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

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).

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)?

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.

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.

Previously read:

Similar questions:

Why does speed of light have to be constant?

The Speed of Light

• This question is kind of broad and brings in a lot of different issues and questions. I think you could reduce your confusion and narrow things down a lot by considering the following: (1) It's not meaningful to talk about a value of $c$ that varies from one point in spacetime to another: physics.stackexchange.com/q/34874 . Popularizations describe it that way, but they're wrong. (2) The $c$ in relativity is not really the speed of light, it's more like a conversion factor between space and time units.
– user4552
Nov 5 '19 at 1:13
• Please ask one question, not ten. Nov 5 '19 at 1:35
• Not only is this question too broad, but it is based on so many misconceptions that virtually every statement in it is incorrect - the speed of light is not constant anywhere, but locally, and is direcrly affected by gravity. Nov 5 '19 at 2:45
• The science of astronomy is based on the assumption that the laws of physics are the same everywhere in this universe. So far, our observations seem to be consistent with this assumption. Nov 5 '19 at 18:18
• @TCooper "why isn't this taken into account in any interstellar calculations?" - It is taken as the Shapiro delay in the Solar system. In cosmology, distant space can expand 3+ times faster than light, so we would measure the speed of light there to be much different. In interstellar calculations, the Shapiro effect just doesn't contribute enough to worry about, but it is there. Locally the speed of light is always the same, because measuring a slower speed by using an equally slower clock always yields the same result. Nov 5 '19 at 21:41

## 3 Answers

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).

• Honestly, reading the link helped me as much/more than your explanation. I think what I was really trying to get at was, why isn't the Shapiro time delay accounted for on smaller scales, if it has that effect over a long distance, why isn't there a proportional effect over a short distance - why doesn't the speed a photon is traveling change very slightly as it passes Mars, Jupiter, etc(even in a vacuum)? and if it does, why it's defined as constant. Nov 5 '19 at 17:43
• @TCooper You might want to google the effects of refraction as light travels through a medium which, even when that "medium" consists of very little more than other light arriving from different directions, can reverse some of its apparent effects. Most good descriptions of Eddington's 1919 observational proof of GR will describe how this can happen. Nov 5 '19 at 18:39

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.

• or that electric charge and Planck $\hbar$ to vary in such a way to keep $\alpha$ constant Nov 5 '19 at 15:41
• Fine structure constant - en.wikipedia.org/wiki/Fine-structure_constant - Wikipedia Nov 5 '19 at 17:33
• Also +1. Thanks for taking the time, the concise explanation, and a huge rabbit hole to jump down Nov 5 '19 at 17:40
• The speed of light is just a conversion factor between spatial and temporal distance. It really is just one light second per second as a unit. The Planck constant $\hbar$ is also a conversion factor between momentum and position, or the uncertainty thereof, with $\Delta p\Delta q\ge\hbar/2$ As a result both these constants are in better units of measure unit elements. Only the electric charge might vary, and with renormalization group flow it does. The fine structure constant is $\alpha~\simeq~1/137$ and at the LHC energy it is $1/128$. Nov 6 '19 at 1:25

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.

• I'm not sure if I buy this answer, although I do understand and appreciate where it is coming from. If the speed of light was not constant throughout the galaxy, wouldn't we first need to verify that there are no other laws of physics we do not understand first before we conclude what this answer says? i.e. wouldn't we have to determine that the effect is not due to just being at a different place in the universe? Nov 5 '19 at 2:42
• I guess it depends on the extent to which you are willing to accept that the universe is the way it is because of the laws we do understand. Have you read any treatments of cosmological models in which the speed of light is nonconstant over time? Nov 5 '19 at 6:55
• I have not. Just a thought about your answer. Nov 5 '19 at 10:09
• A take I would've never managed/found... thank you. I'll definitely have to research this more Nov 5 '19 at 17:41
• @Edouard you're comment makes me think most of my confusion comes from modern popularization of physics. I'm thinking the attempts to push these complex topics into layman's terms is what led to my question, and so many other similar on this forum. Just taking the time to write it out after researching, and trying to be open minded reading these answers... I feel like I have a much better grasp. But until now I've never read Einstein's mention of our localities top speed vs another. Literally would've nipped this question in the bud/given me a different point to research from. Nov 7 '19 at 18:20