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Is there a way to detect it if light was slowing down universally, i.e. if speed of light $c$ in vacuum was getting smaller?

Edit

I was directed to this question. But I did not find the answer I expected over there.

What I am asking is quite related with if speed of light governs all the other constants in the universe or not. If speed of light affected everything immediately and in the right proportion, we would not be able to detect any change. So, it looks like variance with time and variance in proportion could give us a clue on that. We could use this information as a kind of a reference point (or not, I don't know and this is why I am asking).

Do we know more fundamental anchors in the universe than the light itself that would allow us to define/detect a change on the speed of light? Have we end up with any mathematical concepts and approaches for that?

Alternatively, you can consider the question like "we require 'what' to know whether there is a universal and gradual change in the speed of light?".

Please note that I am not talking about rulers made out of atoms. If you define a meter a little bit longer, you would say speed of light decreased.

Edit 2

This question is not about any universal constant. It is on light specifically and looking for possible methods and approaches to be able to detect such a change. It is not a "what if..." question also. I am not asking if speed of light is actually changing or not, but asking about the "methods and concepts" that we can/could utilize.

Maybe it is me who could not explain the question well, but if what I am saying and what the moderation understood are the same, then it looks like moderation already concluded that speed of light in vacuum is the most fundamental part of the universe, i.e. it cannot be depending on even more fundamental concepts, that there is no way we could detect it. If the moderation was willing to inspect light as a separate entity from the potentially more fundamental aspects of the universe, they would not direct this question to a generic one and it could receive answers on possible methods and requirements specific to light.

An example to the type of an answer expected:

Assume 2D creatures living on the surface of a very large spherical universe. One of them claimed their universe was curved but they don't know. How would they test it?

If they made a very large triangle on their spherical universe, they would find that the sum of the angles would be more than 180 degrees, concluding that their universe must be curved. They utilized topology to figure it out. Alternatively, they could travel their universe in all directions on a straight line and always return to the same place, which is practically impossible but theoretically works.

In summary, this is the type of the question I am asking. It is about methods and concepts, specific to the speed of light.

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    $\begingroup$ Yes, it would be detectable. However, if metres, also universally, and in the right proportion, were also getting smaller, then it would be undetectable. Mathematically, we would say the two different spacetimes are isomorphic. In fact, because of general covariance, and again mathematically speaking, we should consider all isomorphic spacetimes at once. Physically, and very often mathematically, we just deal with one representative spacetime. $\endgroup$
    – Mozibur Ullah
    Commented Sep 23, 2021 at 18:51
  • $\begingroup$ The speed of light is directly associated with the speed of time. We could say that the speed of light determines the speed of time, or perhaps vice versa. We know this because time slows as we approach c and stops at c. Since we use the speed of time to measure many things, including c, then a change in c would not be noticable. This is the very basis of relativity, that c is the same in all reference frames. A man on a very large planet would say that his is the proper measure of time, just as a man on a very small planet would say. Neither would see any difference and both are right. $\endgroup$
    – foolishmuse
    Commented Sep 24, 2021 at 14:40
  • $\begingroup$ @foolishmuse But we might have mathematical tools to work around the time concept like Fourier Series or something more advanced. Secondly, it is like you take the relativity theorem as the ultimate truth / final point and see no need to check beyond. $\endgroup$
    – Xfce4
    Commented Sep 24, 2021 at 14:54
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    $\begingroup$ It seems like you've rejected the idea of "rulers made of atoms" and you want to instead somehow measure the speed of light without using that. But without that, I don't see a way to infer the distance between two points, and so you couldn't measure a speed. I might suggest that you try to think of a way that you could do it; if you come up with an idea, you could post a separate question asking whether it would work. $\endgroup$
    – Michael Seifert
    Commented Sep 24, 2021 at 15:23
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    $\begingroup$ @MichaelSeifert Thank you. Actually, it is true that this question was far from being clear and defining the expected answer. The moderation wouldn't read my mind, so they provided a link on how they understood it. It is also possible that this question matured and also evolved a little bit as I could not find the answer on the link and tried to find arguments about why it should not be closed. $\endgroup$
    – Xfce4
    Commented Sep 24, 2021 at 16:15

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