What tells us the speed of light is constant in another galaxy?

Question

I've read, and I hope to keep reading, so please send me all your links, and I apologize in advance if this is a duplicate, or non-mainstream physics question as the speed of light is widely accepted as a constant. While it's only a slight variation of numerous questions on this site - several of those listed below - I do believe it's unique. Or the specific answer is hidden, at least for a layman (that's me).

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Why do we assume the speed of light is constant outside our solar system and/or galaxy and/or some other [relatively] local construct?

Or another way I might try to phrase this - why doesn't gravity affect light? I know it's not supposed to have mass, so it wouldn't - but it also seems like the general consensus is that it does have mass, we just can't measure it (like electrons), and it's considered so negligible in our equations we can ignore it.

To bring one example of my question not being answered in the below sources: While you read the detailed and well-explained answer here, isn't every value used in the explanation derived from the assumption that the speed of light is constant throughout the universe? Couldn't every one of those calculations be performed and provide "satisfactory" answers even if light was varying based on some level? Why not?

Going to the derived from Maxwell's equation's response I've also seen a lot - Why wouldn't changes in gravity also affect these? Am I taking the statement "It's all relative" too literally here?

Further, I just thought back to the fact light can't escape a black hole, which means it is affected by gravity, right? So why is that effect ignored in all our modern equations? Is it really nothing/negligible when measuring the distance of something like another galaxy (or the particle horizon for that matter)?

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From the reading I've done I'm guessing I have some fundamental misunderstanding... seems to always be the answer to these questions. I'm thinking maybe something regarding the way I'm thinking about time, or I'm somehow excluding it's relativity? Really don't know (obviously) But if someone can help me out, I'd appreciate learning more about this.

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EDIT: I appreciate all the answers, I chose my accepted answer based on what helped me wrap my mind around this most easily. I'm also thinking of re-framing this as a new, more focused, question. I spent too long writing this and it got away from me/began to become multiple questions in one.

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Previously read:

https://www.sciencenews.org/article/speed-light-not-so-constant-after-all http://www.desy.de/user/projects/Physics/Relativity/SpeedOfLight/speed_of_light.html http://www.desy.de/user/projects/Physics/ParticleAndNuclear/constants.html http://www.desy.de/user/projects/Physics/ParticleAndNuclear/photon_mass.html https://www.livescience.com/29111-speed-of-light-not-constant.html https://en.wikipedia.org/wiki/List_of_electromagnetism_equations

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Answer 1

The most certain way is that we can observe the atomic transitions in distant galaxies. They are the same as what we observe here. This indicates the fine structure constant $\alpha=\frac{1}{4\pi\epsilon_0}\frac{e^2}{\hbar c}$ is the same everywhere. This then lends support for the speed of light being a universal constant.

Answer 2

Theoretically, you have seen the other answers.

Experimentally, really nothing tells us.

The speed of light is c in vacuum, when measured locally. It is very important to understand the difference between local and non-local measurements.

For non-local measurements, there is the Shapiro delay.

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

But that does not say anything about the speed of light in a local measurement (in a very different gravitational field like in your case).

To prove what you are asking, we would need to make a local measurement somewhere far from Earth, where the gravitational potential is very different, like in your case in another galaxy, or at least near our Sun. This has not been done yet.

If we could travel somewhere like near the Sun, and measure the speed of light there locally, then that would be proof that the speed of light is c in vacuum, when measured locally in gravitational zones very different from the Earth's.

You are basically asking why doesn't gravity affect light? It does, but the speed of light is c in vacuum when measured locally. The speed of light varies only in non-local measurements (relative to a different gravitational zone).

Answer 3

One reason to accept the postulate that the speed of light does not vary from place to place (that is, the laws of physics have no spatial dependence) is if it did, then momentum would not be conserved. This in turn would mean that an object could suddenly and for no reason acquire or lose some arbitrary velocity in some random direction- something we do not observe in the universe we inhabit.

Answer 4

The short answer is the cosmological inflation theory.

The more analytical:

The speed of light $c$ in a vacuum is given by the equation:

$$ c=\frac{1}{\sqrt{\varepsilon_0 \mu_0}} $$

where $\varepsilon_0$ and $\mu_0$ the permittivity and permeability of vacuum space.

It is not possible these parameters to had the same constant values at the first milliseconds of the Big Bang since there was no vacuum space and space was filled with energy therefore a much more condensed Universe.

image source: https://en.wikipedia.org/wiki/Big_Bang

Within one second after the BB the observable Universe expanded (including spacetime) more or less to its current size today. This means that the Universe expanded with a much larger speed than c value at the first second of creation therefore the speed of light during this period must have been much larger than the current value c. After this 1 second the speed of light was more or less as its current value today $c$.

One may think that since the Universe is continuing expanding with an exponential rate the speed of light should become slower over the millennia? However, Dark energy phenomenon is keeping the volumetric energy density of vacuum space constant! Therefore the speed of light remains unchanged and a constant c everywhere in our observable Universe.

These two phenomena of inflation and dark energy result in only a minuscule error of ~1 second in the calculation of the red shift of galaxies and their distance from our home planet which is negligible over a ~13.8 Byrs period.

As long as the vacuum energy density remains the same everywhere in the observable Universe (including within galaxies) expect the speed of light at the vacuum to be at the constant value $c$.

Nevertheless, if in the far future the vacuum energy density will for whatever reason decrease it is possible the speed of light in a vacuum $c$ to actually drop:

$$ \Lambda=8 \pi \rho_{v a c} G / c^4=\kappa \rho_{\text {vac }} $$

where $\rho_{v a c}$ is the vacuum energy density currently a constant.