<p>A couple of good answers already, but this might be an easier way of thinking about it.</p>
<p>The light you see from a star comes only from the photons emitted at the tiny specific angle just right enough to enter your eye.  That angle is very close to zero, but not zero.  As a star moves further away, that angle gets smaller and smaller, so more photons miss your eye, the result is the star appears dimmer because a tiny portion of the sky that was sending photons to your eye is now dark sky.  Those photons reaching your eye are not less intense, there are just fewer of them.  If, instead of dark sky, you fill that darkness with another star (or stars) of equal brightness.  So, your eye will interpret that region just as bright as it was before.  Extrapolate that across the whole sky, and there is no region not sending photons directly towards your eye at full intensity.</p>

CC BY-SA 4.0
2022-12-20T17:35:17.403Z
2022-12-20T17:35:17.403Z
Greg Miller
<p>It's an easy integral assuming four things:</p>
<ul>
<li>The universe is infinite in extent,</li>
<li>Stars are uniformly distributed in this infinite universe,</li>
<li>The universe is infinitely old,</li>
<li>Newtonian mechanics applies, implying that light from remote stars is inversely proportional to the distance squared.</li>
</ul>
<p>Given these assumptions, we not only would not have non-dark skies, we wouldn't even exist because the sky would be infinitely bright. As I mentioned at the top, it's an easy integral with these four assumptions: the brightness is <span class="math-container">$\int_0^\infty \text{some constant}\, dr$</span>. In other words, infinitely bright. This is Olber's Paradox.</p>
<p>General relativity combined with big bang theory offers a solution: The last two assumptions are false. The universe is not infinitely old, and light from ever more remote stars is diminished not only by distance but also by redshift due to expansion.</p>

CC BY-SA 4.0
2022-12-20T17:00:00.940Z
2022-12-20T17:00:00.940Z
David Hammen
<p>Another version of Olber's Paradox: consider a cube with side length, say, 1kLY (1000 light years). This cube will have stars inside of it, and the light from those stars will be exiting the cube through its sides. But we can make a symmetry argument that there should also be light coming into the cube through the sides, and for the average cube, the light coming in will equal the light going out; there's no reason for one quantity to be larger than the other. So while there will be individual photons leaving the cube, there won't be any <em>net</em> light leaving the cube, and so we might as well imagine the cube being surrounded by mirrors, reflecting all the light back into the cube. If the stars are infinitely old, and have been producing light infinitely long, and none of that light has left the cube, then there is an infinite amount of light in the cube.</p>
<p>Thermodynamically, if heat is being produced, but the region producing the heat is at finite temperature, it must be shedding that heat to somewhere. And that somewhere must be cooler than the region. But if the universe is at large scale uniform, then each region is on average the same temperature as everywhere else, so there's nowhere for the heat to go.</p>

CC BY-SA 4.0
2024-03-07T19:24:10.627Z
Stars are not infinitely old as such. Stars are born and stars die. It is only the average number of stars that stays the same. Still, this would lead to an ever increasing light intensity unless there is some physical process which destroys the light after some time. Only in this case could you achieve a steady state.
Thomas
CC BY-SA 4.0
2022-12-21T04:06:51.177Z
2022-12-21T04:06:51.177Z
Acccumulation
<p>It seems there are generally some misunderstandings regarding the nature of Olber's paradox: it is usually claimed that the paradox arises from the assumption of a universe infinite in space and time. This is not at all the case. The crucial point of Olber's paradox is that it assumes permanent production of energy in any given volume element but no losses of energy. We can write the local change of energy as</p>
<p><span class="math-container">$$
\frac{dE}{dt} = P_L - L_L + P_T -L_T
$$</span></p>
<p>where <span class="math-container">$P_L$</span> is the local production rate of energy in the volume element (assumed sufficiently large), <span class="math-container">$L_L$</span> the local loss rate, and <span class="math-container">$P_T$</span> and <span class="math-container">$L_T$</span> the 'transport' production and loss rates associated with energy entering and leaving the volume from/to neighbouring volumes. Hovever, for a homogeneous universe, we have obviously <span class="math-container">$P_T$</span>=<span class="math-container">$L_T$</span>, so we are just left with the local terms</p>
<p><span class="math-container">$$
\frac{dE}{dt} = P_L - L_L
$$</span></p>
<p>and for <span class="math-container">$L_L=0$</span> (as assumed in the formulation of the Olber's paradox) we would then have <span class="math-container">$dE/dt = P_L$</span> , that is the energy per volume element would be increasing with time, so no steady state would be possible. For the latter we require <span class="math-container">$P_L=L_L$</span> so that <span class="math-container">$dE/dt=0$</span>.</p>
<p>This shows that Olber's paradox is not directly related to the question whether the universe is finite or infinite but merely whether the local energy loss rate balances the local production rate. Olber's paradox inconsistently implies that it does not, as it assumes that a given volume element has sources of radiation continuously producing energy but no sinks removing energ. This is inconsistent because in a closed system (and even an infinite universe is closed as no energy can enter or leave it) the energy conservation law would be violated as the total energy would not be constant. And this should not be interpreted as an equality of energies mysteriously entering and leaving the system (which would still mean the system is not closed despite energy conservation being preserved) but as the existence of some cycle that changes the different forms of energy into each other within the closed system.</p>

CC BY-SA 4.0
2024-03-11T19:47:48.210Z
There is no problem with having $dE/dt \neq 0$ in a universe of finite age. Neither is $P_T= L_T$ required in a universe where the stars are limited to a finite volume. Olbers paradox, the paradox restated by Olbers, is that the darkness of the night sky is inconsistent with an infinite, eternal, unchanging universe.
ProfRob
CC BY-SA 4.0
2024-03-11T23:17:50.997Z
@ProfRob Yes, Olber's paradox claims that $dE/dt \neq 0$ necessarily rules out an infinite universe, but this conclusion is merely reached on the basis of the inconsistent assumption of having only sources of radiation/energy in the universe but no sinks. Including the latter you would have $dE/dt=0$ also for an infinite and eternal universe (the net zero energy flux ($P_T=L_T$) is as such not required for this, this just follows in general from the assumption of a homogeneous universe, whether this is finite or infinite).
Thomas
CC BY-SA 4.0
2024-03-10T19:47:55.087Z
2024-03-16T20:52:16.027Z
2024-03-16T20:52:16.027Z
Thomas
<p>Olbers's Paradox actually fails to demonstrate a finite or nonuniform universe and was supposed to be a paradox because its model for the night sky was missing crucial aspects that have since been filled in, at least in part.
It ignores the existence of non-luminous <strong>interstellar matter</strong>, which we have since learned about (and which modern astronomical theories <a href="https://en.wikipedia.org/wiki/Dark_matter" rel="nofollow noreferrer">explicitly rely on</a>). Such matter is known to attenuate light according to an <a href="https://en.wikipedia.org/wiki/Exponential_decay" rel="nofollow noreferrer">exponential decay law</a> (see the <a href="https://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law" rel="nofollow noreferrer">Beer-Lambert attenuation law</a>).
Olbers himself disregarded this law as it <a href="https://en.wikipedia.org/wiki/Extinction_(astronomy)" rel="nofollow noreferrer">was not documented with respect to starlight until 1930</a>, more than a century after he proposed this supposed paradox as a thought experiment. Those arguing against the existence and prevalence of such matter are asking us to <strong>presuppose the non-existence</strong> of planets, moons, asteroids, <strong>dust and gas</strong> (from which the stars themselves are said to form), nebulae, <strong>dark matter</strong>, etc.</p>
<p><a href="https://i.sstatic.net/hsZV2.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/hsZV2.png" alt="Visible effects of interstellar absorptive matter" /></a></p>
<p>I have written <a href="https://stewartsetha.github.io/PhysicsSimulations/OlbersParadox.html" rel="nofollow noreferrer">a basic simulation</a> to validate the effects of non-luminous matter quantitatively and qualitatively. <a href="https://github.com/StewartSethA/PhysicsSimulations/blob/main/OlbersParadox.html" rel="nofollow noreferrer">Code here</a>. It directly applies the exponential decay law by assuming a uniform random density of stars and a uniform density of non-luminous matter throughout space.
The simulation even <em>cheats massively in favor of</em> Olbers's Paradox by modeling the infinite backdrop of stars at varying distances as a purely luminous wall of light at a fixed, finite and even shortest possible distance beyond the foreground model of direct sampling. This means we have a strict theoretical <strong>upper bound</strong> on the total light emanating from distant stars. The density of non-luminous matter is controllable as a parameter <em>p</em>. The simulation shows that for even very small values of <em>p</em>, a purely luminous wall would be practically invisible, or else be indistinguishable from <a href="https://en.wikipedia.org/wiki/Cosmic_microwave_background" rel="nofollow noreferrer">cosmic microwave background radiation</a> (interstellar attenuation not only decreases apparent intensity, it also <a href="https://en.wikipedia.org/wiki/Extinction_(astronomy)" rel="nofollow noreferrer">induces reddening</a>).</p>
<p>In other words, Olbers's thought experiment would fail to falsify even the hypothetical existence of a contiguous sphere of light as luminous as the surface of the brightest star enveloping the entire visible portion of the universe. It can say <strong>nothing</strong> about what is beyond the photons that reach us--nor does it tell us anything about the photons that <em>didn't</em> reach us.</p>
<p>If one sets <em>p=0</em>, the entire field of view is indeed saturated by pure, contiguous starlight under this simulation. But for any <em>non-infinitesimal</em> density <em>p</em> of attenuating matter, the visualization -- and the mathematical solution for expected light intensity over all points in space--converges sharply towards a model that perfectly resembles what we see in our night sky, <em>regardless of all other parameter settings</em>.</p>
<p>In the following two images, the absorption value is increased only slightly, starting as close as the simulation allows to zero at first:
<a href="https://i.sstatic.net/aveem.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/aveem.png" alt="Very low absorption parameter" /></a></p>
<p><a href="https://i.sstatic.net/UlQ72.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/UlQ72.png" alt="Low absorption parameter" /></a></p>
<p>In both images, there is a perfectly bright wall of simulated stars a short, fixed distance away from the observer. Radiation from that wall leaks and is visible as a uniform grey background when the simulated wall is very close and the density of attenuating matter approaches zero, but if the wall of light is slightly more distant or the density of attenuating matter is only slightly increased, the background approaches pitch black, despite there still being an infinite number of perfectly bright stars intersecting every possible line of sight.</p>
<p>You can bump up the stellar density, radii and luminosity as high as you want, and even a tiny percentage of non-luminous matter still overwhelms the resultant apparent brightness calculations with the exponential decay induced by material attenuation.</p>
<p>Of course arguments about <strong>thermodynamics</strong> are just begging the question. How nonluminous matter is able to be there and coexist with stars is a separate matter of discussion. (<a href="https://www.youtube.com/watch?v=CzyQbOQ0dv0" rel="nofollow noreferrer">How stars got there</a> is too, come to think of it). The fact that <strong>it is there and that we know it is there</strong>, even at great distances, disproves the idea that Olbers's paradox is a paradox at all, as it completely fails to falsify an infinite universe given what we know.</p>
<p>In case someone thinks this idea is flamingly absurd, that even a small amount of matter between stars can block nearly all of the light from them, remember that despite how brightly the Sun shines at noonday and how close it is to the Earth, you can block almost all of that light using a thin cardboard cereal box or a parasol consisting of cloth a couple millimeters thick. This gives you an idea of how effective exponential attenuation is. Can there not be the equivalent matter of one millimeter of cardboard between you and a star 3 billion light years away? If not then what are stars made of?</p>

CC BY-SA 4.0
2024-03-05T23:03:29.373Z
"It becomes literally invisible" - bingo. The intensity, energy and frequency of light are all diminished, absorbed or downshifted respectively by their interactions with matter. Uncanny prediction of cosmic microwave background radiation right here, straight from 18th-century laws of optics and thermodynamics.
pygosceles
CC BY-SA 4.0
2024-03-06T07:21:10.217Z
As the leading answer correctly explains, absorbing matter would heat up until it emitted at the same temperature as the stars themselves if the universe was infinitely old and infinite in extent. This is actually 19th century thermodynamics.There is of course no paradox at all if the universe is finite in age.
ProfRob
CC BY-SA 4.0
2024-03-06T07:25:14.560Z
@ProfRob This is a huge non sequitur. There are stars and there are nebulae in the universe, and these models fail to account for the existence of stars, let alone the existence of dust. This is a very unserious objection given that current models fail so much as to allow any such things to exist.
There is no paradox in a universe of infinite age, as has been proven.
pygosceles
CC BY-SA 4.0
2024-03-06T08:24:36.463Z
@ProfRob It would be inconsistent to assume that stellar radiation is produced continuously out of nothing whilst not allowing for loss processes. If you assume sources you also have to assume sinks. So the argument of the temperature heating up indefinitily is not correct.
Thomas
CC BY-SA 4.0
2024-03-06T09:00:46.987Z
@Thomas Olber's paradox is precisely that the radiation should have been produced continuously infinitely far into the past and infinitely far into space. Any suggestion to the contrary immediately invalidates any attempt at disproof. Where is the absorbed energy from all the stars that have ever existed supposed to go? You have also not grasped the argument if you think I suggested that the "temperature heats up indefinitely".
ProfRob
CC BY-SA 4.0
2024-03-06T21:23:18.053Z
@ProfRob If you continuously pump energy into a given volume without having some sort of energy sink, than the energy will increase indefinitely. You can only have a steady state if you have some loss process that balances out the production process. This true in any branch of physics and beyond. Olber's paradox has nothing to do with infinity as such but rather with inconsistently assuming there are no physical loss processes for the radiation (which is a contradiction in terms to the assumption of having a steady state). The question is then only what the nature of this loss process  is.
Thomas
CC BY-SA 4.0
2024-03-06T22:59:59.430Z
@Thomas the material heats up until it is as hot as the surface of the stars irradiating it. Then it radiates just as much as it absorbs. As the leading answer correctly states. Hang on, haven't I said this before somewhere...
ProfRob
CC BY-SA 4.0
2024-03-06T23:54:59.803Z
@ProfRob This ignores radiative equilibrium, which for a given material, distance from energy sources and radiative influx can occur at a different temperature than that of a radiative source such as a star. This is a known process whereby you may have a planet or nebula some distance away from a star for billions of years and still be close to absolute zero rather than trending towards the same temperature as the nearest star.
pygosceles
CC BY-SA 4.0
2024-03-07T08:11:02.133Z
The universe would be providing starlight from all directions, not from a single direction. The equilibrium temperature in this case is the temperature of the incident blackbody radiation. Distance is irrelevant, since every sightline ends at the surface of a star, or, in an infinitely old universe, something that is the same temperature as the surface of a star. In a sense, that is the paradox right there. The situation you describe would not be possible in an infinite, infinitely old, unchanging universe.
ProfRob
CC BY-SA 4.0
2024-03-07T08:18:55.810Z
@ProfRob *"the material heats up until it is as hot as the surface of the stars irradiating it. Then it radiates just as much as it absorbs."* This may be true, but the temperature of both would be increasing ever further if the source star keeps on pumping out radiation without energy being lost somehow. This is required because of energy conservatiion
Thomas
CC BY-SA 4.0
2024-03-07T08:26:25.097Z
@ProfRob *"The situation you describe would not be possible in an infinite, infinitely old, unchanging universe."* Even in an an infinite, infinitely old, unchanging universe Olber's paradox would not arise if there is some loss process which limits the light propagation to a finite distance. Only in thiis case you could actually have an unchanging steady-state.universe.
Thomas
CC BY-SA 4.0
2024-03-07T08:36:34.230Z
@Thomas first comment ok, but the second comment suggests you still don't accept that material that absorbs light (which is what we are discussing) heats up. You cannot have an infinite, static, unchanging universe for many reasons, but Olber did not know about nuclear physics or how stars work, and didn't need to.
ProfRob
CC BY-SA 4.0
2024-03-07T17:56:20.507Z
@ProfRob Suppose you are right that everything would be the same temperature in an infinitely old universe. But then there would be no matter undergoing any exothermic or endothermic reaction except at a very, very local scale in tiny quanta according to a Boltzmann law with a uniform temperature everywhere above the quantum scale. Do you agree with this? If so, then how could stars exist? If stars do not exist, this would circularly presuppose the most basic premise of Olbers' question to be false. It assumes that stars can't exist for long enough to give the paradox claim a fair test.
pygosceles
CC BY-SA 4.0
2024-03-07T18:06:14.373Z
@ProfRob Our Earth maintains a stable non-stellar temperature because it is in radiative equilibrium; it will not heat up no matter how many billions of years of starlight hit it. Extrastellar objects tend towards radiative equilibrium, regulating their own temperatures as they re-radiate on average as much energy as they absorb, and each arrives at its own non-stellar temperature. Radiative equilibrium explains why all the planets are still cold relative to the Sun despite supposed billions of years absorbing starlight. Radiative equilibrium implies that thermal uniformity is not inevitable.
pygosceles
CC BY-SA 4.0
2024-03-07T18:40:41.443Z
@ProfRob *"you still don't accept that material that absorbs light (which is what we are discussing) heats up. "* You still seem to misunderstand. For a steady state situation you need *true* sinks that remove energy from the system (and thus balance the energy input from the sources), not just turn it into different forms. It is inconsistent to propose a (quasi)-static universe where in each volume element energy is continuously created but not lost at the same rate due to some processes. Doing so is exactly the reason for Olber's paradox.
Thomas
CC BY-SA 4.0
2024-03-07T19:22:40.850Z
The planets are all cold because we do not live in an infinitely old, static universe - this **is** Olber's paradox - the whole sky would be like the Sun if it were and the planets would be fried.  The impossibility of isolated stars existing in an infinitely old, static universe is also just another restatement of Olber's paradox. All this has nothing to do with your dust argument..
ProfRob
CC BY-SA 4.0
2024-03-08T05:46:05.013Z
@ProfRob Radiative equilibrium demonstrates that objects can maintain distinct temperatures indefinitely. Planets will not be fried except in a supernova event or other stellar catastrophe involving ample material contact. And what then? Will new stars form? As long as stars exist, there will always be thermal gradients and low entropy, high-temperature thermal islands in the universe. In the hypothetical temperature equivalence scenario, stars can't exist. Isolated stars? Or stars at all! This is a glaring hole in such logic. "Assume there are no stars. Paradox solved!". Nothing to do indeed.
pygosceles
CC BY-SA 4.0
2024-03-05T21:15:26.777Z
2024-03-05T21:15:26.777Z
pygosceles
<p>Olber's paradox is - as you state - the phenomenon, that the night sky is dark, but would have to be bright as the sun if the universe was infinite <em>and</em> infinitely old. The unspoken assumption here is also that the universe is at least on larger scales isotropic, that is about the same everywhere.</p>
<p>So if the universe is the same everywhere (and with everywhere we can be generous and consider distances between our galaxy and its neighbours still small), then it means that we <em>will</em> see some star or galaxy whereever we look. Galaxies are made of stars, so we will see stars everywhere - and every star is approximately as bright as the Sun - thus we would have a sky as bright everywhere as the disk of our sun. Maybe put the argument differently: consider the sky covered by suns at different distances. But in every direction you see a sun. So in essence it means that every direction you look at a Sun's surface. The contribution of every single Sun may be tiny (depending on how far it is) - but there are infinitely many Suns and thus the surface brightness is the same everywhere. The stars are only so faint because they are so far. Mathematically: you double the distance, you get a quarter of the intensity from every single star (inverse square law). But doubling the distance also means we have four times as many stars (the volume of a spherical shell is <span class="math-container">$\propto d^2$</span>. Thus both effects taken together, effectively every distance doubled adds the same brightness as the previous one as the reduction in the brightness of each single source is exactly countered by the amount of sources we look at. Now, in an infinite, static universe there are infinitely many such shells, and we add infinitely many constant brightness values, leading to an infinite brightness (or at least the same brightness if we (wrongly) assume that the foreground stars hide the stars behind them.</p>
<p>Now, the argument may be &quot;there is matter between the distant stars and us which absorbs the light&quot;. Yes. But we are talking of a static, infinitely old universe. The matter will be heated by the incoming light - and eventually it will become similarily hot as the source(s) which are heating it, thus also reach the temperature of stellar surfaces and emit light at the same intensity. Stellar opacity is not an argument here either - it also just is matter and energy does not get lost and will simply heat up all the same like all other non-stellar matter up to the same temperature as it is heated by: the radiation from the stellar surfaces.</p>

CC BY-SA 4.0
2022-12-20T17:35:54.677Z
Thanks, that makes sense. I made the error of assuming that any starlight originating at an infinitesimal (or atomic, for a discrete universe) point in the night sky will continue to experience a drop off in luminosity with distance, but obviously this is incorrect since the photon/light-wave energy remains constant.
Alex Popescu
CC BY-SA 4.0
2022-12-21T17:00:32.390Z
Would this answer not have to assume that 1) photons can't decay; 2) photons can't be blocked by other objects; and 3) photons don't get deflected by gravity. Surely after some distance the odds of a photon encountering something opaque; decaying (if they do decay); or being deflected out of the way by gravity would tend toward 100%
ScottishTapWater
CC BY-SA 4.0
2022-12-21T17:23:19.687Z
@ScottishTapWater: I think 1 is true, we do have to assume no photon decay. Regarding 2, Planetmaker already addressed the reason why intervening objects won’t make a difference. As for 3, it won’t matter that photons in the night sky experience curvature, as long as every point in the night sky is filled with photons. While there will be an infinite number of photons deflected away from earth, there will also be an infinite number deflected towards earth. 

Curvature just redistributes the paths of the individual photons; it doesn’t change the number reaching earth (assuming isotropy).
Alex Popescu
CC BY-SA 4.0
2022-12-21T20:07:09.340Z
@ScottishTapWater if photons decay into nothing, then you have a pretty stark violation of energy conservation (which we should be able to observe). If they decay into something else, that should itself be observable, unless they decay into dark matter/energy/something that is very weakly interacting.
Lawnmower Man
CC BY-SA 4.0
2022-12-21T20:30:35.597Z
@AlexPopescu you raise valid points
ScottishTapWater
CC BY-SA 4.0
2022-12-22T18:27:34.577Z
If I consider a cone from my eye to a far away star, where the star fills the entire width of the cone at it's position, then (A) it would block ~all light from stars behind it, so we only have to consider the one star, and (B) only so many photon/second from that star will reach my eye, leaving the possibility that the number is less than my detection threshold. So to preserve the paradox, something about my assumption (A) must be flawed? Even though the star absorbs (some) light from the infinite stars behind (transitive), that is already included in its own brightness.
Mooing Duck
CC BY-SA 4.0
2022-12-22T21:14:34.213Z
@MooingDuck
Sure, that individual star cone by itself might not be bright enough to be noticed, by virtue of it not being wide enough. But the point is that the cone of light that has a  cross section big enough to fill your entire retina will be noticed, as it will be composed of an aggregate of smaller, individual, starlight cones. 

We can also divide the sun into small enough cross-sections that you wouldn’t notice the light coming from a single section (it would be like staring into a very very small pinhole). But obviously the sun still remains noticeable.
Alex Popescu
CC BY-SA 4.0
2022-12-22T21:37:50.923Z
But the retina would be filled with a limited count of these star cones, each of which provides a limited amount of photons/second.  If an (2d) eye cone perceives about 28 arcseconds, and a star is about 0.25 arcseconds, then each eye cone is only receiving light from at least 112 star cones, probably no more than 352. Our eye cones absorb ~500k photons/sec from the sun, so as long as we get less than ~1k photons/sec from each remote star, the sky would be dimmer than the sun. suns farther away have fewer photons/sec and therefore are dimmer. Not infinite.
Mooing Duck
CC BY-SA 4.0
2022-12-22T22:31:25.277Z
@MooingDuck    
Do you agree that a distant sun taking up a 1d cross section of .25 arcs seconds will have the same brightness as a closer sun (the same sun) covered by a wall with a pinhole .25 arc seconds across letting in light? From there it is a trivial fact to infer that the aggregate cross sections of all the stars 1800 arcseconds across (the width of the sun) will add up to the same brightness as the sun. So, every patch of the sky 1800 arcseconds across will be as bright as the sun (ignoring the infinite heating of matter).
Alex Popescu
CC BY-SA 4.0
2022-12-23T01:15:45.127Z
since its further away, its photons would be more spread out (distance squared in 2d) resulting in FAR fewer photons/srcond in that 0.25arcsecond space.
Mooing Duck
CC BY-SA 4.0
2022-12-23T01:52:52.390Z
@MooingDuck  
The photons spread out, but the surface area decreases to compensate. Apparent brightness = Total luminosity/4pi(R^2)       
But notice that the surface area of a star in a night sky is also proportional to the inverse square of the distance. Therefore, apparent brightness is directly proportional to surface area (B=W/m^2).                          So, the photons per second received per surface area of the night sky is a fixed constant for a given star. That far away sun taking up .25 arcseconds will be just as bright as the close sun observed through a .25 arcseconds pinhole.
Alex Popescu
CC BY-SA 4.0
2022-12-23T04:54:11.270Z
@MooingDuck maybe read again the paragraph starting with 'mathematical' in my answer. Or read David Hammen's answer
planetmaker
CC BY-SA 4.0
2022-12-25T01:24:09.230Z
Isaac Asimov couldn't have explained it better.
Arthur Kalliokoski
CC BY-SA 4.0
2024-03-06T16:17:02.207Z
@Moonduck Surface brightness is independent of distance.  When every line of sight hits the surface of some star the surface brightness everywhere is the surface brightness of a star.  Since the stars behind stars are blocked, the surface brightness does not become infinite.
eshaya
CC BY-SA 4.0
2024-03-06T16:26:38.370Z
@Moonduck But, if the surface brightness of the sky is that of a star, then, in net, stars cannot release energy to collapse.  They all expand until they shutdown.  When the sky darkens, they can collapse again.
eshaya
CC BY-SA 4.0
2024-03-06T16:33:12.517Z
@Moonduck So maybe the universe is infinite but most of it is shutdown.
eshaya
CC BY-SA 4.0
2024-03-11T07:14:34.423Z
As @eshaya noted - existence of stars (capable of radiating energy) is not independent on the radiation field around them. When the mirror walled cube from one answer or comment is being filled up with radiation stars cannot exist to produce more radiation.
Leos Ondra
CC BY-SA 4.0
2022-12-20T16:53:59.613Z
2022-12-20T18:21:36.627Z
2022-12-20T18:21:36.627Z
planetmaker
<p>I'm not quite grasping the reasoning behind Olbers' Paradox, or why an eternal, non-expanding and spatially infinite universe would be incompatible with a dark sky. For simplicity, let's suppose that all the stellar matter in the universe is transparent, such that to look at any direction in the night sky is equivalent to looking at an infinite number of stars or light sources. Yet I still don't see why it must follow that every point in the night sky will be infinitely bright (or at least sufficiently bright), provided that the sum of the apparent luminosity for all the stars at a given point converges to some finite value. For example, assume we drew a line to the infinite horizon and the first star intersecting that line had an apparent luminosity of 1 lumen, the second star .1 lumen, the third star .01 lumen and so on and so forth...</p>
<p>Furthermore, if this finite convergent value should happen to be lower than the detectable optical threshold of the human eye, that point of the night sky would still appear to be dark. Of course, this assumes that all the stars are transparent, and that they do not occlude any light. In the real world this effect will be lessened due to stellar opacity, but even this hypothetical scenario involving complete transparency doesn't seem to necessarily invoke a paradox, provided that the stellar density is such that the apparent brightness falls off at a level fast enough.</p>
<p>To put it another way, in an eternal, non-expanding, and spatially infinite universe, every point in the night sky will indeed intersect with some distant star, but there is no reason to think that the received luminosity of that star will be bright enough to be noticed. So, what I am I missing? Why is it commonly assumed that Olbers' paradox precludes an infinite static universe?</p>

CC BY-SA 4.0
2022-12-22T18:23:24.143Z
My first thought was that no matter how far away, every point you look at will receive light directly from a star, but when you mention lumens, I realize that photons are *discreet*, and since lumens correlates roughly with photons/second, that you're right, there would be points in the sky where the photons/second due to distance would be less than the human eye could perceive, even if it is directly at a star.
Mooing Duck
CC BY-SA 4.0
2024-03-05T21:31:02.533Z
Does this answer your question? [What exactly is the "paradox" in Olber's Paradox?](https://astronomy.stackexchange.com/questions/21843/what-exactly-is-the-paradox-in-olbers-paradox)
James K
CC BY-SA 4.0
2024-03-07T08:08:09.243Z
I don't agree it is a duplicate. The other Q is not asking about how the paradox works, just why it is called a paradox.
ProfRob
<cosmology><history><luminosity>
What's the issue with Olbers' paradox?
Alex Popescu
# What's the issue with Olbers' paradox?

(Asked by: username_0 on 2022-12-20)

I'm not quite grasping the reasoning behind Olbers' Paradox, or why an eternal, non-expanding and spatially infinite universe would be incompatible with a dark sky. For simplicity, let's suppose that all the stellar matter in the universe is transparent, such that to look at any direction in the night sky is equivalent to looking at an infinite number of stars or light sources. Yet I still don't see why it must follow that every point in the night sky will be infinitely bright (or at least sufficiently bright), provided that the sum of the apparent luminosity for all the stars at a given point converges to some finite value. For example, assume we drew a line to the infinite horizon and the first star intersecting that line had an apparent luminosity of 1 lumen, the second star .1 lumen, the third star .01 lumen and so on and so forth...

Furthermore, if this finite convergent value should happen to be lower than the detectable optical threshold of the human eye, that point of the night sky would still appear to be dark. Of course, this assumes that all the stars are transparent, and that they do not occlude any light. In the real world this effect will be lessened due to stellar opacity, but even this hypothetical scenario involving complete transparency doesn't seem to necessarily invoke a paradox, provided that the stellar density is such that the apparent brightness falls off at a level fast enough.

To put it another way, in an eternal, non-expanding, and spatially infinite universe, every point in the night sky will indeed intersect with some distant star, but there is no reason to think that the received luminosity of that star will be bright enough to be noticed. So, what I am I missing? Why is it commonly assumed that Olbers' paradox precludes an infinite static universe?

**Tags:** cosmology, history, luminosity
> **Comments:**
> **username_1**: My first thought was that no matter how far away, every point you look at will receive light directly from a star, but when you mention lumens, I realize that photons are *discreet*, and since lumens correlates roughly with photons/second, that you're right, there would be points in the sky where the photons/second due to distance would be less than the human eye could perceive, even if it is directly at a star.  
> **username_2**: Does this answer your question? [What exactly is the "paradox" in Olber's Paradox?](https://astronomy.stackexchange.com/questions/21843/what-exactly-is-the-paradox-in-olbers-paradox)  
> **username_3**: I don't agree it is a duplicate. The other Q is not asking about how the paradox works, just why it is called a paradox.  

---

## 6 answers

### Answer by username_9 on 2022-12-20. Score: 26 | Accepted answer

Olber's paradox is - as you state - the phenomenon, that the night sky is dark, but would have to be bright as the sun if the universe was infinite *and* infinitely old. The unspoken assumption here is also that the universe is at least on larger scales isotropic, that is about the same everywhere.

So if the universe is the same everywhere (and with everywhere we can be generous and consider distances between our galaxy and its neighbours still small), then it means that we *will* see some star or galaxy whereever we look. Galaxies are made of stars, so we will see stars everywhere - and every star is approximately as bright as the Sun - thus we would have a sky as bright everywhere as the disk of our sun. Maybe put the argument differently: consider the sky covered by suns at different distances. But in every direction you see a sun. So in essence it means that every direction you look at a Sun's surface. The contribution of every single Sun may be tiny (depending on how far it is) - but there are infinitely many Suns and thus the surface brightness is the same everywhere. The stars are only so faint because they are so far. Mathematically: you double the distance, you get a quarter of the intensity from every single star (inverse square law). But doubling the distance also means we have four times as many stars (the volume of a spherical shell is $\propto d^2$. Thus both effects taken together, effectively every distance doubled adds the same brightness as the previous one as the reduction in the brightness of each single source is exactly countered by the amount of sources we look at. Now, in an infinite, static universe there are infinitely many such shells, and we add infinitely many constant brightness values, leading to an infinite brightness (or at least the same brightness if we (wrongly) assume that the foreground stars hide the stars behind them.

Now, the argument may be "there is matter between the distant stars and us which absorbs the light". Yes. But we are talking of a static, infinitely old universe. The matter will be heated by the incoming light - and eventually it will become similarily hot as the source(s) which are heating it, thus also reach the temperature of stellar surfaces and emit light at the same intensity. Stellar opacity is not an argument here either - it also just is matter and energy does not get lost and will simply heat up all the same like all other non-stellar matter up to the same temperature as it is heated by: the radiation from the stellar surfaces.

> **Comments:**
> **username_0**: Thanks, that makes sense. I made the error of assuming that any starlight originating at an infinitesimal (or atomic, for a discrete universe) point in the night sky will continue to experience a drop off in luminosity with distance, but obviously this is incorrect since the photon/light-wave energy remains constant.  
> **username_10**: Would this answer not have to assume that 1) photons can't decay; 2) photons can't be blocked by other objects; and 3) photons don't get deflected by gravity. Surely after some distance the odds of a photon encountering something opaque; decaying (if they do decay); or being deflected out of the way by gravity would tend toward 100%  
> **username_0**: @ScottishTapWater: I think 1 is true, we do have to assume no photon decay. Regarding 2, Planetmaker already addressed the reason why intervening objects won’t make a difference. As for 3, it won’t matter that photons in the night sky experience curvature, as long as every point in the night sky is filled with photons. While there will be an infinite number of photons deflected away from earth, there will also be an infinite number deflected towards earth.   Curvature just redistributes the paths of the individual photons; it doesn’t change the number reaching earth (assuming isotropy).  
> **username_11**: @ScottishTapWater if photons decay into nothing, then you have a pretty stark violation of energy conservation (which we should be able to observe). If they decay into something else, that should itself be observable, unless they decay into dark matter/energy/something that is very weakly interacting.  
> **username_10**: @AlexPopescu you raise valid points  
> **username_1**: If I consider a cone from my eye to a far away star, where the star fills the entire width of the cone at it's position, then (A) it would block ~all light from stars behind it, so we only have to consider the one star, and (B) only so many photon/second from that star will reach my eye, leaving the possibility that the number is less than my detection threshold. So to preserve the paradox, something about my assumption (A) must be flawed? Even though the star absorbs (some) light from the infinite stars behind (transitive), that is already included in its own brightness.  
> **username_0**: @MooingDuck Sure, that individual star cone by itself might not be bright enough to be noticed, by virtue of it not being wide enough. But the point is that the cone of light that has a  cross section big enough to fill your entire retina will be noticed, as it will be composed of an aggregate of smaller, individual, starlight cones.   We can also divide the sun into small enough cross-sections that you wouldn’t notice the light coming from a single section (it would be like staring into a very very small pinhole). But obviously the sun still remains noticeable.  
> **username_1**: But the retina would be filled with a limited count of these star cones, each of which provides a limited amount of photons/second.  If an (2d) eye cone perceives about 28 arcseconds, and a star is about 0.25 arcseconds, then each eye cone is only receiving light from at least 112 star cones, probably no more than 352. Our eye cones absorb ~500k photons/sec from the sun, so as long as we get less than ~1k photons/sec from each remote star, the sky would be dimmer than the sun. suns farther away have fewer photons/sec and therefore are dimmer. Not infinite.  
> **username_0**: @MooingDuck     Do you agree that a distant sun taking up a 1d cross section of .25 arcs seconds will have the same brightness as a closer sun (the same sun) covered by a wall with a pinhole .25 arc seconds across letting in light? From there it is a trivial fact to infer that the aggregate cross sections of all the stars 1800 arcseconds across (the width of the sun) will add up to the same brightness as the sun. So, every patch of the sky 1800 arcseconds across will be as bright as the sun (ignoring the infinite heating of matter).  
> **username_1**: since its further away, its photons would be more spread out (distance squared in 2d) resulting in FAR fewer photons/srcond in that 0.25arcsecond space.  
> **username_0**: @MooingDuck   The photons spread out, but the surface area decreases to compensate. Apparent brightness = Total luminosity/4pi(R^2)        But notice that the surface area of a star in a night sky is also proportional to the inverse square of the distance. Therefore, apparent brightness is directly proportional to surface area (B=W/m^2).                          So, the photons per second received per surface area of the night sky is a fixed constant for a given star. That far away sun taking up .25 arcseconds will be just as bright as the close sun observed through a .25 arcseconds pinhole.  
> **username_9**: @MooingDuck maybe read again the paragraph starting with 'mathematical' in my answer. Or read David Hammen's answer  
> **username_12**: Isaac Asimov couldn't have explained it better.  
> **username_13**: @Moonduck Surface brightness is independent of distance.  When every line of sight hits the surface of some star the surface brightness everywhere is the surface brightness of a star.  Since the stars behind stars are blocked, the surface brightness does not become infinite.  
> **username_13**: @Moonduck But, if the surface brightness of the sky is that of a star, then, in net, stars cannot release energy to collapse.  They all expand until they shutdown.  When the sky darkens, they can collapse again.  
> **username_13**: @Moonduck So maybe the universe is infinite but most of it is shutdown.  
> **username_14**: As @eshaya noted - existence of stars (capable of radiating energy) is not independent on the radiation field around them. When the mirror walled cube from one answer or comment is being filled up with radiation stars cannot exist to produce more radiation.  

---

### Answer by username_4 on 2022-12-20. Score: 9

A couple of good answers already, but this might be an easier way of thinking about it.

The light you see from a star comes only from the photons emitted at the tiny specific angle just right enough to enter your eye. That angle is very close to zero, but not zero. As a star moves further away, that angle gets smaller and smaller, so more photons miss your eye, the result is the star appears dimmer because a tiny portion of the sky that was sending photons to your eye is now dark sky. Those photons reaching your eye are not less intense, there are just fewer of them. If, instead of dark sky, you fill that darkness with another star (or stars) of equal brightness. So, your eye will interpret that region just as bright as it was before. Extrapolate that across the whole sky, and there is no region not sending photons directly towards your eye at full intensity.


---

### Answer by username_5 on 2022-12-20. Score: 8

It's an easy integral assuming four things:

* The universe is infinite in extent,
* Stars are uniformly distributed in this infinite universe,
* The universe is infinitely old,
* Newtonian mechanics applies, implying that light from remote stars is inversely proportional to the distance squared.

Given these assumptions, we not only would not have non-dark skies, we wouldn't even exist because the sky would be infinitely bright. As I mentioned at the top, it's an easy integral with these four assumptions: the brightness is $\int\_0^\infty \text{some constant}\, dr$. In other words, infinitely bright. This is Olber's Paradox.

General relativity combined with big bang theory offers a solution: The last two assumptions are false. The universe is not infinitely old, and light from ever more remote stars is diminished not only by distance but also by redshift due to expansion.


---

### Answer by username_6 on 2022-12-21. Score: 6

Another version of Olber's Paradox: consider a cube with side length, say, 1kLY (1000 light years). This cube will have stars inside of it, and the light from those stars will be exiting the cube through its sides. But we can make a symmetry argument that there should also be light coming into the cube through the sides, and for the average cube, the light coming in will equal the light going out; there's no reason for one quantity to be larger than the other. So while there will be individual photons leaving the cube, there won't be any *net* light leaving the cube, and so we might as well imagine the cube being surrounded by mirrors, reflecting all the light back into the cube. If the stars are infinitely old, and have been producing light infinitely long, and none of that light has left the cube, then there is an infinite amount of light in the cube.

Thermodynamically, if heat is being produced, but the region producing the heat is at finite temperature, it must be shedding that heat to somewhere. And that somewhere must be cooler than the region. But if the universe is at large scale uniform, then each region is on average the same temperature as everywhere else, so there's nowhere for the heat to go.

> **Comments:**
> **username_7**: Stars are not infinitely old as such. Stars are born and stars die. It is only the average number of stars that stays the same. Still, this would lead to an ever increasing light intensity unless there is some physical process which destroys the light after some time. Only in this case could you achieve a steady state.  

---

### Answer by username_7 on 2024-03-10. Score: 1

It seems there are generally some misunderstandings regarding the nature of Olber's paradox: it is usually claimed that the paradox arises from the assumption of a universe infinite in space and time. This is not at all the case. The crucial point of Olber's paradox is that it assumes permanent production of energy in any given volume element but no losses of energy. We can write the local change of energy as

$$
\frac{dE}{dt} = P\_L - L\_L + P\_T -L\_T
$$

where $P\_L$ is the local production rate of energy in the volume element (assumed sufficiently large), $L\_L$ the local loss rate, and $P\_T$ and $L\_T$ the 'transport' production and loss rates associated with energy entering and leaving the volume from/to neighbouring volumes. Hovever, for a homogeneous universe, we have obviously $P\_T$=$L\_T$, so we are just left with the local terms

$$
\frac{dE}{dt} = P\_L - L\_L
$$

and for $L\_L=0$ (as assumed in the formulation of the Olber's paradox) we would then have $dE/dt = P\_L$ , that is the energy per volume element would be increasing with time, so no steady state would be possible. For the latter we require $P\_L=L\_L$ so that $dE/dt=0$.

This shows that Olber's paradox is not directly related to the question whether the universe is finite or infinite but merely whether the local energy loss rate balances the local production rate. Olber's paradox inconsistently implies that it does not, as it assumes that a given volume element has sources of radiation continuously producing energy but no sinks removing energ. This is inconsistent because in a closed system (and even an infinite universe is closed as no energy can enter or leave it) the energy conservation law would be violated as the total energy would not be constant. And this should not be interpreted as an equality of energies mysteriously entering and leaving the system (which would still mean the system is not closed despite energy conservation being preserved) but as the existence of some cycle that changes the different forms of energy into each other within the closed system.

> **Comments:**
> **username_3**: There is no problem with having $dE/dt \neq 0$ in a universe of finite age. Neither is $P_T= L_T$ required in a universe where the stars are limited to a finite volume. Olbers paradox, the paradox restated by Olbers, is that the darkness of the night sky is inconsistent with an infinite, eternal, unchanging universe.  
> **username_7**: @ProfRob Yes, Olber's paradox claims that $dE/dt \neq 0$ necessarily rules out an infinite universe, but this conclusion is merely reached on the basis of the inconsistent assumption of having only sources of radiation/energy in the universe but no sinks. Including the latter you would have $dE/dt=0$ also for an infinite and eternal universe (the net zero energy flux ($P_T=L_T$) is as such not required for this, this just follows in general from the assumption of a homogeneous universe, whether this is finite or infinite).  

---

### Answer by username_8 on 2024-03-05. Score: -6

Olbers's Paradox actually fails to demonstrate a finite or nonuniform universe and was supposed to be a paradox because its model for the night sky was missing crucial aspects that have since been filled in, at least in part.
It ignores the existence of non-luminous **interstellar matter**, which we have since learned about (and which modern astronomical theories [explicitly rely on](https://en.wikipedia.org/wiki/Dark_matter)). Such matter is known to attenuate light according to an [exponential decay law](https://en.wikipedia.org/wiki/Exponential_decay) (see the [Beer-Lambert attenuation law](https://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law)).
Olbers himself disregarded this law as it [was not documented with respect to starlight until 1930](https://en.wikipedia.org/wiki/Extinction_(astronomy)), more than a century after he proposed this supposed paradox as a thought experiment. Those arguing against the existence and prevalence of such matter are asking us to **presuppose the non-existence** of planets, moons, asteroids, **dust and gas** (from which the stars themselves are said to form), nebulae, **dark matter**, etc.

[![Visible effects of interstellar absorptive matter](https://i.sstatic.net/hsZV2.png)](https://i.sstatic.net/hsZV2.png)

I have written [a basic simulation](https://stewartsetha.github.io/PhysicsSimulations/OlbersParadox.html) to validate the effects of non-luminous matter quantitatively and qualitatively. [Code here](https://github.com/StewartSethA/PhysicsSimulations/blob/main/OlbersParadox.html). It directly applies the exponential decay law by assuming a uniform random density of stars and a uniform density of non-luminous matter throughout space.
The simulation even *cheats massively in favor of* Olbers's Paradox by modeling the infinite backdrop of stars at varying distances as a purely luminous wall of light at a fixed, finite and even shortest possible distance beyond the foreground model of direct sampling. This means we have a strict theoretical **upper bound** on the total light emanating from distant stars. The density of non-luminous matter is controllable as a parameter *p*. The simulation shows that for even very small values of *p*, a purely luminous wall would be practically invisible, or else be indistinguishable from [cosmic microwave background radiation](https://en.wikipedia.org/wiki/Cosmic_microwave_background) (interstellar attenuation not only decreases apparent intensity, it also [induces reddening](https://en.wikipedia.org/wiki/Extinction_(astronomy))).

In other words, Olbers's thought experiment would fail to falsify even the hypothetical existence of a contiguous sphere of light as luminous as the surface of the brightest star enveloping the entire visible portion of the universe. It can say **nothing** about what is beyond the photons that reach us--nor does it tell us anything about the photons that *didn't* reach us.

If one sets *p=0*, the entire field of view is indeed saturated by pure, contiguous starlight under this simulation. But for any *non-infinitesimal* density *p* of attenuating matter, the visualization -- and the mathematical solution for expected light intensity over all points in space--converges sharply towards a model that perfectly resembles what we see in our night sky, *regardless of all other parameter settings*.

In the following two images, the absorption value is increased only slightly, starting as close as the simulation allows to zero at first:
[![Very low absorption parameter](https://i.sstatic.net/aveem.png)](https://i.sstatic.net/aveem.png)

[![Low absorption parameter](https://i.sstatic.net/UlQ72.png)](https://i.sstatic.net/UlQ72.png)

In both images, there is a perfectly bright wall of simulated stars a short, fixed distance away from the observer. Radiation from that wall leaks and is visible as a uniform grey background when the simulated wall is very close and the density of attenuating matter approaches zero, but if the wall of light is slightly more distant or the density of attenuating matter is only slightly increased, the background approaches pitch black, despite there still being an infinite number of perfectly bright stars intersecting every possible line of sight.

You can bump up the stellar density, radii and luminosity as high as you want, and even a tiny percentage of non-luminous matter still overwhelms the resultant apparent brightness calculations with the exponential decay induced by material attenuation.

Of course arguments about **thermodynamics** are just begging the question. How nonluminous matter is able to be there and coexist with stars is a separate matter of discussion. ([How stars got there](https://www.youtube.com/watch?v=CzyQbOQ0dv0) is too, come to think of it). The fact that **it is there and that we know it is there**, even at great distances, disproves the idea that Olbers's paradox is a paradox at all, as it completely fails to falsify an infinite universe given what we know.

In case someone thinks this idea is flamingly absurd, that even a small amount of matter between stars can block nearly all of the light from them, remember that despite how brightly the Sun shines at noonday and how close it is to the Earth, you can block almost all of that light using a thin cardboard cereal box or a parasol consisting of cloth a couple millimeters thick. This gives you an idea of how effective exponential attenuation is. Can there not be the equivalent matter of one millimeter of cardboard between you and a star 3 billion light years away? If not then what are stars made of?

> **Comments:**
> **username_8**: "It becomes literally invisible" - bingo. The intensity, energy and frequency of light are all diminished, absorbed or downshifted respectively by their interactions with matter. Uncanny prediction of cosmic microwave background radiation right here, straight from 18th-century laws of optics and thermodynamics.  
> **username_3**: As the leading answer correctly explains, absorbing matter would heat up until it emitted at the same temperature as the stars themselves if the universe was infinitely old and infinite in extent. This is actually 19th century thermodynamics.There is of course no paradox at all if the universe is finite in age.  
> **username_8**: @ProfRob This is a huge non sequitur. There are stars and there are nebulae in the universe, and these models fail to account for the existence of stars, let alone the existence of dust. This is a very unserious objection given that current models fail so much as to allow any such things to exist. There is no paradox in a universe of infinite age, as has been proven.  
> **username_7**: @ProfRob It would be inconsistent to assume that stellar radiation is produced continuously out of nothing whilst not allowing for loss processes. If you assume sources you also have to assume sinks. So the argument of the temperature heating up indefinitily is not correct.  
> **username_3**: @Thomas Olber's paradox is precisely that the radiation should have been produced continuously infinitely far into the past and infinitely far into space. Any suggestion to the contrary immediately invalidates any attempt at disproof. Where is the absorbed energy from all the stars that have ever existed supposed to go? You have also not grasped the argument if you think I suggested that the "temperature heats up indefinitely".  
> **username_7**: @ProfRob If you continuously pump energy into a given volume without having some sort of energy sink, than the energy will increase indefinitely. You can only have a steady state if you have some loss process that balances out the production process. This true in any branch of physics and beyond. Olber's paradox has nothing to do with infinity as such but rather with inconsistently assuming there are no physical loss processes for the radiation (which is a contradiction in terms to the assumption of having a steady state). The question is then only what the nature of this loss process  is.  
> **username_3**: @Thomas the material heats up until it is as hot as the surface of the stars irradiating it. Then it radiates just as much as it absorbs. As the leading answer correctly states. Hang on, haven't I said this before somewhere...  
> **username_8**: @ProfRob This ignores radiative equilibrium, which for a given material, distance from energy sources and radiative influx can occur at a different temperature than that of a radiative source such as a star. This is a known process whereby you may have a planet or nebula some distance away from a star for billions of years and still be close to absolute zero rather than trending towards the same temperature as the nearest star.  
> **username_3**: The universe would be providing starlight from all directions, not from a single direction. The equilibrium temperature in this case is the temperature of the incident blackbody radiation. Distance is irrelevant, since every sightline ends at the surface of a star, or, in an infinitely old universe, something that is the same temperature as the surface of a star. In a sense, that is the paradox right there. The situation you describe would not be possible in an infinite, infinitely old, unchanging universe.  
> **username_7**: @ProfRob *"the material heats up until it is as hot as the surface of the stars irradiating it. Then it radiates just as much as it absorbs."* This may be true, but the temperature of both would be increasing ever further if the source star keeps on pumping out radiation without energy being lost somehow. This is required because of energy conservatiion  
> **username_7**: @ProfRob *"The situation you describe would not be possible in an infinite, infinitely old, unchanging universe."* Even in an an infinite, infinitely old, unchanging universe Olber's paradox would not arise if there is some loss process which limits the light propagation to a finite distance. Only in thiis case you could actually have an unchanging steady-state.universe.  
> **username_3**: @Thomas first comment ok, but the second comment suggests you still don't accept that material that absorbs light (which is what we are discussing) heats up. You cannot have an infinite, static, unchanging universe for many reasons, but Olber did not know about nuclear physics or how stars work, and didn't need to.  
> **username_8**: @ProfRob Suppose you are right that everything would be the same temperature in an infinitely old universe. But then there would be no matter undergoing any exothermic or endothermic reaction except at a very, very local scale in tiny quanta according to a Boltzmann law with a uniform temperature everywhere above the quantum scale. Do you agree with this? If so, then how could stars exist? If stars do not exist, this would circularly presuppose the most basic premise of Olbers' question to be false. It assumes that stars can't exist for long enough to give the paradox claim a fair test.  
> **username_8**: @ProfRob Our Earth maintains a stable non-stellar temperature because it is in radiative equilibrium; it will not heat up no matter how many billions of years of starlight hit it. Extrastellar objects tend towards radiative equilibrium, regulating their own temperatures as they re-radiate on average as much energy as they absorb, and each arrives at its own non-stellar temperature. Radiative equilibrium explains why all the planets are still cold relative to the Sun despite supposed billions of years absorbing starlight. Radiative equilibrium implies that thermal uniformity is not inevitable.  
> **username_7**: @ProfRob *"you still don't accept that material that absorbs light (which is what we are discussing) heats up. "* You still seem to misunderstand. For a steady state situation you need *true* sinks that remove energy from the system (and thus balance the energy input from the sources), not just turn it into different forms. It is inconsistent to propose a (quasi)-static universe where in each volume element energy is continuously created but not lost at the same rate due to some processes. Doing so is exactly the reason for Olber's paradox.  
> **username_3**: The planets are all cold because we do not live in an infinitely old, static universe - this **is** Olber's paradox - the whole sky would be like the Sun if it were and the planets would be fried.  The impossibility of isolated stars existing in an infinitely old, static universe is also just another restatement of Olber's paradox. All this has nothing to do with your dust argument..  
> **username_8**: @ProfRob Radiative equilibrium demonstrates that objects can maintain distinct temperatures indefinitely. Planets will not be fried except in a supernova event or other stellar catastrophe involving ample material contact. And what then? Will new stars form? As long as stars exist, there will always be thermal gradients and low entropy, high-temperature thermal islands in the universe. In the hypothetical temperature equivalence scenario, stars can't exist. Isolated stars? Or stars at all! This is a glaring hole in such logic. "Assume there are no stars. Paradox solved!". Nothing to do indeed.  

---

