<p>Yes, light travels faster through the cosmic voids than it does through the more &quot;populated&quot; parts of the cosmos.</p>
<p>In General Relativity, the <em>local</em> speed of light is always <span class="math-container">$c$</span>. However, the speed of light may be slowed for a distant observer because of gravitational time dilation. This effect is known as the <a href="https://en.wikipedia.org/wiki/Shapiro_time_delay" rel="nofollow noreferrer">Shapiro delay</a>. The delay is quite small, but it has been measured using radar beams passing near the Sun.</p>
<p>If observers make local measurements of the speed of the beam at any point along its length they will all get a value of <span class="math-container">$c$</span>. But the clocks of those observers are all ticking at different rates, due to gravitational time dilation. The closer you are to the Sun, the slower your clock ticks, relative to the clock of an observer far from the Sun. The cumulative effect of the time dilation causes the <em>nonlocal</em> measurement of the speed of the beam to be lower than <span class="math-container">$c$</span>. Please see the Wikipedia article for further details.</p>
<hr />
<p>For a spherical body with small rotation (like the Sun or the Earth), we can calculate gravitational time dilation using the <a href="https://en.m.wikipedia.org/wiki/Schwarzschild_metric" rel="nofollow noreferrer">Schwarzschild metric</a>. We get:</p>
<p><span class="math-container">$$\tau = t_\infty\sqrt{1 - \frac{r_s}{r}}$$</span></p>
<p>where <span class="math-container">$\tau$</span> is the proper time of an observer (outside the body) at a distance of <span class="math-container">$r$</span> from the centre of the body with <a href="https://en.wikipedia.org/wiki/Schwarzschild_radius" rel="nofollow noreferrer">Schwarzschild radius</a> <span class="math-container">$r_s$</span>, and <span class="math-container">$t_\infty$</span> is the time of an ideal observer outside the gravitational field.</p>
<p>For the Sun, <span class="math-container">$r_s\approx 2953.250$</span> m, for the Earth, <span class="math-container">$r_s\approx 88.70056$</span> mm. The official <a href="https://en.wikipedia.org/wiki/Solar_radius" rel="nofollow noreferrer">solar radius</a> is <span class="math-container">$695,700$</span> km, so even at the &quot;surface&quot; of the Sun, the time dilation factor is <em>very</em> close to one. We get <span class="math-container">$\frac\tau{t_\infty}\approx  0.9999978775$</span>, which means the Sun surface clock loses about <span class="math-container">$0.1834$</span> seconds per day, relative to a clock outside the Sun's gravitational field.</p>
<hr />
<p>All forms of energy contribute to the <a href="https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor" rel="nofollow noreferrer">stress-energy-momentum tensor</a> which causes spacetime curvature, so they all affect gravitational time dilation. So clocks in intergalactic voids tick faster than clocks in denser parts of the universe, and hence light experiences less Shapiro delay in those voids.</p>
<p>However, the actual speed of light propagation isn't only determined by spacetime curvature. Space isn't a perfect vacuum, and light travels slower through a gas than it does through a perfect vacuum. Of course, the gas density in space is usually low, even inside a stellar system, so the effect is small, but it is significant when the light travels millions or billions of light-years.</p>
<hr />
<p>Incidentally, the gas between the galaxies is sparse, but it isn't necessarily cold. From Wikipedia,</p>
<p><strong><a href="https://en.wikipedia.org/wiki/Warm%E2%80%93hot_intergalactic_medium" rel="nofollow noreferrer">Warm–hot intergalactic medium</a></strong></p>
<blockquote>
<p>The warm–hot intergalactic medium (WHIM) is the sparse, warm-to-hot (<span class="math-container">$10^5$</span> to <span class="math-container">$10^7$</span> K) plasma that cosmologists believe to exist in the spaces between galaxies and to contain 40–50% of the baryonic 'normal matter' in the universe at the current epoch.</p>
<p>The WHIM can be described as a web of hot, diffuse gas stretching between galaxies, and consists of plasma, as well as atoms and molecules, in contrast to dark matter. The WHIM is a proposed solution to the missing baryon problem, where the observed amount of baryonic matter does not match theoretical predictions from cosmology.</p>
</blockquote>
<p>Of course, the WHIM has a very low density, so despite its high temperature, a cubic kilometre of WHIM doesn't actually hold much energy.</p>

CC BY-SA 4.0
2022-01-04T13:09:36.563Z
2022-01-04T13:09:36.563Z
PM 2Ring
<p>If temperature affects the speed of light (a contentious issue, I gather) then is it possible that the speed of light outside our solar system or galaxy, which might be minimally warmer than the cosmic void, is infinitesimally slower? Such an effect would only been seen in great astronomical distances, but I don't know how it could be measured.</p>

CC BY-SA 4.0
2022-01-04T06:53:24.367Z
@JustinTackett more like 9sf.  Henry, "temperature", which is a statistical consequence of the average energy of interacting particles becomes rather ill-defined if there aren't any particles, or those particles are so widely spaced that they rarely interact.
James K
CC BY-SA 4.0
2022-01-04T08:14:31.780Z
It would help if you could link to the source of the idea that "temperature affects the speed of light in a vacuum"
James K
CC BY-SA 4.0
2022-01-04T09:30:34.043Z
This assumption needs good reasoning or it falls prey to occam's razor.
planetmaker
CC BY-SA 4.0
2022-01-04T12:00:01.270Z
@JamesK Perhaps this paper? https://arxiv.org/abs/1706.01319 However, it seems to provide a very simple answer to the OP's question: the temperature dependence is only possibly relevant at extremely high temperatures, such as in the early universe, not in a cosmic void.
Daddy Kropotkin
CC BY-SA 4.0
2022-01-04T15:30:02.900Z
@JamesK I have no idea how I got that information (I thought I had a professor tell me that and then I looked it up yesterday and must be dyslexic because I thought it said 5) but you’re totally right, it’s 9, and I have since deleted my comment to avoid misinformation
Justin T
<light>
Speed of light in cosmic voids
Henry
# Speed of light in cosmic voids

(Asked by: username_0 on 2022-01-04)

If temperature affects the speed of light (a contentious issue, I gather) then is it possible that the speed of light outside our solar system or galaxy, which might be minimally warmer than the cosmic void, is infinitesimally slower? Such an effect would only been seen in great astronomical distances, but I don't know how it could be measured.

**Tags:** light

> **Comments:**
> **username_1**: @JustinTackett more like 9sf.  username_0, "temperature", which is a statistical consequence of the average energy of interacting particles becomes rather ill-defined if there aren't any particles, or those particles are so widely spaced that they rarely interact.  
> **username_1**: It would help if you could link to the source of the idea that "temperature affects the speed of light in a vacuum"  
> **username_2**: This assumption needs good reasoning or it falls prey to occam's razor.  
> **username_3**: @JamesK Perhaps this paper? https://arxiv.org/abs/1706.01319 However, it seems to provide a very simple answer to the OP's question: the temperature dependence is only possibly relevant at extremely high temperatures, such as in the early universe, not in a cosmic void.  
> **username_4**: @JamesK I have no idea how I got that information (I thought I had a professor tell me that and then I looked it up yesterday and must be dyslexic because I thought it said 5) but you’re totally right, it’s 9, and I have since deleted my comment to avoid misinformation  

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## 1 answers

### Answer by username_5 on 2022-01-04. Score: 3

Yes, light travels faster through the cosmic voids than it does through the more "populated" parts of the cosmos.

In General Relativity, the *local* speed of light is always $c$. However, the speed of light may be slowed for a distant observer because of gravitational time dilation. This effect is known as the [Shapiro delay](https://en.wikipedia.org/wiki/Shapiro_time_delay). The delay is quite small, but it has been measured using radar beams passing near the Sun.

If observers make local measurements of the speed of the beam at any point along its length they will all get a value of $c$. But the clocks of those observers are all ticking at different rates, due to gravitational time dilation. The closer you are to the Sun, the slower your clock ticks, relative to the clock of an observer far from the Sun. The cumulative effect of the time dilation causes the *nonlocal* measurement of the speed of the beam to be lower than $c$. Please see the Wikipedia article for further details.

---

For a spherical body with small rotation (like the Sun or the Earth), we can calculate gravitational time dilation using the [Schwarzschild metric](https://en.m.wikipedia.org/wiki/Schwarzschild_metric). We get:

$$\tau = t\_\infty\sqrt{1 - \frac{r\_s}{r}}$$

where $\tau$ is the proper time of an observer (outside the body) at a distance of $r$ from the centre of the body with [Schwarzschild radius](https://en.wikipedia.org/wiki/Schwarzschild_radius) $r\_s$, and $t\_\infty$ is the time of an ideal observer outside the gravitational field.

For the Sun, $r\_s\approx 2953.250$ m, for the Earth, $r\_s\approx 88.70056$ mm. The official [solar radius](https://en.wikipedia.org/wiki/Solar_radius) is $695,700$ km, so even at the "surface" of the Sun, the time dilation factor is *very* close to one. We get $\frac\tau{t\_\infty}\approx 0.9999978775$, which means the Sun surface clock loses about $0.1834$ seconds per day, relative to a clock outside the Sun's gravitational field.

---

All forms of energy contribute to the [stress-energy-momentum tensor](https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor) which causes spacetime curvature, so they all affect gravitational time dilation. So clocks in intergalactic voids tick faster than clocks in denser parts of the universe, and hence light experiences less Shapiro delay in those voids.

However, the actual speed of light propagation isn't only determined by spacetime curvature. Space isn't a perfect vacuum, and light travels slower through a gas than it does through a perfect vacuum. Of course, the gas density in space is usually low, even inside a stellar system, so the effect is small, but it is significant when the light travels millions or billions of light-years.

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Incidentally, the gas between the galaxies is sparse, but it isn't necessarily cold. From Wikipedia,

**[Warm–hot intergalactic medium](https://en.wikipedia.org/wiki/Warm%E2%80%93hot_intergalactic_medium)**

> The warm–hot intergalactic medium (WHIM) is the sparse, warm-to-hot ($10^5$ to $10^7$ K) plasma that cosmologists believe to exist in the spaces between galaxies and to contain 40–50% of the baryonic 'normal matter' in the universe at the current epoch.
>
> The WHIM can be described as a web of hot, diffuse gas stretching between galaxies, and consists of plasma, as well as atoms and molecules, in contrast to dark matter. The WHIM is a proposed solution to the missing baryon problem, where the observed amount of baryonic matter does not match theoretical predictions from cosmology.

Of course, the WHIM has a very low density, so despite its high temperature, a cubic kilometre of WHIM doesn't actually hold much energy.


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