the second.

The definition of second depends on the atomic clock.

So the local definition of speed of light depends on the atomic clock.

Now we know that the gravitational field has an effect on the atomic clock's speed, relatively when viewed from a far away observer, it will tick differently (Shapiro delay).

But none of these answers were talking about the effects of expanding space on an atomic clock.

The vacuum in the voids of the inter galaxy cluster space, where gravity has no effect, and dark energy is dominant, and space is expanding, in those regions, we do not know how atomic clocks tick.

I do not know whether atomic clocks would tick differently in those regions of space.

Question:

  1. Do we know of atomic clock tick differently in expanding space (relatively), has there been any experiment on this?

  2. will this affect the speed of light there (relatively)?

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  • $\begingroup$ $c$ is a defined constant (since the early 1980s), so it does not depend on the second. $\endgroup$ – Kyle Kanos Jul 4 '18 at 18:21
  • $\begingroup$ what is its value? it is m/s. the meter is defined in c so it depends on the second. If the atomic clocks would change ticking, it would change. How else would you measure it? I understand what you are saying, but that precludes the constancy of atomic clocks (gravitational field). Relativity says that c is different in different gravitational fields (Shapiro). So that exactly means what I say, that the speed of light is relative depending on the gravitational field, that defines the ticking of atomic clocks. Atomic clocks tick differently near the Sun. $\endgroup$ – Árpád Szendrei Jul 4 '18 at 18:29
  • $\begingroup$ So they might tick differently in expanding space. $\endgroup$ – Árpád Szendrei Jul 4 '18 at 18:29
  • $\begingroup$ The questions can be "How does expanding space change time dilation?" $\endgroup$ – Árpád Szendrei Jul 4 '18 at 18:29
  • $\begingroup$ As I've mentioned earlier and Kyle Kanos confirms here, the local speed of light does not depend on the definition of the second. The speed of light is not a measured value, but a predefined number c = 299,792,458 m/s = 1 ls/s (whole numbers with no fractions). A remote speed of light depends on the difference in the atomic clocks locally and remotely (and also on the length contraction). The space expansion does indeed cause a time dilation and affects the remote speed of light: en.wikipedia.org/wiki/Redshift#Expansion_of_space (the time dilation and redshift are closely related). $\endgroup$ – safesphere Jul 5 '18 at 3:37
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Do we know of atomic clock tick differently in expanding space (relatively), has there been any experiment on this?

Yes. The light we receive from far away galaxies was emitted by atoms. Whereby the measured redshift is due to the relative increase of the scale factor between emission and absorption. So from our perspective those atoms tick more slowly accordingly. The same is true for a supernova far away, the full process seems slower compared to a supernova in our vicinity. So anything which happens far away including peculiar velocities e.g. the speed of light seems slower in our accelerated expanding universe from our view.

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  • $\begingroup$ Thank you. I understand the atomic clock part, and emission and absorption scale. And supernova process. Now the speed of light should be faster in expanding space no? And in the voids where there is no gravity field, just dark energy, speed of light should be faster then c (when viewed from earth)? $\endgroup$ – Árpád Szendrei Jul 6 '18 at 0:00
  • $\begingroup$ In contrast to galaxy superclusters supervoids can be considered as “gravity hills” (in the sense of lower gravitational potential) which means that photons crossing a supervoid should experience something like a negative Shapiro time delay. Then yes as seen from outside the void the lightspeed should be faster in its center. But I’m not really sure, because if one applies Newtons shell theorem then the potential at the rim is the same as in the center. $\endgroup$ – timm Jul 6 '18 at 17:15

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