<p>The speed of light is a defined constant so cannot vary - or at least it's variation cannot be measured since it is used to define the measurement system. However <span class="math-container">$c^2 = (\mu_0 \epsilon_0)^{-1}$</span> and so both <span class="math-container">$\mu_0$</span> and <span class="math-container">$\epsilon_0$</span> could vary in opposite directions.</p>
<p>If <span class="math-container">$\epsilon_0$</span> varied then this would fundamentally change the spectrum due to the various transitions in any given element. For example, the energy levels of a hydrogen atom are
<span class="math-container">$$E_n = \frac{m_e e^4}{8h^2 \epsilon_0^2 n^2}\ , $$</span>
where all the symbols for the fundamental constants are conventional. If <span class="math-container">$\epsilon_0$</span> changed, this would mean the separation between energy levels and hence the intrinsic frequency/wavelength of the associated spectral line would change. But all the spectral lines would change their wavelengths by the same factor, so this isn't diagnostically useful and would just lead to a different redshift measurement.</p>
<p>Further, a variation in <span class="math-container">$\epsilon_0$</span> could be disguised by a variation in <span class="math-container">$h, e$</span> or  <span class="math-container">$m_e$</span> and so we arrive at a fundamental issue that the only &quot;constants&quot; it is meaningful to discuss the variation of, in either time or space, are the fundamental <em>dimensionless</em> (i.e. they don't have units) constants like the <a href="https://en.wikipedia.org/wiki/Fine-structure_constant" rel="noreferrer">fine structure constant</a>.</p>
<p>However, there <em>is</em> physics and diagnostically observable consequences that <em>are</em> sensitive to a variation in the fine structure constant. For example, the fine-structure (spin-orbit) splitting between transitions with the same principle quantum numbers does depend on the fine structure constant and can be measured in distant galaxies.</p>
<p>People have been trying to constrain such variations, either by measuring the separations of various atomic transitions in distant galaxies or by looking at the history of radioactive decay in geological uranium deposits (see <a href="https://en.wikipedia.org/wiki/Fine-structure_constant#Potential_time-variation" rel="noreferrer">here</a> for a summary). The evidence at present suggests there may be some variation at the level of about 1 part in a million on geological timescales or looking back to redshifts of 3 (corresponding to around 10 billion years in the past). The results are still under debate.</p>
<p>These levels of variation would have no impact whatsoever on the interpretation of cosmological redshift.</p>

CC BY-SA 4.0
2022-06-15T18:48:00.667Z
So if I understand correctly : there are (possibly) known variation in (what I call "the speed of light" but it could be any other variable used to compute the speed of faraway galaxy) but the variations aren't significant enough to fundamentally change the conclusion. correct ? thank you for the answer and the links, I never heard about "fine structure constant" so it will be a good read.
ker2x
CC BY-SA 4.0
2022-06-16T01:31:41.780Z
The speed of light is only a defined constant if you're measuring using SI units.  If you're using some other system of measurement (eg. the foot-pound-second system), it's perfectly possible to measure the speed of light.
Mark
CC BY-SA 4.0
2022-06-16T05:40:14.620Z
@Mark To my understanding, the official definition of the foot is a certain fraction of the meter, so $c$ in ft/s is also fixed definitionally. Of course, one could revert to past standards and base a unit system on, say, a prototype bar, and OP's question could be rephrased as asking whether the prototype bar's length (in meters) changes over time/space. Ultimately, that's a question about the distance and time scales, relative to $c$, of the fundamental interactions of the matter comprising the prototype, which is exactly what fundamental dimensionless constants like $\alpha$ encode.
jawheele
CC BY-SA 4.0
2022-06-16T14:33:09.253Z
ISTR that non-constant speed of light was an alternate hypothesis to dark energy at one time.
Barmar
CC BY-SA 4.0
2022-06-15T16:30:39.240Z
2022-06-15T16:30:39.240Z
ProfRob
<p>A very naive question related to galaxy recessional velocity. In simple term : <em>The further away it is, the faster it goes.</em></p>
<p>And we know it's redshifting because we can mesure a change in frequency of the hydrogen &quot;line&quot;. Sure, fine. Make total sense to me.</p>
<p>But :</p>
<ol>
<li>Is it a situation of &quot;we assume the speed of light in vacuum is contant until proven otherwise&quot; ? (which is a fair assumption)</li>
<li>Or what if it simply was the speed of light changing over distance/time ? Are there some distant &quot;slow&quot; galaxy that help us guarantee that this redshift is due to speed and not due to a change in the speed of light &quot;constant&quot; ?</li>
<li>or we know it's not constant but this change is a known variable and has been taken into account when calculating recessional velocity.</li>
</ol>

CC BY-SA 4.0
2022-06-15T13:46:02.473Z
Redshift is a change in the colour (due to relative velocities). Change in the speed-of-light is a change when something arrives here. How do you see them correlated? You can simply test that the colour is unaffected by the speed of light... look out of your window, and open it and look at the same thing(s). It's the same colour (unless your window is coloured itself)
planetmaker
CC BY-SA 4.0
2022-06-15T23:06:34.283Z
@planetmaker what I meant (using improper wording) was that the light could have changed in frequency ("slowing down") over billions of year / light-year and that the redshift isn't due to speed but to distance. some kind of "old photon are naturally redshifting" (it sound ridiculous said like that but I'm trying my best here). Unless there is a proof that it is indeed redshifted due to speed. I was asking if such a proof existed or if we just assume the light frequency never change over time/distance/space-witchcraft (until proven otherwise).
ker2x
CC BY-SA 4.0
2022-06-16T06:00:55.197Z
@ker2x ProfRob's answer is great, but it's worth commenting that your idea of "redshift due to distance" isn't totally off the mark. In fact, the cosmological redshift you seem to be referring to is better described as due to distance than speed. This is because the redshift's underlying mechanism isn't really relative "movement", per se, as in the usual doppler effect (or spatiotemporal variations in fundamental constants), but rather the universe's expansion, i.e. that the universe is stretching over the light's time of flight. If it starts farther, it flies longer and stretches more.
jawheele
CC BY-SA 4.0
2022-06-16T06:35:21.737Z
"Tired light" is a totally different question (that has been asked about before on Physics SE and Astronomy SE). It is disproved by, for example, the time dilation observed in supernova light curves with redshift.
ProfRob
CC BY-SA 4.0
2022-06-16T14:09:36.593Z
Light can also be "slowed down" due to gravitational lensing.  It's of course not *actually* slowed down, it's just travelling a longer path due to space/time curvature, so it takes longer to get here.  This was evidenced by detecting e.g. the same supernova at multiple different times because it was occurring behind a large gravity well from a black hole in between.
Darrel Hoffman
<hubble-constant>
How sure are we about the speed of light in vacuum in deep/far space?
ker2x
# How sure are we about the speed of light in vacuum in deep/far space?

(Asked by: username_0 on 2022-06-15)

A very naive question related to galaxy recessional velocity. In simple term : *The further away it is, the faster it goes.*

And we know it's redshifting because we can mesure a change in frequency of the hydrogen "line". Sure, fine. Make total sense to me.

But :

1. Is it a situation of "we assume the speed of light in vacuum is contant until proven otherwise" ? (which is a fair assumption)
2. Or what if it simply was the speed of light changing over distance/time ? Are there some distant "slow" galaxy that help us guarantee that this redshift is due to speed and not due to a change in the speed of light "constant" ?
3. or we know it's not constant but this change is a known variable and has been taken into account when calculating recessional velocity.

**Tags:** hubble-constant
> **Comments:**
> **username_1**: Redshift is a change in the colour (due to relative velocities). Change in the speed-of-light is a change when something arrives here. How do you see them correlated? You can simply test that the colour is unaffected by the speed of light... look out of your window, and open it and look at the same thing(s). It's the same colour (unless your window is coloured itself)  
> **username_0**: @planetmaker what I meant (using improper wording) was that the light could have changed in frequency ("slowing down") over billions of year / light-year and that the redshift isn't due to speed but to distance. some kind of "old photon are naturally redshifting" (it sound ridiculous said like that but I'm trying my best here). Unless there is a proof that it is indeed redshifted due to speed. I was asking if such a proof existed or if we just assume the light frequency never change over time/distance/space-witchcraft (until proven otherwise).  
> **username_2**: @ker2x ProfRob's answer is great, but it's worth commenting that your idea of "redshift due to distance" isn't totally off the mark. In fact, the cosmological redshift you seem to be referring to is better described as due to distance than speed. This is because the redshift's underlying mechanism isn't really relative "movement", per se, as in the usual doppler effect (or spatiotemporal variations in fundamental constants), but rather the universe's expansion, i.e. that the universe is stretching over the light's time of flight. If it starts farther, it flies longer and stretches more.  
> **username_3**: "Tired light" is a totally different question (that has been asked about before on Physics SE and Astronomy SE). It is disproved by, for example, the time dilation observed in supernova light curves with redshift.  
> **username_4**: Light can also be "slowed down" due to gravitational lensing.  It's of course not *actually* slowed down, it's just travelling a longer path due to space/time curvature, so it takes longer to get here.  This was evidenced by detecting e.g. the same supernova at multiple different times because it was occurring behind a large gravity well from a black hole in between.  

---

## 1 answers

### Answer by username_3 on 2022-06-15. Score: 11 | Accepted answer

The speed of light is a defined constant so cannot vary - or at least it's variation cannot be measured since it is used to define the measurement system. However $c^2 = (\mu\_0 \epsilon\_0)^{-1}$ and so both $\mu\_0$ and $\epsilon\_0$ could vary in opposite directions.

If $\epsilon\_0$ varied then this would fundamentally change the spectrum due to the various transitions in any given element. For example, the energy levels of a hydrogen atom are
$$E\_n = \frac{m\_e e^4}{8h^2 \epsilon\_0^2 n^2}\ , $$
where all the symbols for the fundamental constants are conventional. If $\epsilon\_0$ changed, this would mean the separation between energy levels and hence the intrinsic frequency/wavelength of the associated spectral line would change. But all the spectral lines would change their wavelengths by the same factor, so this isn't diagnostically useful and would just lead to a different redshift measurement.

Further, a variation in $\epsilon\_0$ could be disguised by a variation in $h, e$ or $m\_e$ and so we arrive at a fundamental issue that the only "constants" it is meaningful to discuss the variation of, in either time or space, are the fundamental *dimensionless* (i.e. they don't have units) constants like the [fine structure constant](https://en.wikipedia.org/wiki/Fine-structure_constant).

However, there *is* physics and diagnostically observable consequences that *are* sensitive to a variation in the fine structure constant. For example, the fine-structure (spin-orbit) splitting between transitions with the same principle quantum numbers does depend on the fine structure constant and can be measured in distant galaxies.

People have been trying to constrain such variations, either by measuring the separations of various atomic transitions in distant galaxies or by looking at the history of radioactive decay in geological uranium deposits (see [here](https://en.wikipedia.org/wiki/Fine-structure_constant#Potential_time-variation) for a summary). The evidence at present suggests there may be some variation at the level of about 1 part in a million on geological timescales or looking back to redshifts of 3 (corresponding to around 10 billion years in the past). The results are still under debate.

These levels of variation would have no impact whatsoever on the interpretation of cosmological redshift.

> **Comments:**
> **username_0**: So if I understand correctly : there are (possibly) known variation in (what I call "the speed of light" but it could be any other variable used to compute the speed of faraway galaxy) but the variations aren't significant enough to fundamentally change the conclusion. correct ? thank you for the answer and the links, I never heard about "fine structure constant" so it will be a good read.  
> **username_5**: The speed of light is only a defined constant if you're measuring using SI units.  If you're using some other system of measurement (eg. the foot-pound-second system), it's perfectly possible to measure the speed of light.  
> **username_2**: @Mark To my understanding, the official definition of the foot is a certain fraction of the meter, so $c$ in ft/s is also fixed definitionally. Of course, one could revert to past standards and base a unit system on, say, a prototype bar, and OP's question could be rephrased as asking whether the prototype bar's length (in meters) changes over time/space. Ultimately, that's a question about the distance and time scales, relative to $c$, of the fundamental interactions of the matter comprising the prototype, which is exactly what fundamental dimensionless constants like $\alpha$ encode.  
> **username_6**: ISTR that non-constant speed of light was an alternate hypothesis to dark energy at one time.  

---

